Collider physics at the precision frontier. (English) Zbl 1509.81614
Summary: The precision frontier in collider physics is being pushed at impressive speed, from both the experimental and the theoretical side. The aim of this review is to give an overview of recent developments in precision calculations within the Standard Model of particle physics, in particular in the Higgs sector. While the first part focuses on phenomenological results, the second part reviews some of the techniques which allowed the rapid progress in the field of precision calculations. The focus is on analytic and semi-numerical techniques for multi-loop amplitudes, however fully numerical methods as well as subtraction schemes for infrared divergent real radiation beyond NLO are also briefly described.
MSC:
| 81V22 | Unified quantum theories |
| 81U35 | Inelastic and multichannel quantum scattering |
| 81V80 | Quantum optics |
| 81V35 | Nuclear physics |
| 81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |
| 81-05 | Experimental work for problems pertaining to quantum theory |
Keywords:
high energy colliders; Higgs physics; precision calculations; amplitudes; multi-loop integralsSoftware:
MATAD; Cuba; BOKASUN; AMBRE; DREAM; Azurite; HPOLY.f; PineAPPL; Fuchsia; Loopedia; FeynArts; PentagonFunctions; Kira; MBsums; SumProduction; PolyLogTools; ggzh; CHAPLIN; Caravel; HIGLU; DiffExp; GiNaC_elipticFeynman; Forcer; HAWK; MBnumerics; FIESTA 3; pySecDec; FiniteFlow; MPL; FIRE; feyncop; RationalizeRoots; OpenLoops; feyntrop; fastNLO; LiteRed; epsilon; MultivariateApart; FIRE5; GPI-Space; APPLgrid; feyngen; HyperInt; RECOLA; GitHub; TVID; AutoDipole; iHixs; AIR; MadFKS; VBFNLO; POWHEG BOX; FORM; Nestedsums; TSIL; Herwig++; SusHi; Reduze; MBresolve; sunem; MBasymptotics; Mincer; FIESTA; XSummer; FEWZ; SecDec; FeynCalc; EvaluateMultiSumsReferences:
| [1] | Aad, G., Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B, 716, 1-29 (2012), arXiv:1207.7214 |
| [2] | Chatrchyan, S., Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B, 716, 30-61 (2012), arXiv:1207.7235 |
| [3] | de Blas, J., Higgs boson studies at future particle colliders, J. High Energy Phys., 01, 139 (2020), arXiv:1905.03764 |
| [4] | Ellis, R. K., Physics briefing book: Input for the European strategy for particle physics update 2020 (2019), arXiv:1910.11775 |
| [5] | Buttar, C., Les Houches Physics at TeV Colliders 2005, Standard Model and Higgs working group: Summary report, (4th Les Houches Workshop on Physics At TeV Colliders (2006)), arXiv:hep-ph/0604120 |
| [6] | Bern, Z.; Diana, G.; Dixon, L.; Febres Cordero, F.; Höche, S.; Kosower, D.; Ita, H.; Maître, D.; Ozeren, K., Four-jet production at the large hadron collider at next-to-leading order in QCD, Phys. Rev. Lett., 109, Article 042001 pp. (2012), arXiv:1112.3940 |
| [7] | Bern, Z.; Dixon, L.; Febres Cordero, F.; Höche, S.; Ita, H.; Kosower, D.; Maître, D.; Ozeren, K., Next-to-leading order \(W + 5\)-jet production at the LHC, Phys. Rev. D, 88, 1, Article 014025 pp. (2013), arXiv:1304.1253 |
| [8] | Badger, S.; Guffanti, A.; Yundin, V., Next-to-leading order QCD corrections to di-photon production in association with up to three jets at the Large Hadron Collider, J. High Energy Phys., 03, 122 (2014), arXiv:1312.5927 |
| [9] | Denner, A.; Lang, J.-N.; Pellen, M.; Uccirati, S., Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC, J. High Energy Phys., 02, 053 (2017), arXiv:1612.07138 |
| [10] | Denner, A.; Lang, J.-N.; Pellen, M., Full NLO QCD corrections to off-shell ttbb production (2020), arXiv:2008.00918 |
| [11] | Denner, A.; Dittmaier, S., Electroweak radiative corrections for collider physics, Phys. Rep., 864, 1-163 (2020), arXiv:1912.06823 · Zbl 1476.81155 |
| [12] | Dawson, S.; Englert, C.; Plehn, T., Higgs physics: It ain’t over till it’s over, Phys. Rep., 816, 1-85 (2019), arXiv:1808.01324 |
| [13] | Alison, J., Higgs boson pair production at colliders: Status and perspectives, (Di Micco, B.; Gouzevitch, M.; Mazzitelli, J.; Vernieri, C., Double Higgs Production At Colliders (2019)), arXiv:1910.00012 |
| [14] | Spira, M., Higgs boson production and decay at hadron colliders, Prog. Part. Nucl. Phys., 95, 98-159 (2017), arXiv:1612.07651 |
| [15] | Amoroso, S., Les houches 2019: Physics at TeV colliders: Standard model working group report, (11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches (PhysTeV 2019) Les Houches, France, June 10-28, 2019 (2020)), arXiv:2003.01700 |
| [16] | Chen, X.; Gehrmann, T.; Glover, E. W.N.; Huss, A.; Mistlberger, B.; Pelloni, A., Fully differential Higgs boson production to third order in QCD (2021), arXiv:2102.07607 |
| [17] | Cieri, L.; Chen, X.; Gehrmann, T.; Glover, E. W.N.; Huss, A., Higgs boson production at the LHC using the \(q_T\) subtraction formalism at \(N{}^3\) LO QCD, J. High Energy Phys., 02, 096 (2019), arXiv:1807.11501 |
| [18] | Dulat, F.; Mistlberger, B.; Pelloni, A., Precision predictions at \(N{}^3\) LO for the Higgs boson rapidity distribution at the LHC, Phys. Rev. D, 99, 3, Article 034004 pp. (2019), arXiv:1810.09462 |
| [19] | Billis, G.; Dehnadi, B.; Ebert, M. A.; Michel, J. K.L.; Tackmann, F. J., The Higgs \(p_T\) spectrum and total cross section with fiducial cuts at \(N{}^3\) LL \({}^\prime +N{}^3\) LO (2021), arXiv:2102.08039 |
| [20] | Anastasiou, C.; Duhr, C.; Dulat, F.; Herzog, F.; Mistlberger, B., Higgs boson gluon-fusion production in QCD at three loops, Phys. Rev. Lett., 114, Article 212001 pp. (2015), arXiv:1503.06056 |
| [21] | Anastasiou, C.; Duhr, C.; Dulat, F.; Furlan, E.; Gehrmann, T.; Herzog, F.; Lazopoulos, A.; Mistlberger, B., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, J. High Energy Phys., 05, 058 (2016), arXiv:1602.00695 |
| [22] | Mistlberger, B., Higgs boson production at hadron colliders at \(N{}^3\) LO in QCD, J. High Energy Phys., 05, 028 (2018), arXiv:1802.00833 |
| [23] | Das, G.; Moch, S.; Vogt, A., Approximate four-loop QCD corrections to the Higgs-boson production cross section, Phys. Lett. B, 807, Article 135546 pp. (2020), arXiv:2004.00563 · Zbl 1473.81197 |
| [24] | Ahmed, T.; Ajjath, A. H.; Das, G.; Mukherjee, P.; Ravindran, V.; Tiwari, S., Soft-virtual correction and threshold resummation for \(n\)-colorless particles to fourth order in QCD: Part I (2020), arXiv:2010.02979 |
| [25] | Mondini, R.; Schiavi, M.; Williams, C., \(N{}^3\) LO predictions for the decay of the Higgs boson to bottom quarks, J. High Energy Phys., 06, 079 (2019), arXiv:1904.08960 |
| [26] | Duhr, C.; Dulat, F.; Mistlberger, B., Higgs production in bottom-quark fusion to third order in the strong coupling, Phys. Rev. Lett., 125, 5, Article 051804 pp. (2020), arXiv:1904.09990 |
| [27] | Duhr, C.; Dulat, F.; Hirschi, V.; Mistlberger, B., Higgs production in bottom quark fusion: matching the 4- and 5-flavour schemes to third order in the strong coupling, J. High Energy Phys., 08, 08, 017 (2020), arXiv:2004.04752 |
| [28] | Dreyer, F. A.; Karlberg, A., Vector-boson fusion Higgs production at three loops in QCD, Phys. Rev. Lett., 117, 7, Article 072001 pp. (2016), arXiv:1606.00840 |
| [29] | Dreyer, F. A.; Karlberg, A., Vector-boson fusion Higgs pair production at \(N{}^3\) LO, Phys. Rev. D, 98, 11, Article 114016 pp. (2018), arXiv:1811.07906 |
| [30] | Han, T.; Valencia, G.; Willenbrock, S., Structure function approach to vector boson scattering in p p collisions, Phys. Rev. Lett., 69, 3274-3277 (1992), arXiv:hep-ph/9206246 |
| [31] | Cacciari, M.; Dreyer, F. A.; Karlberg, A.; Salam, G. P.; Zanderighi, G., Fully differential vector-boson-fusion Higgs production at next-to-next-to-leading order, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 120, 13, 139901 (2018), (erratum) |
| [32] | Chen, L.-B.; Li, H. T.; Shao, H.-S.; Wang, J., Higgs boson pair production via gluon fusion at \(N{}^3\) LO in QCD, Phys. Lett. B, 803, Article 135292 pp. (2020), arXiv:1909.06808 |
| [33] | Banerjee, P.; Borowka, S.; Dhani, P. K.; Gehrmann, T.; Ravindran, V., Two-loop massless QCD corrections to the \(g + g \to H + H\) four-point amplitude, J. High Energy Phys., 11, 130 (2018), arXiv:1809.05388 |
| [34] | Chen, L.-B.; Li, H. T.; Shao, H.-S.; Wang, J., The gluon-fusion production of Higgs boson pair: \(N{}^3\) LO QCD corrections and top-quark mass effects, J. High Energy Phys., 03, 072 (2020), arXiv:1912.13001 |
| [35] | Duhr, C.; Dulat, F.; Mistlberger, B., The Drell-Yan cross section to third order in the strong coupling constant, Phys. Rev. Lett., 125, 17, 172001 (2020), arXiv:2001.07717 |
| [36] | Duhr, C.; Dulat, F.; Mistlberger, B., Charged current Drell-Yan production at N^3LO, JHEP, 11, 143 (2020), arXiv:2007.13313 |
| [37] | Camarda, S.; Cieri, L.; Ferrera, G., Drell-Yan lepton-pair production: \( q_T\) resummation at \(N{}^3\) LL accuracy and fiducial cross sections at \(N{}^3\) LO (2021), arXiv:2103.04974 |
| [38] | Currie, J.; Gehrmann, T.; Glover, E. W.N.; Huss, A.; Niehues, J.; Vogt, A., \(N{}^3\) LO corrections to jet production in deep inelastic scattering using the Projection-to-Born method, J. High Energy Phys., 05, 209 (2018), arXiv:1803.09973 |
| [39] | Gehrmann, T.; Huss, A.; Niehues, J.; Vogt, A.; Walker, D., Jet production in charged-current deep-inelastic scattering to third order in QCD, Phys. Lett. B, 792, 182-186 (2019), arXiv:1812.06104 |
| [40] | Vermaseren, J.; Vogt, A.; Moch, S., The Third-order QCD corrections to deep-inelastic scattering by photon exchange, Nuclear Phys. B, 724, 3-182 (2005), arXiv:hep-ph/0504242 · Zbl 1178.81286 |
| [41] | Baikov, P.; Chetyrkin, K.; Kühn, J. H., Scalar correlator at \(O ( \alpha_s^4 )\), Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett., 96, Article 012003 pp. (2006), arXiv:hep-ph/0511063 |
| [42] | Baikov, P.; Chetyrkin, K.; Kühn, J. H., Order \(\alpha_s^4\) QCD Corrections to Z and tau Decays, Phys. Rev. Lett., 101, Article 012002 pp. (2008), arXiv:0801.1821 |
| [43] | Baikov, P.; Chetyrkin, K.; Kühn, J., Adler function, Bjorken sum rule, and the Crewther relation to order \(\alpha_s^4\) in a general gauge theory, Phys. Rev. Lett., 104, Article 132004 pp. (2010), arXiv:1001.3606 |
| [44] | Baikov, P.; Chetyrkin, K.; Kühn, J.; Rittinger, J., Complete \(\mathcal{O} ( \alpha_s^4 )\) QCD corrections to hadronic \(Z\)-decays, Phys. Rev. Lett., 108, Article 222003 pp. (2012), arXiv:1201.5804 |
| [45] | Davies, J.; Steinhauser, M.; Wellmann, D., Completing the hadronic Higgs boson decay at order \(\alpha_s^4\), Nuclear Phys. B, 920, 20-31 (2017), arXiv:1703.02988 · Zbl 1364.81253 |
| [46] | Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J.; Vogt, A., On Higgs decays to hadrons and the R-ratio at \(N{}^4\) LO, J. High Energy Phys., 08, 113 (2017), arXiv:1707.01044 |
| [47] | Spira, M.; Djouadi, A.; Graudenz, D.; Zerwas, P. M., Higgs boson production at the LHC, Nuclear Phys. B, 453, 17-82 (1995), arXiv:hep-ph/9504378 |
| [48] | Harlander, R.; Kant, P., Higgs production and decay: Analytic results at next-to-leading order QCD, J. High Energy Phys., 12, 015 (2005), arXiv:hep-ph/0509189 |
| [49] | Anastasiou, C.; Beerli, S.; Bucherer, S.; Daleo, A.; Kunszt, Z., Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop, J. High Energy Phys., 01, 082 (2007), arXiv:hep-ph/0611236 |
| [50] | Aglietti, U.; Bonciani, R.; Degrassi, G.; Vicini, A., Analytic results for virtual QCD corrections to Higgs production and decay, J. High Energy Phys., 01, 021 (2007), arXiv:hep-ph/0611266 |
| [51] | Anastasiou, C.; Bucherer, S.; Kunszt, Z., HPro: A NLO Monte-Carlo for Higgs production via gluon fusion with finite heavy quark masses, J. High Energy Phys., 10, 068 (2009), arXiv:0907.2362 |
| [52] | Harlander, R. V.; Kilgore, W. B., Next-to-next-to-leading order Higgs production at hadron colliders, Phys. Rev. Lett., 88, Article 201801 pp. (2002), arXiv:hep-ph/0201206 |
| [53] | Catani, S.; de Florian, D.; Grazzini, M., Direct Higgs production and jet veto at the Tevatron and the LHC in NNLO QCD, J. High Energy Phys., 01, 015 (2002), arXiv:hep-ph/0111164 |
| [54] | Anastasiou, C.; Melnikov, K., Higgs boson production at hadron colliders in NNLO QCD, Nuclear Phys. B, 646, 220-256 (2002), arXiv:hep-ph/0207004 |
| [55] | Ravindran, V.; Smith, J.; van Neerven, W. L., NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nuclear Phys. B, 665, 325-366 (2003), arXiv:hep-ph/0302135 |
| [56] | Harlander, R. V.; Ozeren, K. J., Top mass effects in Higgs production at next-to-next-to-leading order QCD: Virtual corrections, Phys. Lett. B, 679, 467-472 (2009), arXiv:0907.2997 |
| [57] | Pak, A.; Rogal, M.; Steinhauser, M., Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass, Phys. Lett. B, 679, 473-477 (2009), arXiv:0907.2998 |
| [58] | Harlander, R. V.; Ozeren, K. J., Finite top mass effects for hadronic Higgs production at next-to-next-to-leading order, J. High Energy Phys., 11, 088 (2009), arXiv:0909.3420 |
| [59] | Pak, A.; Rogal, M.; Steinhauser, M., Finite top quark mass effects in NNLO Higgs boson production at LHC, J. High Energy Phys., 02, 025 (2010), arXiv:0911.4662 · Zbl 1270.81220 |
| [60] | Harlander, R. V.; Mantler, H.; Marzani, S.; Ozeren, K. J., Higgs production in gluon fusion at next-to-next-to-leading order QCD for finite top mass, Eur. Phys. J. C, 66, 359-372 (2010), arXiv:0912.2104 |
| [61] | Pak, A.; Rogal, M.; Steinhauser, M., Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders, J. High Energy Phys., 09, 088 (2011), arXiv:1107.3391 |
| [62] | Spira, M., HIGLU: A program for the calculation of the total Higgs production cross-section at hadron colliders via gluon fusion including qcd corrections (1995), arXiv:hep-ph/9510347 |
| [63] | Anastasiou, C.; Buehler, S.; Herzog, F.; Lazopoulos, A., Total cross-section for Higgs boson hadroproduction with anomalous Standard Model interactions, J. High Energy Phys., 12, 058 (2011), arXiv:1107.0683 · Zbl 1306.81385 |
| [64] | Anastasiou, C.; Buehler, S.; Herzog, F.; Lazopoulos, A., Inclusive Higgs boson cross-section for the LHC at 8 TeV, J. High Energy Phys., 04, 004 (2012), arXiv:1202.3638 |
| [65] | Harlander, R. V.; Liebler, S.; Mantler, H., SusHi: A program for the calculation of Higgs production in gluon fusion and bottom-quark annihilation in the Standard Model and the MSSM, Comput. Phys. Comm., 184, 1605-1617 (2013), arXiv:1212.3249 · Zbl 1297.81163 |
| [66] | Ball, R. D.; Bonvini, M.; Forte, S.; Marzani, S.; Ridolfi, G., Higgs production in gluon fusion beyond NNLO, Nuclear Phys. B, 874, 746-772 (2013), arXiv:1303.3590 · Zbl 1282.81203 |
| [67] | Bonvini, M.; Ball, R. D.; Forte, S.; Marzani, S.; Ridolfi, G., Updated Higgs cross section at approximate \(N{}^3\) LO, J. Phys. G, 41, Article 095002 pp. (2014), arXiv:1404.3204 |
| [68] | Bonvini, M.; Marzani, S., Resummed Higgs cross section at \(N{}^3\) LL, J. High Energy Phys., 09, 007 (2014), arXiv:1405.3654 |
| [69] | Bonvini, M.; Marzani, S.; Muselli, C.; Rottoli, L., On the Higgs cross section at \(N{}^3\) LO+\(N{}^3\) LL and its uncertainty, J. High Energy Phys., 08, 105 (2016), arXiv:1603.08000 |
| [70] | Bonvini, M.; Marzani, S., Four-loop splitting functions at small \(x\), J. High Energy Phys., 06, 145 (2018), arXiv:1805.06460 |
| [71] | Marzani, S.; Ball, R. D.; Del Duca, V.; Forte, S.; Vicini, A., Higgs production via gluon-gluon fusion with finite top mass beyond next-to-leading order, Nuclear Phys. B, 800, 127-145 (2008), arXiv:0801.2544 |
| [72] | Davies, J.; Gröber, R.; Maier, A.; Rauh, T.; Steinhauser, M., Top quark mass dependence of the Higgs boson-gluon form factor at three loops, Phys. Rev. D, 100, 3, Article 034017 pp. (2019), arXiv:1906.00982 |
| [73] | Harlander, R. V.; Prausa, M.; Usovitsch, J., The light-fermion contribution to the exact higgs-gluon form factor in QCD, J. High Energy Phys., 10, 148 (2019), arXiv:1907.06957 |
| [74] | Davies, J.; Herren, F.; Steinhauser, M., Top quark mass effects in next-to-next-to-next-to-leading order Higgs boson production: Virtual corrections, Phys. Rev. Lett., 124, 11, Article 112002 pp. (2020), arXiv:1911.10214 |
| [75] | Liu, T.; Penin, A. A., High-energy limit of QCD beyond the Sudakov approximation, Phys. Rev. Lett., 119, 26, Article 262001 pp. (2017), arXiv:1709.01092 |
| [76] | Liu, T.; Penin, A., High-energy limit of mass-suppressed amplitudes in gauge theories, J. High Energy Phys., 11, 158 (2018), arXiv:1809.04950 · Zbl 1404.81289 |
| [77] | Caola, F.; Lindert, J. M.; Melnikov, K.; Monni, P. F.; Tancredi, L.; Wever, C., Bottom-quark effects in Higgs production at intermediate transverse momentum, J. High Energy Phys., 09, 035 (2018), arXiv:1804.07632 |
| [78] | Bizon, W.; Melnikov, K.; Quarroz, J., On the interference of \(g g H\) and \(c \overline{c} H\) Higgs production mechanisms and the determination of charm Yukawa coupling at the LHC (2021), arXiv:2102.04242 |
| [79] | Czakon, M. L.; Niggetiedt, M., Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD, J. High Energy Phys., 05, 149 (2020), arXiv:2001.03008 |
| [80] | Prausa, M.; Usovitsch, J., The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO, JHEP, 03, 127 (2021), arXiv:2008.11641 |
| [81] | Harlander, R. V.; Liebler, S.; Mantler, H., SusHi Bento: Beyond NNLO and the heavy-top limit, Comput. Phys. Comm., 212, 239-257 (2017), arXiv:1605.03190 |
| [82] | Dulat, F.; Lazopoulos, A.; Mistlberger, B., iHixs 2 — Inclusive Higgs cross sections, Comput. Phys. Comm., 233, 243-260 (2018), arXiv:1802.00827 |
| [83] | Actis, S.; Passarino, G.; Sturm, C.; Uccirati, S., NLO electroweak corrections to Higgs boson production at hadron colliders, Phys. Lett. B, 670, 12-17 (2008), arXiv:0809.1301 |
| [84] | Dulat, F.; Mistlberger, B.; Pelloni, A., Differential Higgs production at \(N{}^3\) LO beyond threshold, J. High Energy Phys., 01, 145 (2018), arXiv:1710.03016 |
| [85] | Banerjee, P.; Das, G.; Dhani, P. K.; Ravindran, V., Threshold resummation of the rapidity distribution for Higgs production at NNLO+NNLL, Phys. Rev. D, 97, 5, Article 054024 pp. (2018), arXiv:1708.05706 |
| [86] | Catani, S.; Grazzini, M., An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett., 98, Article 222002 pp. (2007), arXiv:hep-ph/0703012 |
| [87] | Grazzini, M., NNLO predictions for the Higgs boson signal in the \(H \to W W \to l \nu l \nu\) and \(H \to Z Z \to 4 l\) decay channels, J. High Energy Phys., 02, 043 (2008), arXiv:0801.3232 |
| [88] | Dulat, F.; Lionetti, S.; Mistlberger, B.; Pelloni, A.; Specchia, C., Higgs-differential cross section at NNLO in dimensional regularisation, J. High Energy Phys., 07, 017 (2017), arXiv:1704.08220 |
| [89] | de Florian, D., Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector (2016), arXiv:1610.07922 |
| [90] | Bonetti, M.; Melnikov, K.; Tancredi, L., Two-loop electroweak corrections to Higgs-gluon couplings to higher orders in the dimensional regularization parameter, Nuclear Phys. B, 916, 709-726 (2017), arXiv:1610.05497 · Zbl 1356.81224 |
| [91] | Bonetti, M.; Melnikov, K.; Tancredi, L., Three-loop mixed QCD-electroweak corrections to Higgs boson gluon fusion, Phys. Rev. D, 97, 3, Article 034004 pp. (2018), arXiv:1711.11113 |
| [92] | Bonetti, M.; Melnikov, K.; Tancredi, L., Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion, Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, 97, 5, 099906 (2018), (erratum) |
| [93] | Anastasiou, C.; del Duca, V.; Furlan, E.; Mistlberger, B.; Moriello, F.; Schweitzer, A.; Specchia, C., Mixed QCD-electroweak corrections to Higgs production via gluon fusion in the small mass approximation, J. High Energy Phys., 03, 162 (2019), arXiv:1811.11211 |
| [94] | Bonetti, M.; Panzer, E.; Smirnov, V. A.; Tancredi, L., Two-loop mixed QCD-EW corrections to \(g g \to H g\), JHEP, 11, 045 (2020), arXiv:2007.09813 |
| [95] | Aglietti, U.; Bonciani, R.; Degrassi, G.; Vicini, A., Two loop light fermion contribution to Higgs production and decays, Phys. Lett. B, 595, 432-441 (2004), arXiv:hep-ph/0404071 |
| [96] | Degrassi, G.; Maltoni, F., Two-loop electroweak corrections to Higgs production at hadron colliders, Phys. Lett. B, 600, 255-260 (2004), arXiv:hep-ph/0407249 |
| [97] | Anastasiou, C.; Boughezal, R.; Petriello, F., Mixed QCD-electroweak corrections to Higgs boson production in gluon fusion, J. High Energy Phys., 04, 003 (2009), arXiv:0811.3458 |
| [98] | Becchetti, M.; Bonciani, R.; Del Duca, V.; Hirschi, V.; Moriello, F.; Schweitzer, A., Next-to-leading corrections to light-quark mixed QCD-EW contributions to Higgs production, Phys. Rev. D, 103, 5, 054037 (2021), arXiv:2010.09451 |
| [99] | Hirschi, V.; Lionetti, S.; Schweitzer, A., One-loop weak corrections to Higgs production, J. High Energy Phys., 05, 002 (2019), arXiv:1902.10167 |
| [100] | Anastasiou, C.; Deutschmann, N.; Schweitzer, A., Quark mass effects in two-loop Higgs amplitudes, J. High Energy Phys., 07, 113 (2020), arXiv:2001.06295 |
| [101] | Frellesvig, H.; Hidding, M.; Maestri, L.; Moriello, F.; Salvatori, G., The complete set of two-loop master integrals for Higgs + jet production in QCD, J. High Energy Phys., 06, 093 (2020), arXiv:1911.06308 |
| [102] | Melnikov, K.; Penin, A., On the light quark mass effects in Higgs boson production in gluon fusion, J. High Energy Phys., 05, 172 (2016), arXiv:1602.09020 |
| [103] | Anastasiou, C.; Penin, A., Light quark mediated Higgs boson threshold production in the next-to-leading logarithmic approximation, J. High Energy Phys., 07, 195 (2020), arXiv:2004.03602 |
| [104] | Monni, P. F.; Re, E.; Torrielli, P., Higgs transverse-momentum resummation in direct space, Phys. Rev. Lett., 116, 24, Article 242001 pp. (2016), arXiv:1604.02191 |
| [105] | Chen, X.; Gehrmann, T.; Glover, E. N.; Huss, A.; Li, Y.; Neill, D.; Schulze, M.; Stewart, I. W.; Zhu, H. X., Precise QCD description of the Higgs boson transverse momentum spectrum, Phys. Lett. B, 788, 425-430 (2019), arXiv:1805.00736 |
| [106] | Bizoń, W.; Chen, X.; Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, N.; Huss, A.; Monni, P. F.; Re, E.; Rottoli, L.; Torrielli, P., Fiducial distributions in Higgs and Drell-Yan production at \(N{}^3\) LL+NNLO, J. High Energy Phys., 12, 132 (2018), arXiv:1805.05916 |
| [107] | Monni, P. F.; Rottoli, L.; Torrielli, P., Higgs transverse momentum with a jet veto: a double-differential resummation, Phys. Rev. Lett., 124, 25, Article 252001 pp. (2020), arXiv:1909.04704 |
| [108] | Hamilton, K.; Nason, P.; Re, E.; Zanderighi, G., NNLOPS simulation of Higgs boson production, J. High Energy Phys., 10, 222 (2013), arXiv:1309.0017 |
| [109] | Höche, S.; Li, Y.; Prestel, S., Higgs-boson production through gluon fusion at NNLO QCD with parton showers, Phys. Rev. D, 90, 5, Article 054011 pp. (2014), arXiv:1407.3773 |
| [110] | Hamilton, K.; Nason, P.; Zanderighi, G., Finite quark-mass effects in the NNLOPS POWHEG+MiNLO Higgs generator, J. High Energy Phys., 05, 140 (2015), arXiv:1501.04637 |
| [111] | Bizoń, W.; Re, E.; Zanderighi, G., NNLOPS description of the \(H \to b \overline{b}\) decay with MiNLO, J. High Energy Phys., 06, 006 (2020), arXiv:1912.09982 |
| [112] | Hu, Y.; Sun, C.; Shen, X.-M.; Gao, J., Hadronic decays of Higgs boson at NNLO matched with parton shower (2021), arXiv:2101.08916 |
| [113] | Dittmaier, S.; Krämer, M.; Spira, M., Higgs radiation off bottom quarks at the Tevatron and the CERN LHC, Phys. Rev. D, 70, Article 074010 pp. (2004), arXiv:hep-ph/0309204 |
| [114] | Dawson, S.; Jackson, C.; Reina, L.; Wackeroth, D., Exclusive Higgs boson production with bottom quarks at hadron colliders, Phys. Rev. D, 69, Article 074027 pp. (2004), arXiv:hep-ph/0311067 |
| [115] | Wiesemann, M.; Frederix, R.; Frixione, S.; Hirschi, V.; Maltoni, F.; Torrielli, P., Higgs production in association with bottom quarks, J. High Energy Phys., 02, 132 (2015), arXiv:1409.5301 |
| [116] | Dawson, S.; Jackson, C.; Reina, L.; Wackeroth, D., Higgs production in association with bottom quarks at hadron colliders, Modern Phys. Lett. A, 21, 89-110 (2006), arXiv:hep-ph/0508293 |
| [117] | Liu, N.; Wu, L.; Wu, P.; Yang, J. M., Complete one-loop effects of SUSY QCD in \(b \overline{b} h\) production at the LHC under current experimental constraints, J. High Energy Phys., 01, 161 (2013), arXiv:1208.3413 |
| [118] | Dittmaier, S.; Häfliger, P.; Krämer, M.; Spira, M.; Walser, M., Neutral MSSM Higgs-boson production with heavy quarks: NLO supersymmetric QCD corrections, Phys. Rev. D, 90, 3, Article 035010 pp. (2014), arXiv:1406.5307 |
| [119] | Forte, S.; Napoletano, D.; Ubiali, M., Higgs production in bottom-quark fusion: matching beyond leading order, Phys. Lett. B, 763, 190-196 (2016), arXiv:1607.00389 |
| [120] | Bonvini, M.; Papanastasiou, A. S.; Tackmann, F. J., Matched predictions for the \(b \overline{b} H\) cross section at the 13 TeV LHC, J. High Energy Phys., 10, 053 (2016), arXiv:1605.01733 |
| [121] | Bonvini, M.; Papanastasiou, A. S.; Tackmann, F. J., Resummation and matching of b-quark mass effects in \(b \overline{b} H\) production, J. High Energy Phys., 11, 196 (2015), arXiv:1508.03288 |
| [122] | Forte, S.; Napoletano, D.; Ubiali, M., Higgs production in bottom-quark fusion in a matched scheme, Phys. Lett. B, 751, 331-337 (2015), arXiv:1508.01529 |
| [123] | Harlander, R.; Krämer, M.; Schumacher, M., Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach (2011), arXiv:1112.3478 |
| [124] | Ajjath, A.; Chakraborty, A.; Das, G.; Mukherjee, P.; Ravindran, V., Resummed prediction for Higgs boson production through \(b \overline{b}\) annihilation at \(N{}^3\) LL, J. High Energy Phys., 11, 006 (2019), arXiv:1905.03771 |
| [125] | Ajjath, A.; Banerjee, P.; Chakraborty, A.; Dhani, P. K.; Mukherjee, P.; Rana, N.; Ravindran, V., NNLO QCD \(\oplus\) QED corrections to Higgs production in bottom quark annihilation, Phys. Rev. D, 100, 11, Article 114016 pp. (2019), arXiv:1906.09028 |
| [126] | Kogler, R., Jet substructure at the large hadron collider: Experimental review, Rev. Modern Phys., 91, 4, Article 045003 pp. (2019), arXiv:1803.06991 |
| [127] | Sirunyan, A. M., Inclusive search for a highly boosted Higgs boson decaying to a bottom quark-antiquark pair, Phys. Rev. Lett., 120, 7, Article 071802 pp. (2018), arXiv:1709.05543 |
| [128] | Search for boosted resonances decaying to two b-quarks and produced in association with a jet at \(\sqrt{ s} = 13\) TeV with the ATLAS detector (2018), arXiv:ATLAS-CONF-2018-052 |
| [129] | Dabelstein, A.; Hollik, W., Electroweak corrections to the fermionic decay width of the standard Higgs boson, Z. Phys. C, 53, 507-516 (1992) |
| [130] | Kataev, A., The Order \(O ( \alpha \alpha_s )\) and \(O ( \alpha^2 )\) corrections to the decay width of the neutral Higgs boson to the anti-b b pair, JETP Lett., 66, 327-330 (1997), arXiv:hep-ph/9708292 |
| [131] | Mihaila, L.; Schmidt, B.; Steinhauser, M., \( \Gamma ( H \to b \overline{b} )\) to order \(\alpha \alpha_s\), Phys. Lett. B, 751, 442-447 (2015), arXiv:1509.02294 |
| [132] | Anastasiou, C.; Herzog, F.; Lazopoulos, A., The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, J. High Energy Phys., 03, 035 (2012), arXiv:1110.2368 · Zbl 1309.81257 |
| [133] | Del Duca, V.; Duhr, C.; Somogyi, G.; Tramontano, F.; Trocsanyi, Z., Higgs boson decay into b-quarks at NNLO accuracy, J. High Energy Phys., 04, 036 (2015), arXiv:1501.07226 |
| [134] | Bernreuther, W.; Chen, L.; Si, Z.-G., Differential decay rates of CP-even and CP-odd Higgs bosons to top and bottom quarks at NNLO QCD, J. High Energy Phys., 07, 159 (2018), arXiv:1805.06658 |
| [135] | Primo, A.; Sasso, G.; Somogyi, G.; Tramontano, F., Exact Top Yukawa corrections to Higgs boson decay into bottom quarks, Phys. Rev. D, 99, 5, Article 054013 pp. (2019), arXiv:1812.07811 |
| [136] | Mondini, R.; Schubert, U.; Williams, C., Top-induced contributions to \(H \to b \overline{b}\) and \(H \to c \overline{c}\) at \(\mathcal{O} ( \alpha_s^3 ) (2020)\), arXiv:2006.03563 |
| [137] | Alioli, S.; Broggio, A.; Gavardi, A.; Kallweit, S.; Lim, M. A.; Nagar, R.; Napoletano, D.; Rottoli, L., Resummed predictions for hadronic Higgs boson decays (2020), arXiv:2009.13533 |
| [138] | Ferrera, G.; Somogyi, G.; Tramontano, F., Associated production of a Higgs boson decaying into bottom quarks at the LHC in full NNLO QCD, Phys. Lett. B, 780, 346-351 (2018), arXiv:1705.10304 |
| [139] | Caola, F.; Luisoni, G.; Melnikov, K.; Röntsch, R., NNLO QCD corrections to associated \(W H\) production and \(H \to b \overline{b}\) decay, Phys. Rev. D, 97, 7, Article 074022 pp. (2018), arXiv:1712.06954 |
| [140] | Behring, A.; Bizoń, W., Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme, J. High Energy Phys., 01, 189 (2020), arXiv:1911.11524 |
| [141] | Gauld, R.; Gehrmann-De Ridder, A.; Glover, E.; Huss, A.; Majer, I., Associated production of a Higgs boson decaying into bottom quarks and a weak vector boson decaying leptonically at NNLO in QCD, J. High Energy Phys., 10, 002 (2019), arXiv:1907.05836 |
| [142] | Alioli, S.; Broggio, A.; Kallweit, S.; Lim, M. A.; Rottoli, L., Higgsstrahlung at NNLL \({}^\prime +\) NNLO matched to parton showers in GENEVA, Phys. Rev. D, 100, 9, Article 096016 pp. (2019), arXiv:1909.02026 |
| [143] | Behring, A.; Bizoń, W.; Caola, F.; Melnikov, K.; Röntsch, R., Bottom quark mass effects in associated \(W H\) production with the \(H \to b \overline{b}\) decay through NNLO QCD, Phys. Rev. D, 101, 11, Article 114012 pp. (2020), arXiv:2003.08321 |
| [144] | Ferrera, G.; Grazzini, M.; Tramontano, F., Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett., 107, Article 152003 pp. (2011), arXiv:1107.1164 |
| [145] | Ferrera, G.; Grazzini, M.; Tramontano, F., Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation, Phys. Lett. B, 740, 51-55 (2015), arXiv:1407.4747 |
| [146] | Campbell, J. M.; Ellis, R. K.; Williams, C., Associated production of a Higgs boson at NNLO, J. High Energy Phys., 06, 179 (2016), arXiv:1601.00658 |
| [147] | Zhang, Y., NLO electroweak effects on the Higgs boson production in association with a bottom quark pair at the LHC, Phys. Rev. D, 96, 11, Article 113009 pp. (2017), arXiv:1708.08790 |
| [148] | Pagani, D.; Shao, H.-S.; Zaro, M., RIP \(H b \overline{b} \): How other Higgs production modes conspire to kill a rare signal at the LHC (2020), arXiv:2005.10277 |
| [149] | Chen, X.; Gehrmann, T.; Glover, E.; Jaquier, M., Precise QCD predictions for the production of Higgs + jet final states, Phys. Lett. B, 740, 147-150 (2015), arXiv:1408.5325 |
| [150] | Boughezal, R.; Caola, F.; Melnikov, K.; Petriello, F.; Schulze, M., Higgs boson production in association with a jet at next-to-next-to-leading order, Phys. Rev. Lett., 115, 8, Article 082003 pp. (2015), arXiv:1504.07922 |
| [151] | Boughezal, R.; Focke, C.; Giele, W.; Liu, X.; Petriello, F., Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B, 748, 5-8 (2015), arXiv:1505.03893 |
| [152] | Caola, F.; Melnikov, K.; Schulze, M., Fiducial cross sections for Higgs boson production in association with a jet at next-to-next-to-leading order in QCD, Phys. Rev. D, 92, 7, Article 074032 pp. (2015), arXiv:1508.02684 |
| [153] | Chen, X.; Cruz-Martinez, J.; Gehrmann, T.; Glover, E.; Jaquier, M., NNLO QCD Corrections to Higgs boson production at large transverse momentum, J. High Energy Phys., 10, 066 (2016), arXiv:1607.08817 |
| [154] | Campbell, J. M.; Ellis, R. K.; Seth, S., H + 1 jet production revisited, J. High Energy Phys., 10, 136 (2019), arXiv:1906.01020 |
| [155] | Buschmann, M.; Goncalves, D.; Kuttimalai, S.; Schönherr, M.; Krauss, F.; Plehn, T., Mass effects in the higgs-gluon coupling: Boosted vs off-shell production, J. High Energy Phys., 02, 038 (2015), arXiv:1410.5806 |
| [156] | Frederix, R.; Frixione, S.; Vryonidou, E.; Wiesemann, M., Heavy-quark mass effects in Higgs plus jets production, J. High Energy Phys., 08, 006 (2016), arXiv:1604.03017 |
| [157] | Neumann, T.; Williams, C., The Higgs boson at high \(p_T\), Phys. Rev. D, 95, 1, Article 014004 pp. (2017), arXiv:1609.00367 |
| [158] | Jones, S. P.; Kerner, M.; Luisoni, G., Next-to-leading-order QCD corrections to Higgs boson plus jet production with full top-quark mass dependence, Phys. Rev. Lett., 120, 16, Article 162001 pp. (2018), arXiv:1802.00349 |
| [159] | Melnikov, K.; Tancredi, L.; Wever, C., Two-loop \(g g \to H g\) amplitude mediated by a nearly massless quark, J. High Energy Phys., 11, 104 (2016), arXiv:1610.03747 |
| [160] | Melnikov, K.; Tancredi, L.; Wever, C., Two-loop amplitudes for \(q g \to H q\) and \(q \overline{q} \to H g\) mediated by a nearly massless quark, Phys. Rev. D, 95, 5, Article 054012 pp. (2017), arXiv:1702.00426 |
| [161] | Lindert, J. M.; Melnikov, K.; Tancredi, L.; Wever, C., Top-bottom interference effects in Higgs plus jet production at the LHC, Phys. Rev. Lett., 118, 25, Article 252002 pp. (2017), arXiv:1703.03886 |
| [162] | Lindert, J. M.; Kudashkin, K.; Melnikov, K.; Wever, C., Higgs bosons with large transverse momentum at the LHC, Phys. Lett. B, 782, 210-214 (2018), arXiv:1801.08226 |
| [163] | Neumann, T., NLO Higgs+jet production at large transverse momenta including top quark mass effects, J. Phys. Comm., 2, 9, Article 095017 pp. (2018), arXiv:1802.02981 |
| [164] | Kudashkin, K.; Melnikov, K.; Wever, C., Two-loop amplitudes for processes \(g g \to H g , q g \to H q\) and \(q \overline{q} \to H g\) at large Higgs transverse momentum, J. High Energy Phys., 02, 135 (2018), arXiv:1712.06549 |
| [165] | Mondini, R.; Williams, C., Bottom-induced contributions to Higgs plus jet at next-to-next-to-leading order (2021), arXiv:2102.05487 |
| [166] | Chen, X.; Gehrmann, T.; Glover, E.; Huss, A., Fiducial cross sections for the four-lepton decay mode in Higgs-plus-jet production up to NNLO QCD, J. High Energy Phys., 07, 052 (2019), arXiv:1905.13738 |
| [167] | Becker, K., Precise predictions for boosted Higgs production (2020), arXiv:2005.07762 |
| [168] | Alioli, S.; Nason, P.; Oleari, C.; Re, E., NLO Higgs Boson production via gluon fusion matched with shower in POWHEG, J. High Energy Phys., 04, 002 (2009), arXiv:0812.0578 |
| [169] | Campbell, J. M.; Ellis, R.; Frederix, R.; Nason, P.; Oleari, C.; Williams, C., NLO Higgs Boson production plus one and two jets using the POWHEG BOX, MadGraph4 and MCFM, J. High Energy Phys., 07, 092 (2012), arXiv:1202.5475 |
| [170] | Hamilton, K.; Nason, P.; Oleari, C.; Zanderighi, G., Merging H/W/Z + 0 and 1 jet at NLO with no merging scale: a path to parton shower + NNLO matching, J. High Energy Phys., 05, 082 (2013), arXiv:1212.4504 |
| [171] | Becchetti, M.; Bonciani, R.; Casconi, V.; Del Duca, V.; Moriello, F., Planar master integrals for the two-loop light-fermion electroweak corrections to Higgs plus jet production, J. High Energy Phys., 12, 019 (2018), arXiv:1810.05138 |
| [172] | Schlaffer, M.; Spannowsky, M.; Takeuchi, M.; Weiler, A.; Wymant, C., Boosted Higgs shapes, Eur. Phys. J. C, 74, 10, 3120 (2014), arXiv:1405.4295 |
| [173] | Dawson, S.; Lewis, I.; Zeng, M., Effective field theory for Higgs boson plus jet production, Phys. Rev. D, 90, 9, Article 093007 pp. (2014), arXiv:1409.6299 |
| [174] | Figy, T.; Oleari, C.; Zeppenfeld, D., Next-to-leading order jet distributions for Higgs boson production via weak boson fusion, Phys. Rev. D, 68, Article 073005 pp. (2003), arXiv:hep-ph/0306109 |
| [175] | Berger, E. L.; Campbell, J. M., Higgs boson production in weak boson fusion at next-to-leading order, Phys. Rev. D, 70, Article 073011 pp. (2004), arXiv:hep-ph/0403194 |
| [176] | Arnold, K., VBFNLO: A Parton level Monte Carlo for processes with electroweak bosons, Comput. Phys. Comm., 180, 1661-1670 (2009), arXiv:0811.4559 · Zbl 07872407 |
| [177] | Baglio, J., VBFNLO: A parton level Monte Carlo for processes with electroweak bosons – manual for version 2.7.0 (2011), arXiv:1107.4038 |
| [178] | Baglio, J., Release note - VBFNLO 2.7.0 (2014), arXiv:1404.3940 |
| [179] | Campbell, J. M.; Ellis, R.; Williams, C., Vector boson pair production at the LHC, J. High Energy Phys., 07, 018 (2011), arXiv:1105.0020 |
| [180] | Campbell, J. M.; Ellis, R. K.; Giele, W. T., A multi-threaded version of MCFM, Eur. Phys. J. C, 75, 6, 246 (2015), arXiv:1503.06182 |
| [181] | Campbell, J.; Neumann, T., Precision phenomenology with MCFM, J. High Energy Phys., 12, 034 (2019), arXiv:1909.09117 |
| [182] | Bolzoni, P.; Maltoni, F.; Moch, S.-O.; Zaro, M., Higgs production via vector-boson fusion at NNLO in QCD, Phys. Rev. Lett., 105, Article 011801 pp. (2010), arXiv:1003.4451 |
| [183] | Cruz-Martinez, J.; Gehrmann, T.; Glover, E.; Huss, A., Second-order QCD effects in Higgs boson production through vector boson fusion, Phys. Lett. B, 781, 672-677 (2018), arXiv:1802.02445 |
| [184] | Liu, T.; Melnikov, K.; Penin, A. A., Nonfactorizable QCD effects in Higgs boson production via vector boson fusion, Phys. Rev. Lett., 123, 12, Article 122002 pp. (2019), arXiv:1906.10899 |
| [185] | Dreyer, F. A.; Karlberg, A.; Tancredi, L., On the impact of non-factorisable corrections in VBF single and double Higgs production, JHEP, 10, 131 (2020), arXiv:2005.11334 |
| [186] | Andersen, J.; Binoth, T.; Heinrich, G.; Smillie, J., Loop induced interference effects in Higgs boson plus two jet production at the LHC, J. High Energy Phys., 02, 057 (2008), arXiv:0709.3513 |
| [187] | Ciccolini, M.; Denner, A.; Dittmaier, S., Strong and electroweak corrections to the production of Higgs + 2jets via weak interactions at the LHC, Phys. Rev. Lett., 99, Article 161803 pp. (2007), arXiv:0707.0381 |
| [188] | Rauch, M.; Zeppenfeld, D., Jet clustering dependence of Higgs boson production in vector-boson fusion, Phys. Rev. D, 95, 11, Article 114015 pp. (2017), arXiv:1703.05676 |
| [189] | Ciccolini, M.; Denner, A.; Dittmaier, S., Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC, Phys. Rev. D, 77, Article 013002 pp. (2008), arXiv:0710.4749 |
| [190] | Figy, T.; Palmer, S.; Weiglein, G., Higgs production via weak boson fusion in the standard model and the MSSM, J. High Energy Phys., 02, 105 (2012), arXiv:1012.4789 · Zbl 1309.81326 |
| [191] | Denner, A.; Dittmaier, S.; Kallweit, S.; Mück, A., Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, J. High Energy Phys., 03, 075 (2012), arXiv:1112.5142 · Zbl 1309.81322 |
| [192] | Denner, A.; Dittmaier, S.; Kallweit, S.; Mück, A., HAWK 2.0: A Monte Carlo program for Higgs production in vector-boson fusion and Higgs strahlung at hadron colliders, Comput. Phys. Comm., 195, 161-171 (2015), arXiv:1412.5390 |
| [193] | Campanario, F.; Figy, T. M.; Plätzer, S.; Sjödahl, M., Electroweak Higgs boson plus three jet production at next-to-leading-order QCD, Phys. Rev. Lett., 111, 21, Article 211802 pp. (2013), arXiv:1308.2932 |
| [194] | Campanario, F.; Figy, T. M.; Plätzer, S.; Rauch, M.; Schichtel, P.; Sjödahl, M., Stress testing the vector-boson-fusion approximation in multijet final states, Phys. Rev. D, 98, 3, Article 033003 pp. (2018), arXiv:1802.09955 |
| [195] | Greiner, N.; Höche, S.; Luisoni, G.; Schönherr, M.; Winter, J.-C.; Yundin, V., Phenomenological analysis of Higgs boson production through gluon fusion in association with jets, J. High Energy Phys., 01, 169 (2016), arXiv:1506.01016 |
| [196] | Greiner, N.; Höche, S.; Luisoni, G.; Schönherr, M.; Winter, J.-C., Full mass dependence in Higgs boson production in association with jets at the LHC and FCC, J. High Energy Phys., 01, 091 (2017), arXiv:1608.01195 |
| [197] | Andersen, J. R.; Cockburn, J. D.; Heil, M.; Maier, A.; Smillie, J. M., Finite quark-mass effects in Higgs boson production with dijets at large energies, J. High Energy Phys., 04, 127 (2019), arXiv:1812.08072 |
| [198] | Andersen, J. R.; Smillie, J. M., The factorisation of the t-channel pole in quark-gluon scattering, Phys. Rev. D, 81, Article 114021 pp. (2010), arXiv:0910.5113 |
| [199] | Andersen, J. R.; Smillie, J. M., Multiple jets at the LHC with high energy jets, J. High Energy Phys., 06, 010 (2011), arXiv:1101.5394 |
| [200] | Andersen, J. R.; Hapola, T.; Maier, A.; Smillie, J. M., Higgs boson plus dijets: Higher order corrections, J. High Energy Phys., 09, 065 (2017), arXiv:1706.01002 |
| [201] | Andersen, J. R.; Hapola, T.; Heil, M.; Maier, A.; Smillie, J. M., Higgs-boson plus dijets: Higher-order matching for high-energy predictions, J. High Energy Phys., 08, 090 (2018), arXiv:1805.04446 |
| [202] | Budge, L.; Campbell, J. M.; De Laurentis, G.; Ellis, R. K.; Seth, S., The one-loop amplitudes for Higgs + 4 partons with full mass effects, J. High Energy Phys., 05, 079 (2020), arXiv:2002.04018 |
| [203] | Jäger, B.; Karlberg, A.; Plätzer, S.; Scheller, J.; Zaro, M., Parton-shower effects in Higgs production via Vector-Boson Fusion, Eur. Phys. J. C, 80, 8, 756 (2020), arXiv:2003.12435 |
| [204] | Cabouat, B.; Sjöstrand, T., Some dipole shower studies, Eur. Phys. J. C, 78, 3, 226 (2018), arXiv:1710.00391 |
| [205] | Brein, O.; Djouadi, A.; Harlander, R., NNLO QCD corrections to the Higgs-strahlung processes at hadron colliders, Phys. Lett. B, 579, 149-156 (2004), arXiv:hep-ph/0307206 |
| [206] | Brein, O.; Harlander, R.; Wiesemann, M.; Zirke, T., Top-quark mediated effects in hadronic Higgs-Strahlung, Eur. Phys. J. C, 72, 1868 (2012), arXiv:1111.0761 |
| [207] | Brein, O.; Harlander, R. V.; Zirke, T. J., vh@nnlo - Higgs Strahlung at hadron colliders, Comput. Phys. Comm., 184, 998-1003 (2013), arXiv:1210.5347 |
| [208] | Harlander, R. V.; Klappert, J.; Liebler, S.; Simon, L., vh@nnlo-v2: New physics in Higgs Strahlung, J. High Energy Phys., 05, 089 (2018), arXiv:1802.04817 |
| [209] | Ciccolini, M.; Dittmaier, S.; Krämer, M., Electroweak radiative corrections to associated WH and ZH production at hadron colliders, Phys. Rev. D, 68, Article 073003 pp. (2003), arXiv:hep-ph/0306234 |
| [210] | Granata, F.; Lindert, J. M.; Oleari, C.; Pozzorini, S., NLO QCD+EW predictions for HV and HV +jet production including parton-shower effects, J. High Energy Phys., 09, 012 (2017), arXiv:1706.03522 |
| [211] | Obul, P.; Dulat, S.; Hou, T.-J.; Tursun, A.; Yalkun, N., Next-to-leading order QCD and electroweak corrections to Higgs-strahlung processes at the LHC, Chin. Phys. C, 42, 9, Article 093105 pp. (2018), arXiv:1801.06851 |
| [212] | Boughezal, R.; Campbell, J. M.; Ellis, R. K.; Focke, C.; Giele, W.; Liu, X.; Petriello, F.; Williams, C., Color singlet production at NNLO in MCFM, Eur. Phys. J. C, 77, 1, 7 (2017), arXiv:1605.08011 |
| [213] | Caola, F.; Melnikov, K.; Röntsch, R., Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J. C, 77, 4, 248 (2017), arXiv:1702.01352 |
| [214] | Luisoni, G.; Nason, P.; Oleari, C.; Tramontano, F., \( H W^\pm \)/HZ + 0 and 1 jet at NLO with the POWHEG BOX interfaced to GoSam and their merging within MiNLO, J. High Energy Phys., 10, 083 (2013), arXiv:1306.2542 |
| [215] | Astill, W.; Bizoń, W.; Re, E.; Zanderighi, G., NNLOPS accurate associated HW production, J. High Energy Phys., 06, 154 (2016), arXiv:1603.01620 |
| [216] | Astill, W.; Bizoń, W.; Re, E.; Zanderighi, G., NNLOPS accurate associated HZ production with \(H \to b \overline{b}\) decay at NLO, J. High Energy Phys., 11, 157 (2018), arXiv:1804.08141 |
| [217] | Hamilton, K.; Nason, P.; Zanderighi, G., MINLO: Multi-scale improved NLO, J. High Energy Phys., 10, 155 (2012), arXiv:1206.3572 |
| [218] | Goncalves, D.; Krauss, F.; Kuttimalai, S.; Maierhöfer, P., Higgs-Strahlung: Merging the NLO Drell-Yan and loop-induced 0+1 jet multiplicities, Phys. Rev. D, 92, 7, Article 073006 pp. (2015), arXiv:1509.01597 |
| [219] | Hespel, B.; Maltoni, F.; Vryonidou, E., Higgs and Z boson associated production via gluon fusion in the SM and the 2HDM, J. High Energy Phys., 06, 065 (2015), arXiv:1503.01656 |
| [220] | Banfi, A.; Salam, G. P.; Zanderighi, G., Infrared safe definition of jet flavor, Eur. Phys. J. C, 47, 113-124 (2006), arXiv:hep-ph/0601139 |
| [221] | Gauld, R.; Gehrmann-De Ridder, A.; Glover, E. W.N.; Huss, A.; Majer, I., Precise predictions for \(\operatorname{WH} \)+jet production at the LHC (2020), arXiv:2009.14209 |
| [222] | Kumar, M.; Mandal, M.; Ravindran, V., Associated production of Higgs boson with vector boson at threshold \(N{}^3\) LO in QCD, J. High Energy Phys., 03, 037 (2015), arXiv:1412.3357 |
| [223] | Dawson, S.; Han, T.; Lai, W.; Leibovich, A.; Lewis, I., Resummation effects in vector-boson and Higgs associated production, Phys. Rev. D, 86, Article 074007 pp. (2012), arXiv:1207.4207 |
| [224] | Harlander, R. V.; Kulesza, A.; Theeuwes, V.; Zirke, T., Soft gluon resummation for gluon-induced Higgs Strahlung, J. High Energy Phys., 11, 082 (2014), arXiv:1410.0217 |
| [225] | Harlander, R. V.; Liebler, S.; Zirke, T., Higgs Strahlung at the large hadron collider in the 2-Higgs-doublet model, J. High Energy Phys., 02, 023 (2014), arXiv:1307.8122 |
| [226] | Englert, C.; McCullough, M.; Spannowsky, M., Gluon-initiated associated production boosts Higgs physics, Phys. Rev. D, 89, 1, Article 013013 pp. (2014), arXiv:1310.4828 |
| [227] | Kniehl, B. A., Associated production of Higgs and z bosons from gluon fusion in hadron collisions, Phys. Rev. D, 42, 2253-2258 (1990) |
| [228] | Altenkamp, L.; Dittmaier, S.; Harlander, R. V.; Rzehak, H.; Zirke, T. J., Gluon-induced Higgs-strahlung at next-to-leading order QCD, J. High Energy Phys., 02, 078 (2013), arXiv:1211.5015 |
| [229] | Hasselhuhn, A.; Luthe, T.; Steinhauser, M., On top quark mass effects to \(g g \to Z H\) at NLO, J. High Energy Phys., 01, 073 (2017), arXiv:1611.05881 |
| [230] | Harlander, R.; Klappert, J.; Pandini, C.; Papaefstathiou, A., Exploiting the WH/ZH symmetry in the search for new physics, Eur. Phys. J. C, 78, 9, 760 (2018), arXiv:1804.02299 |
| [231] | Davies, J.; Mishima, G.; Steinhauser, M., Virtual corrections to \(g g \to Z H\) in the high-energy and large-\( m_t\) limits, J. High Energy Phys., 03, 034 (2021), arXiv:2011.12314 |
| [232] | Alasfar, L.; Degrassi, G.; Giardino, P. P.; Gröber, R.; Vitti, M., Virtual corrections to \(g g \to Z H\) via a transverse momentum expansion (2021), arXiv:2103.06225 |
| [233] | Chen, L.; Heinrich, G.; Jones, S. P.; Kerner, M.; Klappert, J.; Schlenk, J., \( Z H\) production in gluon fusion: two-loop amplitudes with full top quark mass dependence, J. High Energy Phys., 03, 125 (2021), arXiv:2011.12325 |
| [234] | Ahmed, T.; Ajjath, A.; Chen, L.; Dhani, P. K.; Mukherjee, P.; Ravindran, V., Polarised amplitudes and soft-virtual cross sections for \(b \overline{b} \to Z H\) at NNLO in QCD, J. High Energy Phys., 01, 030 (2020), arXiv:1910.06347 |
| [235] | Ahmed, T.; Bernreuther, W.; Chen, L.; Czakon, M., Polarized \(q \overline{q} \to Z +\) Higgs amplitudes at two loops in QCD: the interplay between vector and axial vector form factors and a pitfall in applying a non-anticommuting \(\gamma_5\), J. High Energy Phys., 07, 159 (2020), arXiv:2004.13753 |
| [236] | Aguilar-Saavedra, J. A.; Cano, J. M.; No, J. M., More light on Higgs flavor at the LHC: Higgs couplings to light quarks through \(h + \gamma\) production (2020), arXiv:2008.12538 |
| [237] | Gabrielli, E.; Mele, B.; Piccinini, F.; Pittau, R., Asking for an extra photon in Higgs production at the LHC and beyond, J. High Energy Phys., 07, 003 (2016), arXiv:1601.03635 |
| [238] | Arnold, K.; Figy, T.; Jager, B.; Zeppenfeld, D., Next-to-leading order QCD corrections to Higgs boson production in association with a photon via weak-boson fusion at the LHC, J. High Energy Phys., 08, 088 (2010), arXiv:1006.4237 · Zbl 1290.81187 |
| [239] | Agrawal, P.; Shivaji, A., Gluon fusion contribution to \(V H j\) production at hadron colliders, Phys. Lett. B, 741, 111-116 (2015), arXiv:1409.8059 |
| [240] | Aad, G., \( C P\) properties of Higgs boson interactions with top quarks in the \(t \overline{t} H\) and \(t H\) processes using \(H \to \gamma \gamma\) with the ATLAS detector, Phys. Rev. Lett., 125, 6, Article 061802 pp. (2020), arXiv:2004.04545 |
| [241] | Sirunyan, A. M., Measurements of \(\operatorname{t} \overline{\operatorname{t}} H\) production and the CP structure of the Yukawa interaction between the Higgs boson and top quark in the diphoton decay channel, Phys. Rev. Lett., 125, 6, Article 061801 pp. (2020), arXiv:2003.10866 |
| [242] | Erdmann, M.; Fischer, B.; Rieger, M., Jet-parton assignment in \(t \overline{t} H\) events using deep learning, J. Instrum., 12, 08, P08020 (2017), arXiv:1706.01117 |
| [243] | Butter, A.; Kasieczka, G.; Plehn, T., The machine learning landscape of top taggers, SciPost Phys., 7, 014 (2019), arXiv:1902.09914 |
| [244] | Ren, J.; Wu, L.; Yang, J. M., Unveiling CP property of top-Higgs coupling with graph neural networks at the LHC, Phys. Lett. B, 802, Article 135198 pp. (2020), arXiv:1901.05627 |
| [245] | Abdughani, M.; Ren, J.; Wu, L.; Yang, J. M.; Zhao, J., Supervised deep learning in high energy phenomenology: a mini review, Commun. Theor. Phys., 71, 8, 955 (2019), arXiv:1905.06047 · Zbl 1452.68168 |
| [246] | Beenakker, W.; Dittmaier, S.; Krämer, M.; Plümper, B.; Spira, M.; Zerwas, P., Higgs radiation off top quarks at the Tevatron and the LHC, Phys. Rev. Lett., 87, Article 201805 pp. (2001), arXiv:hep-ph/0107081 |
| [247] | Reina, L.; Dawson, S., Next-to-leading order results for t anti-t h production at the Tevatron, Phys. Rev. Lett., 87, Article 201804 pp. (2001), arXiv:hep-ph/0107101 |
| [248] | Beenakker, W.; Dittmaier, S.; Krämer, M.; Plümper, B.; Spira, M.; Zerwas, P., NLO QCD corrections to t anti-t H production in hadron collisions, Nuclear Phys. B, 653, 151-203 (2003), arXiv:hep-ph/0211352 |
| [249] | Dawson, S.; Orr, L.; Reina, L.; Wackeroth, D., Associated top quark Higgs boson production at the LHC, Phys. Rev. D, 67, Article 071503 pp. (2003), arXiv:hep-ph/0211438 |
| [250] | Dawson, S.; Jackson, C.; Orr, L.; Reina, L.; Wackeroth, D., Associated Higgs production with top quarks at the large hadron collider: NLO QCD corrections, Phys. Rev. D, 68, Article 034022 pp. (2003), arXiv:hep-ph/0305087 |
| [251] | Frederix, R.; Frixione, S.; Hirschi, V.; Maltoni, F.; Pittau, R.; Torrielli, P., Scalar and pseudoscalar Higgs production in association with a top-antitop pair, Phys. Lett. B, 701, 427-433 (2011), arXiv:1104.5613 |
| [252] | Garzelli, M.; Kardos, A.; Papadopoulos, C.; Trocsanyi, Z., Standard model Higgs boson production in association with a top anti-top pair at NLO with parton showering, Europhys. Lett., 96, 1, 11001 (2011), arXiv:1108.0387 |
| [253] | Hartanto, H. B.; Jäger, B.; Reina, L.; Wackeroth, D., Higgs boson production in association with top quarks in the POWHEG BOX, Phys. Rev. D, 91, 9, Article 094003 pp. (2015), arXiv:1501.04498 |
| [254] | Frixione, S.; Hirschi, V.; Pagani, D.; Shao, H.; Zaro, M., Weak corrections to Higgs hadroproduction in association with a top-quark pair, J. High Energy Phys., 09, 065 (2014), arXiv:1407.0823 |
| [255] | Zhang, Y.; Ma, W.-G.; Zhang, R.-Y.; Chen, C.; Guo, L., QCD NLO and EW NLO corrections to \(t \overline{t} H\) production with top quark decays at hadron collider, Phys. Lett. B, 738, 1-5 (2014), arXiv:1407.1110 |
| [256] | Frixione, S.; Hirschi, V.; Pagani, D.; Shao, H. S.; Zaro, M., Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons, J. High Energy Phys., 06, 184 (2015), arXiv:1504.03446 |
| [257] | Denner, A.; Feger, R., NLO QCD corrections to off-shell top-antitop production with leptonic decays in association with a Higgs boson at the LHC, J. High Energy Phys., 11, 209 (2015), arXiv:1506.07448 |
| [258] | Actis, S.; Denner, A.; Hofer, L.; Lang, J.-N.; Scharf, A.; Uccirati, S., RECOLA: Recursive computation of one-loop amplitudes, Comput. Phys. Comm., 214, 140-173 (2017), arXiv:1605.01090 · Zbl 1376.81069 |
| [259] | Denner, A.; Lang, J.-N.; Uccirati, S., Recola2: Recursive computation of one-loop amplitudes 2, Comput. Phys. Comm., 224, 346-361 (2018), arXiv:1711.07388 · Zbl 07694317 |
| [260] | Kulesza, A.; Motyka, L.; Stebel, T.; Theeuwes, V., Soft gluon resummation for associated \(t \overline{t} H\) production at the LHC, J. High Energy Phys., 03, 065 (2016), arXiv:1509.02780 |
| [261] | Broggio, A.; Ferroglia, A.; Pecjak, B. D.; Signer, A.; Yang, L. L., Associated production of a top pair and a Higgs boson beyond NLO, J. High Energy Phys., 03, 124 (2016), arXiv:1510.01914 |
| [262] | Broggio, A.; Ferroglia, A.; Pecjak, B. D.; Yang, L. L., NNLL resummation for the associated production of a top pair and a Higgs boson at the LHC, J. High Energy Phys., 02, 126 (2017), arXiv:1611.00049 |
| [263] | Kulesza, A.; Motyka, L.; Stebel, T.; Theeuwes, V., Associated \(t \overline{t} H\) production at the LHC: Theoretical predictions at NLO+NNLL accuracy, Phys. Rev. D, 97, 11, Article 114007 pp. (2018), arXiv:1704.03363 |
| [264] | Ju, W.-L.; Yang, L. L., Resummation of soft and Coulomb corrections for \(t \overline{t} h\) production at the LHC, J. High Energy Phys., 06, 050 (2019), arXiv:1904.08744 |
| [265] | Kulesza, A.; Motyka, L.; Schwartländer, D.; Stebel, T.; Theeuwes, V., Associated production of a top quark pair with a heavy electroweak gauge boson at NLO \(+\) NNLL accuracy, Eur. Phys. J. C, 79, 3, 249 (2019), arXiv:1812.08622 |
| [266] | Broggio, A.; Ferroglia, A.; Frederix, R.; Pagani, D.; Pecjak, B. D.; Tsinikos, I., Top-quark pair hadroproduction in association with a heavy boson at NLO+NNLL including EW corrections, J. High Energy Phys., 08, 039 (2019), arXiv:1907.04343 |
| [267] | Maltoni, F.; Vryonidou, E.; Zhang, C., Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD, J. High Energy Phys., 10, 123 (2016), arXiv:1607.05330 |
| [268] | Gunion, J. F.; He, X.-G., Determining the CP nature of a neutral Higgs boson at the LHC, Phys. Rev. Lett., 76, 4468-4471 (1996), arXiv:hep-ph/9602226 |
| [269] | Artoisenet, P., A framework for Higgs characterisation, J. High Energy Phys., 11, 043 (2013), arXiv:1306.6464 |
| [270] | Ellis, J.; Hwang, D. S.; Sakurai, K.; Takeuchi, M., Disentangling Higgs-top couplings in associated production, J. High Energy Phys., 04, 004 (2014), arXiv:1312.5736 |
| [271] | Demartin, F.; Maltoni, F.; Mawatari, K.; Page, B.; Zaro, M., Higgs characterisation at NLO in QCD: CP properties of the top-quark Yukawa interaction, Eur. Phys. J. C, 74, 9, 3065 (2014), arXiv:1407.5089 |
| [272] | Boudjema, F.; Godbole, R. M.; Guadagnoli, D.; Mohan, K. A., Lab-frame observables for probing the top-Higgs interaction, Phys. Rev. D, 92, 1, Article 015019 pp. (2015), arXiv:1501.03157 |
| [273] | Buckley, M. R.; Goncalves, D., Boosting the direct CP measurement of the Higgs-top coupling, Phys. Rev. Lett., 116, 9, Article 091801 pp. (2016), arXiv:1507.07926 |
| [274] | Gritsan, A. V.; Röntsch, R.; Schulze, M.; Xiao, M., Constraining anomalous Higgs boson couplings to the heavy flavor fermions using matrix element techniques, Phys. Rev. D, 94, 5, Article 055023 pp. (2016), arXiv:1606.03107 |
| [275] | Amor Dos Santos, S., Probing the CP nature of the Higgs coupling in \(t \overline{t} h\) events at the LHC, Phys. Rev. D, 96, 1, Article 013004 pp. (2017), arXiv:1704.03565 |
| [276] | Goncalves, D.; Kong, K.; Kim, J. H., Probing the top-Higgs Yukawa CP structure in dileptonic \(t \overline{t} h\) with m \({}_2\)-assisted reconstruction, J. High Energy Phys., 06, 079 (2018), arXiv:1804.05874 |
| [277] | Ferroglia, A.; Fiolhais, M. C.; Gouveia, E.; Onofre, A., Role of the \(t \overline{t} h\) rest frame in direct top-quark Yukawa coupling measurements, Phys. Rev. D, 100, 7, Article 075034 pp. (2019), arXiv:1909.00490 |
| [278] | Campbell, J.; Ellis, R. K.; Röntsch, R., Single top production in association with a Z boson at the LHC, Phys. Rev. D, 87, Article 114006 pp. (2013), arXiv:1302.3856 |
| [279] | Demartin, F.; Maltoni, F.; Mawatari, K.; Zaro, M., Higgs production in association with a single top quark at the LHC, Eur. Phys. J. C, 75, 6, 267 (2015), arXiv:1504.00611 |
| [280] | Barger, V.; Hagiwara, K.; Zheng, Y.-J., Probing the top Yukawa coupling at the LHC via associated production of single top and Higgs, JHEP, 09, 101 (2020), arXiv:1912.11795 |
| [281] | Deutschmann, N.; Maltoni, F.; Wiesemann, M.; Zaro, M., Top-Yukawa contributions to bbH production at the LHC, J. High Energy Phys., 07, 054 (2019), arXiv:1808.01660 |
| [282] | Azzi, P., Report from working group 1: Standard model physics at the HL-LHC and HE-LHC, (Dainese, A.; Mangano, M.; Meyer, A. B.; Nisati, A.; Salam, G.; Vesterinen, M. A., Report on the Physics At the HL-LHC,and Perspectives for the HE-LHC, vol. 7 (2019)), 1-220, arXiv:1902.04070 |
| [283] | Aaboud, M., Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector, Phys. Lett. B, 784, 173-191 (2018), arXiv:1806.00425 |
| [284] | Sirunyan, A. M., Observation of \(\operatorname{t} \overline{\operatorname{t}}\) h production, Phys. Rev. Lett., 120, 23, Article 231801 pp. (2018), arXiv:1804.02610 |
| [285] | Catani, S.; Fabre, I.; Grazzini, M.; Kallweit, S., \( t \overline{t} H\) production at NNLO: the flavour off-diagonal channels (2021), arXiv:2102.03256 |
| [286] | Cepeda, M., Report from working group 2: Higgs physics at the HL-LHC and HE-LHC, (Report on the Physics At the HL-LHC,and Perspectives for the HE-LHC, vol. 7 (2019)), 221-584, arXiv:1902.00134 |
| [287] | Adhikary, A.; Banerjee, S.; Barman, R. K.; Bhattacherjee, B.; Niyogi, S., Revisiting the non-resonant Higgs pair production at the HL-LHC, J. High Energy Phys., 07, 116 (2018), arXiv:1712.05346 |
| [288] | Mangano, M. L.; Ortona, G.; Selvaggi, M., Measuring the Higgs self-coupling via Higgs-pair production at a 100 TeV p-p collider, Eur. Phys. J. C, 80, 11, 1030 (2020), arXiv:2004.03505 |
| [289] | Goncalves, D.; Han, T.; Kling, F.; Plehn, T.; Takeuchi, M., Higgs boson pair production at future hadron colliders: From kinematics to dynamics, Phys. Rev. D, 97, 11, Article 113004 pp. (2018), arXiv:1802.04319 |
| [290] | Aad, G., Combination of searches for Higgs boson pairs in \(p p\) collisions at \(\sqrt{ s} =13\) TeV with the ATLAS detector, Phys. Lett. B, 800, Article 135103 pp. (2020), arXiv:1906.02025 |
| [291] | McCullough, M., An indirect model-dependent probe of the Higgs self-coupling, Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, 92, 1, 039903 (2015), (erratum) |
| [292] | Gorbahn, M.; Haisch, U., Indirect probes of the trilinear Higgs coupling: \( g g \to h\) and \(h \to \gamma \gamma \), J. High Energy Phys., 10, 094 (2016), arXiv:1607.03773 |
| [293] | Degrassi, G.; Giardino, P. P.; Maltoni, F.; Pagani, D., Probing the Higgs self coupling via single Higgs production at the LHC, J. High Energy Phys., 12, 080 (2016), arXiv:1607.04251 |
| [294] | Bizoń, W.; Gorbahn, M.; Haisch, U.; Zanderighi, G., Constraints on the trilinear Higgs coupling from vector boson fusion and associated Higgs production at the LHC, J. High Energy Phys., 07, 083 (2017), arXiv:1610.05771 |
| [295] | Maltoni, F.; Pagani, D.; Shivaji, A.; Zhao, X., Trilinear Higgs coupling determination via single-higgs differential measurements at the LHC, Eur. Phys. J. C, 77, 12, 887 (2017), arXiv:1709.08649 |
| [296] | Kribs, G. D.; Maier, A.; Rzehak, H.; Spannowsky, M.; Waite, P., Electroweak oblique parameters as a probe of the trilinear Higgs boson self-interaction, Phys. Rev. D, 95, 9, Article 093004 pp. (2017), arXiv:1702.07678 |
| [297] | Degrassi, G.; Fedele, M.; Giardino, P. P., Constraints on the trilinear Higgs self coupling from precision observables, J. High Energy Phys., 04, 155 (2017), arXiv:1702.01737 |
| [298] | Nakamura, J.; Shivaji, A., Direct measurement of the Higgs self-coupling in \(e^+ e^- \to Z H\), Phys. Lett. B, 797, Article 134821 pp. (2019), arXiv:1812.01576 |
| [299] | Kilian, W.; Sun, S.; Yan, Q.-S.; Zhao, X.; Zhao, Z., Multi-Higgs production and unitarity in vector-boson fusion at future hadron colliders, Phys. Rev. D, 101, Article 076012 pp. (2020), arXiv:1808.05534 |
| [300] | Maltoni, F.; Pagani, D.; Zhao, X., Constraining the Higgs self-couplings at \(e^+ e^-\) colliders, J. High Energy Phys., 07, 087 (2018), arXiv:1802.07616 |
| [301] | Vryonidou, E.; Zhang, C., Dimension-six electroweak top-loop effects in Higgs production and decay, J. High Energy Phys., 08, 036 (2018), arXiv:1804.09766 |
| [302] | Gorbahn, M.; Haisch, U., Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling, J. High Energy Phys., 04, 062 (2019), arXiv:1902.05480 |
| [303] | Constraints on the Higgs boson self-coupling from the combination of single-Higgs and double-Higgs production analyses performed with the ATLAS experiment (2019), arXiv:ATLAS-CONF-2019-049 |
| [304] | Liu, T.; Lyu, K.-F.; Ren, J.; Zhu, H. X., Probing the quartic Higgs boson self-interaction, Phys. Rev. D, 98, 9, Article 093004 pp. (2018), arXiv:1803.04359 |
| [305] | Bizoń, W.; Haisch, U.; Rottoli, L., Constraints on the quartic Higgs self-coupling from double-higgs production at future hadron colliders, J. High Energy Phys., 10, 267 (2019), arXiv:1810.04665 |
| [306] | Borowka, S.; Duhr, C.; Maltoni, F.; Pagani, D.; Shivaji, A.; Zhao, X., Probing the scalar potential via double Higgs boson production at hadron colliders, J. High Energy Phys., 04, 016 (2019), arXiv:1811.12366 |
| [307] | Eboli, O. J.P.; Marques, G. C.; Novaes, S. F.; Natale, A. A., Twin Higgs boson production, Phys. Lett. B, 197, 269-272 (1987) |
| [308] | Glover, E. W.N.; van der Bij, J. J., Higgs boson pair production via gluon fusion, Nuclear Phys. B, 309, 282 (1988) |
| [309] | Plehn, T.; Spira, M.; Zerwas, P. M., Pair production of neutral Higgs particles in gluon-gluon collisions, Nuclear Phys. B. Nuclear Phys. B, Nuclear Phys. B, 531, 655-64 (1998), (erratum) |
| [310] | Dawson, S.; Dittmaier, S.; Spira, M., Neutral Higgs boson pair production at hadron colliders: QCD corrections, Phys. Rev. D, 58, Article 115012 pp. (1998), arXiv:hep-ph/9805244 |
| [311] | Maltoni, F.; Vryonidou, E.; Zaro, M., Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO, J. High Energy Phys., 11, 079 (2014), arXiv:1408.6542 |
| [312] | Borowka, S.; Greiner, N.; Heinrich, G.; Jones, S.; Kerner, M.; Schlenk, J.; Schubert, U.; Zirke, T., Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 117, 7, 079901 (2016), (erratum) |
| [313] | Borowka, S.; Greiner, N.; Heinrich, G.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T., Full top quark mass dependence in Higgs boson pair production at NLO, J. High Energy Phys., 10, 107 (2016), arXiv:1608.04798 |
| [314] | Baglio, J.; Campanario, F.; Glaus, S.; Mühlleitner, M.; Spira, M.; Streicher, J., Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme, Eur. Phys. J. C, 79, 6, 459 (2019), arXiv:1811.05692 |
| [315] | Baglio, J.; Campanario, F.; Glaus, S.; Mühlleitner, M.; Ronca, J.; Spira, M.; Streicher, J., Higgs-pair production via gluon fusion at hadron colliders: NLO QCD corrections, J. High Energy Phys., 04, 181 (2020), arXiv:2003.03227 |
| [316] | Borowka, S.; Heinrich, G.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T., SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Comput. Phys. Comm., 196, 470-491 (2015), arXiv:1502.06595 · Zbl 1360.81013 |
| [317] | Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J.; Zirke, T., pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, Comput. Phys. Comm., 222, 313-326 (2018), arXiv:1703.09692 · Zbl 07693053 |
| [318] | Heinrich, G.; Jones, S. P.; Kerner, M.; Luisoni, G.; Vryonidou, E., NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers, J. High Energy Phys., 08, 088 (2017), arXiv:1703.09252 |
| [319] | Jones, S.; Kuttimalai, S., Parton shower and NLO-matching uncertainties in Higgs boson pair production, J. High Energy Phys., 02, 176 (2018), arXiv:1711.03319 |
| [320] | Heinrich, G.; Jones, S. P.; Kerner, M.; Luisoni, G.; Scyboz, L., Probing the trilinear Higgs boson coupling in di-Higgs production at NLO QCD including parton shower effects, J. High Energy Phys., 06, 066 (2019), arXiv:1903.08137 |
| [321] | Heinrich, G.; Jones, S. P.; Kerner, M.; Scyboz, L., A non-linear EFT description of \(g g \to H H\) at NLO interfaced to POWHEG, JHEP, 10, 021 (2020), arXiv:2006.16877 |
| [322] | de Florian, D.; Mazzitelli, J., Two-loop virtual corrections to Higgs pair production, Phys. Lett. B, 724, 306-309 (2013), arXiv:1305.5206 · Zbl 1331.81219 |
| [323] | de Florian, D.; Mazzitelli, J., Higgs boson pair production at next-to-next-to-leading order in QCD, Phys. Rev. Lett., 111, Article 201801 pp. (2013), arXiv:1309.6594 |
| [324] | Grigo, J.; Melnikov, K.; Steinhauser, M., Virtual corrections to Higgs boson pair production in the large top quark mass limit, Nuclear Phys. B, 888, 17-29 (2014), arXiv:1408.2422 · Zbl 1326.81239 |
| [325] | Grigo, J.; Hoff, J.; Steinhauser, M., Higgs boson pair production: top quark mass effects at NLO and NNLO, Nuclear Phys. B, 900, 412-430 (2015), arXiv:1508.00909 · Zbl 1331.81308 |
| [326] | de Florian, D.; Grazzini, M.; Hanga, C.; Kallweit, S.; Lindert, J. M.; Maierhöfer, P.; Mazzitelli, J.; Rathlev, D., Differential Higgs boson pair production at next-to-next-to-leading order in QCD, J. High Energy Phys., 09, 151 (2016), arXiv:1606.09519 |
| [327] | de Florian, D.; Mazzitelli, J., Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC, J. High Energy Phys., 09, 053 (2015), arXiv:1505.07122 |
| [328] | Grazzini, M.; Heinrich, G.; Jones, S.; Kallweit, S.; Kerner, M.; Lindert, J. M.; Mazzitelli, J., Higgs boson pair production at NNLO with top quark mass effects, J. High Energy Phys., 05, 059 (2018), arXiv:1803.02463 |
| [329] | De Florian, D.; Mazzitelli, J., Soft gluon resummation for Higgs boson pair production including finite m \({}_t\) effects, J. High Energy Phys., 08, 156 (2018), arXiv:1807.03704 |
| [330] | Baglio, J.; Campanario, F.; Glaus, S.; Mühlleitner, M.; Ronca, J.; Spira, M., \( g g \to H H\): Combined uncertainties, Phys. Rev. D, 103, 5, 056002 (2021), arXiv:2008.11626 |
| [331] | Gröber, R.; Maier, A.; Rauh, T., Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes, J. High Energy Phys., 03, 020 (2018), arXiv:1709.07799 |
| [332] | Bonciani, R.; Degrassi, G.; Giardino, P. P.; Gröber, R., Analytical method for next-to-leading-order QCD corrections to double-higgs production, Phys. Rev. Lett., 121, 16, Article 162003 pp. (2018), arXiv:1806.11564 |
| [333] | Xu, X.; Yang, L. L., Towards a new approximation for pair-production and associated-production of the Higgs boson, J. High Energy Phys., 01, 211 (2019), arXiv:1810.12002 |
| [334] | Mishima, G., High-energy expansion of two-loop massive four-point diagrams, J. High Energy Phys., 02, 080 (2019), arXiv:1812.04373 |
| [335] | Davies, J.; Mishima, G.; Steinhauser, M.; Wellmann, D., Double-Higgs boson production in the high-energy limit: planar master integrals, J. High Energy Phys., 03, 048 (2018), arXiv:1801.09696 |
| [336] | Davies, J.; Mishima, G.; Steinhauser, M.; Wellmann, D., Double Higgs boson production at NLO in the high-energy limit: complete analytic results, J. High Energy Phys., 01, 176 (2019), arXiv:1811.05489 |
| [337] | Davies, J.; Heinrich, G.; Jones, S. P.; Kerner, M.; Mishima, G.; Steinhauser, M.; Wellmann, D., Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion, J. High Energy Phys., 11, 024 (2019), arXiv:1907.06408 |
| [338] | Davies, J.; Steinhauser, M., Three-loop form factors for Higgs boson pair production in the large top mass limit, J. High Energy Phys., 10, 166 (2019), arXiv:1909.01361 |
| [339] | Davies, J.; Herren, F.; Mishima, G.; Steinhauser, M., Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops, J. High Energy Phys., 05, 157 (2019), arXiv:1904.11998 |
| [340] | Gerlach, M.; Herren, F.; Steinhauser, M., Wilson coefficients for Higgs boson production and decoupling relations to \(\mathcal{O} ( \alpha_s^4 )\), J. High Energy Phys., 11, 141 (2018), arXiv:1809.06787 |
| [341] | Spira, M., Effective multi-Higgs couplings to gluons, J. High Energy Phys., 10, 026 (2016), arXiv:1607.05548 |
| [342] | Contino, R.; Ghezzi, M.; Moretti, M.; Panico, G.; Piccinini, F.; Wulzer, A., Anomalous couplings in double Higgs production, J. High Energy Phys., 08, 154 (2012), arXiv:1205.5444 |
| [343] | Goertz, F.; Papaefstathiou, A.; Yang, L. L.; Zurita, J., Higgs boson pair production in the D=6 extension of the SM, J. High Energy Phys., 04, 167 (2015), arXiv:1410.3471 |
| [344] | Chen, C.-R.; Low, I., Double take on new physics in double Higgs boson production, Phys. Rev. D, 90, 1, Article 013018 pp. (2014), arXiv:1405.7040 |
| [345] | Azatov, A.; Contino, R.; Panico, G.; Son, M., Effective field theory analysis of double Higgs boson production via gluon fusion, Phys. Rev. D, 92, 3, Article 035001 pp. (2015), arXiv:1502.00539 |
| [346] | Dawson, S.; Ismail, A.; Low, I., What’s in the loop? The anatomy of double Higgs production, Phys. Rev. D, 91, 11, Article 115008 pp. (2015), arXiv:1504.05596 |
| [347] | Carvalho, A.; Dall’Osso, M.; Dorigo, T.; Goertz, F.; Gottardo, C. A.; Tosi, M., Higgs pair production: Choosing benchmarks with cluster analysis, J. High Energy Phys., 04, 126 (2016), arXiv:1507.02245 |
| [348] | Cao, Q.-H.; Yan, B.; Zhang, D.-M.; Zhang, H., Resolving the degeneracy in single Higgs production with Higgs pair production, Phys. Lett. B, 752, 285-290 (2016), arXiv:1508.06512 |
| [349] | Cao, Q.-H.; Li, G.; Yan, B.; Zhang, D.-M.; Zhang, H., Double Higgs production at the 14 TeV LHC and a 100 TeV \(p p\) collider, Phys. Rev. D, 96, 9, Article 095031 pp. (2017), arXiv:1611.09336 |
| [350] | Di Vita, S.; Grojean, C.; Panico, G.; Riembau, M.; Vantalon, T., A global view on the Higgs self-coupling, J. High Energy Phys., 09, 069 (2017), arXiv:1704.01953 |
| [351] | de Blas, J.; Eberhardt, O.; Krause, C., Current and future constraints on Higgs couplings in the nonlinear effective theory, J. High Energy Phys., 07, 048 (2018), arXiv:1803.00939 |
| [352] | Kim, J. H.; Kim, M.; Kong, K.; Matchev, K. T.; Park, M., Portraying double Higgs at the large hadron collider, J. High Energy Phys., 09, 047 (2019), arXiv:1904.08549 |
| [353] | Barducci, D.; Mimasu, K.; No, J.; Vernieri, C.; Zurita, J., Enlarging the scope of resonant di-Higgs searches: Hunting for Higgs-to-Higgs cascades in \(4 b\) final states at the LHC and future colliders, J. High Energy Phys., 02, 002 (2020), arXiv:1910.08574 |
| [354] | Cheung, K.; Jueid, A.; Lu, C.-T.; Song, J.; Yoon, Y. W., Disentangling new physics effects on non-resonant Higgs boson pair production from gluon fusion, Phys. Rev. D, 103, 1, 015019 (2021), arXiv:2003.11043 |
| [355] | Abdughani, M.; Wang, D.; Wu, L.; Yang, J. M.; Zhao, J., Probing triple Higgs coupling with machine learning at the LHC (2020), arXiv:2005.11086 |
| [356] | Adhikary, A.; Barman, R. K.; Bhattacherjee, B., Prospects of non-resonant di-Higgs searches and Higgs boson self-coupling measurement at the HE-LHC using machine learning techniques, JHEP, 12, 179 (2020), arXiv:2006.11879 |
| [357] | Gröber, R.; Mühlleitner, M.; Spira, M.; Streicher, J., aNLO QCD Corrections to Higgs pair production including dimension-6 operators, J. High Energy Phys., 09, 092 (2015), arXiv:1504.06577 · Zbl 1388.81925 |
| [358] | Gröber, R.; Mühlleitner, M.; Spira, M., Signs of composite Higgs pair production at next-to-leading order, J. High Energy Phys., 06, 080 (2016), arXiv:1602.05851 |
| [359] | Gröber, R.; Mühlleitner, M.; Spira, M., Higgs pair production at NLO QCD for CP-violating Higgs sectors, Nuclear Phys. B, 925, 1-27 (2017), arXiv:1705.05314 · Zbl 1375.81247 |
| [360] | de Florian, D.; Fabre, I.; Mazzitelli, J., Higgs boson pair production at NNLO in QCD including dimension 6 operators, J. High Energy Phys., 10, 215 (2017), arXiv:1704.05700 |
| [361] | Buchalla, G.; Capozi, M.; Celis, A.; Heinrich, G.; Scyboz, L., Higgs boson pair production in non-linear Effective Field Theory with full \(m_t\)-dependence at NLO QCD, J. High Energy Phys., 09, 057 (2018), arXiv:1806.05162 |
| [362] | Capozi, M.; Heinrich, G., Exploring anomalous couplings in Higgs boson pair production through shape analysis, J. High Energy Phys., 03, 091 (2020), arXiv:1908.08923 |
| [363] | Ajjath, A.; Banerjee, P.; Chakraborty, A.; Dhani, P. K.; Mukherjee, P.; Rana, N.; Ravindran, V., Higgs pair production from bottom quark annihilation to NNLO in QCD, J. High Energy Phys., 05, 030 (2019), arXiv:1811.01853 |
| [364] | Dreyer, F. A.; Karlberg, A., Fully differential vector-boson fusion Higgs pair production at next-to-next-to-leading order, Phys. Rev. D, 99, 7, Article 074028 pp. (2019), arXiv:1811.07918 |
| [365] | Dolan, M. J.; Englert, C.; Greiner, N.; Nordström, K.; Spannowsky, M., \( h h j j\) Production at the LHC, Eur. Phys. J. C, 75, 8, 387 (2015), arXiv:1506.08008 |
| [366] | Dreyer, F. A.; Karlberg, A.; Lang, J.-N.; Pellen, M., Precise predictions for double-higgs production via vector-boson fusion, Eur. Phys. J. C, 80, 11, 1037 (2020), arXiv:2005.13341 |
| [367] | Baglio, J.; Djouadi, A.; Gröber, R.; Mühlleitner, M.; Quevillon, J.; Spira, M., The measurement of the Higgs self-coupling at the LHC: theoretical status, J. High Energy Phys., 04, 151 (2013), arXiv:1212.5581 |
| [368] | Li, H. T.; Li, C. S.; Wang, J., Fully differential Higgs boson pair production in association with a \(Z\) boson at next-to-next-to-leading order in QCD, Phys. Rev. D, 97, 7, Article 074026 pp. (2018), arXiv:1710.02464 |
| [369] | Li, H. T.; Wang, J., Fully differential Higgs pair production in association with a \(W\) boson at next-to-next-to-leading order in QCD, Phys. Lett. B, 765, 265-271 (2017), arXiv:1607.06382 |
| [370] | Englert, C.; Krauss, F.; Spannowsky, M.; Thompson, J., Di-higgs phenomenology in \(t \overline{t} h h\): The forgotten channel, Phys. Lett. B, 743, 93-97 (2015), arXiv:1409.8074 |
| [371] | Liu, T.; Zhang, H., Measuring Di-Higgs physics via the \(t \overline{t} h h \to t \overline{t} b \overline{b} b \overline{b}\) channel (2014), arXiv:1410.1855 |
| [372] | Banerjee, S.; Krauss, F.; Spannowsky, M., Revisiting the \(t \overline{t} h h\) channel at the FCC-hh, Phys. Rev. D, 100, Article 073012 pp. (2019), arXiv:1904.07886 |
| [373] | Feruglio, F., The Chiral approach to the electroweak interactions, Internat. J. Modern Phys. A, 8, 4937-4972 (1993), arXiv:hep-ph/9301281 |
| [374] | Alonso, R.; Gavela, M.; Merlo, L.; Rigolin, S.; Yepes, J., The effective chiral Lagrangian for a light dynamical “Higgs particle”, Phys. Lett. B. Phys. Lett. B, Phys. Lett. B, 726, 926-335 (2013), (erratum) · Zbl 1331.81330 |
| [375] | Buchalla, G.; Cata, O.; Krause, C., Complete electroweak chiral Lagrangian with a light Higgs at NLO, Nuclear Phys. B. Nuclear Phys. B, Nuclear Phys. B, 913, 475-573 (2016), (erratum) · Zbl 1349.81192 |
| [376] | Cohen, T.; Craig, N.; Lu, X.; Sutherland, D., Is SMEFT enough? (2020), arXiv:2008.08597 |
| [377] | de Florian, D.; Fabre, I.; Mazzitelli, J., Triple Higgs production at hadron colliders at NNLO in QCD, J. High Energy Phys., 03, 155 (2020), arXiv:1912.02760 |
| [378] | Agrawal, P.; Saha, D.; Shivaji, A., Production of \(H H H\) and \(H H V ( V = \gamma , Z )\) at the hadron colliders, Phys. Rev. D, 97, 3, Article 036006 pp. (2018), arXiv:1708.03580 |
| [379] | Agrawal, P.; Saha, D.; Xu, L.-X.; Yu, J.-H.; Yuan, C., Determining the shape of Higgs potential at future colliders, Phys. Rev. D, 101, Article 075023 pp. (2020), arXiv:1907.02078 |
| [380] | Fuks, B.; Kim, J. H.; Lee, S. J., Scrutinizing the Higgs quartic coupling at a future 100 TeV proton-proton collider with taus and b-jets, Phys. Lett. B, 771, 354-358 (2017), arXiv:1704.04298 |
| [381] | Kilian, W.; Sun, S.; Yan, Q.-S.; Zhao, X.; Zhao, Z., New Physics in multi-Higgs boson final states, J. High Energy Phys., 06, 145 (2017), arXiv:1702.03554 |
| [382] | Papaefstathiou, A., Discovering Higgs boson pair production through rare final states at a 100 TeV collider, Phys. Rev. D, 91, 11, Article 113016 pp. (2015), arXiv:1504.04621 |
| [383] | Papaefstathiou, A.; Tetlalmatzi-Xolocotzi, G.; Zaro, M., Triple Higgs boson production to six \(b\)-jets at a 100 TeV proton collider, Eur. Phys. J. C, 79, 11, 947 (2019), arXiv:1909.09166 |
| [384] | Plehn, T.; Rauch, M., The quartic Higgs coupling at hadron colliders, Phys. Rev. D, 72, Article 053008 pp. (2005), arXiv:hep-ph/0507321 |
| [385] | Binoth, T.; Karg, S.; Kauer, N.; Rückl, R., Multi-Higgs boson production in the Standard Model and beyond, Phys. Rev. D, 74, Article 113008 pp. (2006), arXiv:hep-ph/0608057 |
| [386] | de Florian, D.; Mazzitelli, J., Two-loop corrections to the triple Higgs boson production cross section, J. High Energy Phys., 02, 107 (2017), arXiv:1610.05012 |
| [387] | Dicus, D. A.; Kao, C.; Repko, W. W., Self coupling of the Higgs boson in the processes \(p p \to Z H H H + X\) and \(p p \to W H H H + X\), Phys. Rev. D, 93, 11, Article 113003 pp. (2016), arXiv:1602.05849 |
| [388] | Di Vita, S.; Durieux, G.; Grojean, C.; Gu, J.; Liu, Z.; Panico, G.; Riembau, M.; Vantalon, T., A global view on the Higgs self-coupling at lepton colliders, J. High Energy Phys., 02, 178 (2018), arXiv:1711.03978 |
| [389] | Barklow, T.; Fujii, K.; Jung, S.; Peskin, M. E.; Tian, J., Model-independent determination of the triple Higgs coupling at e+e- colliders, Phys. Rev. D, 97, 5, Article 053004 pp. (2018), arXiv:1708.09079 |
| [390] | Chiesa, M.; Maltoni, F.; Mantani, L.; Mele, B.; Piccinini, F.; Zhao, X., Measuring the quartic Higgs self-coupling at a multi-TeV muon collider, JHEP, 09, 098 (2020), arXiv:2003.13628 |
| [391] | Han, T.; Liu, D.; Low, I.; Wang, X., Electroweak couplings of the Higgs boson at a multi-TeV muon collider, Phys. Rev. D, 103, 1, 013002 (2021), arXiv:2008.12204 |
| [392] | Anastasiou, C.; Melnikov, K.; Petriello, F., Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nuclear Phys. B, 724, 197-246 (2005), arXiv:hep-ph/0501130 |
| [393] | Grazzini, M.; Sargsyan, H., Heavy-quark mass effects in Higgs boson production at the LHC, J. High Energy Phys., 09, 129 (2013), arXiv:1306.4581 |
| [394] | Catani, S.; Cieri, L.; de Florian, D.; Ferrera, G.; Grazzini, M., Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 117, 089901 (2016), (erratum) |
| [395] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W.N.; Heinrich, G., EERAD3: Event shapes and jet rates in electron-positron annihilation at order \(\alpha_s^3\), Comput. Phys. Comm., 185, 3331 (2014), arXiv:1402.4140 |
| [396] | Melnikov, K.; Petriello, F., Electroweak gauge boson production at hadron colliders through \(O ( \alpha_s^2 )\), Phys. Rev. D, 74, Article 114017 pp. (2006), arXiv:hep-ph/0609070 |
| [397] | Gavin, R.; Li, Y.; Petriello, F.; Quackenbush, S., FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order, Comput. Phys. Comm., 182, 2388-2403 (2011), arXiv:1011.3540 |
| [398] | Catani, S.; Cieri, L.; Ferrera, G.; de Florian, D.; Grazzini, M., Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett., 103, Article 082001 pp. (2009), arXiv:0903.2120 |
| [399] | Camarda, S., DYTurbo: fast predictions for Drell-Yan processes, Eur. Phys. J. C. Eur. Phys. J. C, Eur. Phys. J. C, 80, 3, 440 (2020), (erratum) |
| [400] | Bozzi, G.; Catani, S.; de Florian, D.; Grazzini, M., Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC, Nuclear Phys. B, 737, 73-120 (2006), arXiv:hep-ph/0508068 · Zbl 1109.81387 |
| [401] | de Florian, D.; Ferrera, G.; Grazzini, M.; Tommasini, D., Transverse-momentum resummation: Higgs boson production at the tevatron and the LHC, J. High Energy Phys., 11, 064 (2011), arXiv:1109.2109 |
| [402] | Catani, S.; Cieri, L.; de Florian, D.; Ferrera, G.; Grazzini, M., Diphoton production at the LHC: a QCD study up to NNLO, J. High Energy Phys., 04, 142 (2018), arXiv:1802.02095 |
| [403] | Campbell, J. M.; Ellis, R.; Li, Y.; Williams, C., Predictions for diphoton production at the LHC through NNLO in QCD, J. High Energy Phys., 07, 148 (2016), arXiv:1603.02663 |
| [404] | Gao, J.; Li, C. S.; Zhu, H. X., Top quark decay at next-to-next-to leading order in QCD, Phys. Rev. Lett., 110, 4, Article 042001 pp. (2013), arXiv:1210.2808 |
| [405] | Gavin, R.; Li, Y.; Petriello, F.; Quackenbush, S., W physics at the LHC with FEWZ 2.1, Comput. Phys. Comm., 184, 208-214 (2013), arXiv:1201.5896 |
| [406] | Bozzi, G.; Catani, S.; Ferrera, G.; de Florian, D.; Grazzini, M., Production of drell-yan lepton pairs in hadron collisions: Transverse-momentum resummation at next-to-next-to-leading logarithmic accuracy, Phys. Lett. B, 696, 207-213 (2011), arXiv:1007.2351 |
| [407] | Grazzini, M.; Kallweit, S.; Wiesemann, M., Fully differential NNLO computations with MATRIX, Eur. Phys. J. C, 78, 7, 537 (2018), arXiv:1711.06631 |
| [408] | Cascioli, F.; Maierhöfer, P.; Pozzorini, S., Scattering amplitudes with open loops, Phys. Rev. Lett., 108, Article 111601 pp. (2012), arXiv:1111.5206 |
| [409] | Buccioni, F.; Lang, J.-N.; Lindert, J. M.; Maierhöfer, P.; Pozzorini, S.; Zhang, H.; Zoller, M. F., OpenLoops 2, Eur. Phys. J. C, 79, 10, 866 (2019), arXiv:1907.13071 |
| [410] | Grazzini, M.; Kallweit, S.; Lindert, J. M.; Pozzorini, S.; Wiesemann, M., NNLO QCD + NLO EW with Matrix+OpenLoops: precise predictions for vector-boson pair production, J. High Energy Phys., 02, 087 (2020), arXiv:1912.00068 |
| [411] | Kallweit, S.; Re, E.; Rottoli, L.; Wiesemann, M., Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RadISH: \( W^+ W^-\) production at the LHC, JHEP, 12, 147 (2020), arXiv:2004.07720 |
| [412] | Catani, S.; Devoto, S.; Grazzini, M.; Kallweit, S.; Mazzitelli, J., Top-quark pair hadroproduction at NNLO: differential predictions with the MSbar mass, J. High Energy Phys., 08, 027 (2020), arXiv:2005.00557 |
| [413] | Currie, J.; Glover, E. W.N.; Pires, J., Next-to-next-to leading order QCD predictions for single jet inclusive production at the LHC, Phys. Rev. Lett., 118, 7, Article 072002 pp. (2017), arXiv:1611.01460 |
| [414] | Currie, J.; Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W.N.; Huss, A.; Pires, J., Precise predictions for dijet production at the LHC, Phys. Rev. Lett., 119, 15, Article 152001 pp. (2017), arXiv:1705.10271 |
| [415] | Britzger, D., Calculations for deep inelastic scattering using fast interpolation grid techniques at NNLO in QCD and the extraction of \(\alpha_s\) from HERA data, Eur. Phys. J. C, 79, 10, 845 (2019), arXiv:1906.05303 |
| [416] | Kluge, T.; Rabbertz, K.; Wobisch, M., FastNLO: Fast pQCD calculations for PDF fits, (14th International Workshop on Deep Inelastic Scattering (2006)), 483-486, arXiv:hep-ph/0609285 |
| [417] | Britzger, D.; Rabbertz, K.; Stober, F.; Wobisch, M., New features in version 2 of the fastNLO project, (20th International Workshop on Deep-Inelastic Scattering and Related Subjects (2012)), 217-221, arXiv:1208.3641 |
| [418] | Czakon, M.; Heymes, D.; Mitov, A., fastNLO tables for NNLO top-quark pair differential distributions (2017), arXiv:1704.08551 |
| [419] | Cooper-Sarkar, A. M.; Czakon, M.; Lim, M. A.; Mitov, A.; Papanastasiou, A. S., Simultaneous extraction of \(\alpha_s\) and \(m_t\) from LHC \(t \overline{t}\) differential distributions (2020), arXiv:2010.04171 |
| [420] | Carli, T.; Clements, D.; Cooper-Sarkar, A.; Gwenlan, C.; Salam, G. P.; Siegert, F.; Starovoitov, P.; Sutton, M., A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: The APPLGRID Project, Eur. Phys. J. C, 66, 503-524 (2010), arXiv:0911.2985 |
| [421] | Carrazza, S.; Nocera, E. R.; Schwan, C.; Zaro, M., PineAPPL: combining EW and QCD corrections for fast evaluation of LHC processes, JHEP, 12, 108 (2020), arXiv:2008.12789 |
| [422] | Maître, D., Ntuples and compact matrix element representations, J. Phys. Conf. Ser., 1525, 1, Article 012014 pp. (2020) |
| [423] | Alioli, S.; Bauer, C. W.; Berggren, C. J.; Hornig, A.; Tackmann, F. J.; Vermilion, C. K.; Walsh, J. R.; Zuberi, S., Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA, J. High Energy Phys., 09, 120 (2013), arXiv:1211.7049 |
| [424] | Alioli, S.; Bauer, C. W.; Berggren, C.; Tackmann, F. J.; Walsh, J. R.; Zuberi, S., Matching fully differential NNLO calculations and parton showers, J. High Energy Phys., 06, 089 (2014), arXiv:1311.0286 |
| [425] | Alioli, S.; Bauer, C. W.; Berggren, C.; Tackmann, F. J.; Walsh, J. R., Drell-Yan production at NNLL’+NNLO matched to parton showers, Phys. Rev. D, 92, 9, Article 094020 pp. (2015), arXiv:1508.01475 |
| [426] | Alioli, S.; Bauer, C. W.; Broggio, A.; Gavardi, A.; Kallweit, S.; Lim, M. A.; Nagar, R.; Napoletano, D.; Rottoli, L., Matching NNLO to parton shower using \(N{}^3\) LL colour-singlet transverse momentum resummation in GENEVA (2021), arXiv:2102.08390 |
| [427] | Höche, S.; Li, Y.; Prestel, S., Drell-Yan lepton pair production at NNLO QCD with parton showers, Phys. Rev. D, 91, 7, Article 074015 pp. (2015), arXiv:1405.3607 |
| [428] | Höche, S.; Kuttimalai, S.; Li, Y., Hadronic final states in DIS at NNLO QCD with parton showers, Phys. Rev. D, 98, 11, Article 114013 pp. (2018), arXiv:1809.04192 |
| [429] | Monni, P. F.; Nason, P.; Re, E.; Wiesemann, M.; Zanderighi, G., MiNNLO \({}_{P S}\): a new method to match NNLO QCD to parton showers, J. High Energy Phys., 05, 143 (2020), arXiv:1908.06987 |
| [430] | Monni, P. F.; Re, E.; Wiesemann, M., MiNNLO \({}_{\text{PS}} \): optimizing \(2 \to 1\) hadronic processes, Eur. Phys. J. C, 80, 11, 1075 (2020), arXiv:2006.04133 |
| [431] | Lombardi, D.; Wiesemann, M.; Zanderighi, G., ADvancing minnLO \({}_{\operatorname{PS}}\) to diboson processes: \( Z \gamma\) production at nnlo+ps (2020), arXiv:2010.10478 |
| [432] | Re, E.; Wiesemann, M.; Zanderighi, G., NNLOPS accurate predictions for \(W^+ W^-\) production, J. High Energy Phys., 12, 121 (2018), arXiv:1805.09857 |
| [433] | Campbell, J. M.; Huston, J.; Stirling, W., Hard interactions of quarks and gluons: A primer for LHC physics, Rept. Prog. Phys., 70, 89 (2007), arXiv:hep-ph/0611148 |
| [434] | Bern, Z.; Dixon, L. J.; Kosower, D. A., On-shell methods in perturbative QCD, Ann. Physics, 322, 1587-1634 (2007), arXiv:0704.2798 · Zbl 1122.81077 |
| [435] | Ellis, R. K.; Kunszt, Z.; Melnikov, K.; Zanderighi, G., One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, Phys. Rep., 518, 141-250 (2012), arXiv:1105.4319 |
| [436] | Dixon, L. J., A brief introduction to modern amplitude methods, (Theoretical Advanced Study Institute in Elementary Particle Physics: Particle Physics: The Higgs Boson and beyond (2014)), 31-67, arXiv:1310.5353 |
| [437] | Britto, R., Loop amplitudes in gauge theories: Modern analytic approaches, J. Phys. A, 44, Article 454006 pp. (2011), arXiv:1012.4493 · Zbl 1270.81132 |
| [438] | Bern, Z.; Huang, Y.-t., Basics of generalized unitarity, J. Phys. A, 44, Article 454003 pp. (2011), arXiv:1103.1869 · Zbl 1270.81209 |
| [439] | Ita, H., Susy theories and QCD: Numerical approaches, J. Phys. A, 44, Article 454005 pp. (2011), arXiv:1109.6527 · Zbl 1231.81076 |
| [440] | Elvang, H.; Huang, Y.-t., Scattering amplitudes (2013), arXiv:1308.1697 |
| [441] | ’t Hooft, G.; Veltman, M. J.G., Regularization and renormalization of gauge fields, Nuclear Phys. B, 44, 189-213 (1972) |
| [442] | Bollini, C. G.; Giambiagi, J. J., Dimensional renormalization: The number of dimensions as a regularizing parameter, Nuovo Cimento B, 12, 20-25 (1972) |
| [443] | von Manteuffel, A.; Studerus, C., Reduze 2 - distributed Feynman integral reduction (2012), arXiv:1201.4330 |
| [444] | ’t Hooft, G.; Veltman, M., Scalar one loop integrals, Nuclear Phys. B, 153, 365-401 (1979) |
| [445] | Tkachov, F., A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B, 100, 65-68 (1981) |
| [446] | Chetyrkin, K. G.; Tkachov, F. V., Integration by parts: The algorithm to calculate beta functions in 4 loops, Nuclear Phys. B, 192, 159-204 (1981) |
| [447] | Smirnov, V. A., (Renormalization and Asymptotic Expansions. Renormalization and Asymptotic Expansions, Progress in Physics, vol. 14 (1991), Birkhäuser: Birkhäuser Basel, Switzerland), 380 · Zbl 0744.46072 |
| [448] | Gluza, J.; Kajda, K.; Kosower, D. A., Towards a basis for planar two-loop integrals, Phys. Rev. D, 83, Article 045012 pp. (2011), arXiv:1009.0472 |
| [449] | Schabinger, R. M., A new algorithm for the generation of unitarity-compatible integration by parts relations, J. High Energy Phys., 01, 077 (2012), arXiv:1111.4220 · Zbl 1306.81359 |
| [450] | Zhang, Y., Integration-by-parts identities from the viewpoint of differential geometry, (19th Itzykson Meeting on Amplitudes 2014 (2014)), arXiv:1408.4004 |
| [451] | Ita, H., Two-loop integrand decomposition into master integrals and surface terms, Phys. Rev. D, 94, 11, Article 116015 pp. (2016), arXiv:1510.05626 |
| [452] | Gehrmann, T.; Remiddi, E., Differential equations for two loop four point functions, Nuclear Phys. B, 580, 485-518 (2000), arXiv:hep-ph/9912329 · Zbl 1071.81089 |
| [453] | Lee, R. N., Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, J. High Energy Phys., 07, 031 (2008), arXiv:0804.3008 |
| [454] | Maierhöfer, P.; Usovitsch, J.; Uwer, P., Kira—A Feynman integral reduction program, Comput. Phys. Comm., 230, 99-112 (2018), arXiv:1705.05610 · Zbl 1498.81004 |
| [455] | Laporta, S., High precision calculation of multiloop feynman integrals by difference equations, Internat. J. Modern Phys. A, 15, 5087-5159 (2000), arXiv:hep-ph/0102033 · Zbl 0973.81082 |
| [456] | Smirnov, V. A., Feynman Integral Calculus (2006), Springer · Zbl 1111.81003 |
| [457] | Grozin, A. G., Integration by parts: An introduction, Computer Algebra and Particle Physics: CAPP 2011 DESY, Zeuthen, Germany, March 21-25, 2011. Computer Algebra and Particle Physics: CAPP 2011 DESY, Zeuthen, Germany, March 21-25, 2011, Internat. J. Modern Phys., A26, 2807-2854 (2011), arXiv:1104.3993 · Zbl 1247.81138 |
| [458] | Mastrolia, P.; Mirabella, E.; Ossola, G.; Peraro, T., Integrand-reduction for two-loop scattering amplitudes through multivariate polynomial division, Phys. Rev. D, 87, 8, Article 085026 pp. (2013), arXiv:1209.4319 |
| [459] | Zhang, Y., Integrand-level reduction of loop amplitudes by computational algebraic geometry methods, J. High Energy Phys., 09, 042 (2012), arXiv:1205.5707 · Zbl 1397.81183 |
| [460] | Larsen, K. J.; Zhang, Y., Integration-by-parts reductions from unitarity cuts and algebraic geometry, Phys. Rev. D, 93, 4, Article 041701 pp. (2016), arXiv:1511.01071 |
| [461] | Zhang, Y., (Lecture Notes on Multi-loop Integral Reduction and Applied Algebraic Geometry (2016)), arXiv:1612.02249 |
| [462] | Nogueira, P., Automatic Feynman graph generation, J. Comput. Phys., 105, 279-289 (1993) · Zbl 0782.68091 |
| [463] | Hahn, T.; Perez-Victoria, M., Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Comm., 118, 153-165 (1999), arXiv:hep-ph/9807565 |
| [464] | Hahn, T., Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Comm., 140, 418-431 (2001), arXiv:hep-ph/0012260 · Zbl 0994.81082 |
| [465] | Shtabovenko, V.; Mertig, R.; Orellana, F., New developments in FeynCalc 9.0, Comput. Phys. Comm., 207, 432-444 (2016), arXiv:1601.01167 · Zbl 1375.68227 |
| [466] | Shtabovenko, V.; Mertig, R.; Orellana, F., FeynCalc 9.3: New features and improvements, Comput. Phys. Comm., 256, Article 107478 pp. (2020), arXiv:2001.04407 · Zbl 1525.81004 |
| [467] | Borinsky, M., Feynman graph generation and calculations in the Hopf algebra of Feynman graphs, Comput. Phys. Comm., 185, 3317-3330 (2014), arXiv:1402.2613 · Zbl 1360.81012 |
| [468] | Badger, S.; Mogull, G.; Peraro, T., Local integrands for two-loop all-plus Yang-Mills amplitudes, J. High Energy Phys., 08, 063 (2016), arXiv:1606.02244 · Zbl 1390.81278 |
| [469] | Peraro, T., Scattering amplitudes over finite fields and multivariate functional reconstruction, J. High Energy Phys., 12, 030 (2016), arXiv:1608.01902 · Zbl 1390.81631 |
| [470] | Abreu, S.; Febres Cordero, F.; Ita, H.; Jaquier, M.; Page, B.; Zeng, M., Two-loop four-gluon amplitudes from numerical unitarity, Phys. Rev. Lett., 119, 14, Article 142001 pp. (2017), arXiv:1703.05273 |
| [471] | Abreu, S.; Page, B.; Zeng, M., Differential equations from unitarity cuts: nonplanar hexa-box integrals, J. High Energy Phys., 01, 006 (2019), arXiv:1807.11522 · Zbl 1409.81157 |
| [472] | Hartanto, H. B.; Badger, S.; Bronnum-Hansen, C.; Peraro, T., A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons, J. High Energy Phys., 09, 119 (2019), arXiv:1906.11862 |
| [473] | Abreu, S.; Ita, H.; Moriello, F.; Page, B.; Tschernow, W.; Zeng, M., Two-loop integrals for planar five-point one-mass processes, JHEP, 11, 117 (2020), arXiv:2005.04195 |
| [474] | Binoth, T.; Glover, E. W.N.; Marquard, P.; van der Bij, J. J., Two loop corrections to light by light scattering in supersymmetric QED, J. High Energy Phys., 05, 060 (2002), arXiv:hep-ph/0202266 |
| [475] | Glover, E. W.N.; Tejeda-Yeomans, M. E., Two loop QCD helicity amplitudes for massless quark massless gauge boson scattering, J. High Energy Phys., 06, 033 (2003), arXiv:hep-ph/0304169 |
| [476] | Actis, S.; Ferroglia, A.; Passarino, G.; Passera, M.; Uccirati, S., Two-loop tensor integrals in quantum field theory, Nuclear Phys. B, 703, 3-126 (2004), arXiv:hep-ph/0402132 · Zbl 1198.81149 |
| [477] | Boels, R. H.; Jin, Q.; Luo, H., Efficient integrand reduction for particles with spin (2018), arXiv:1802.06761 |
| [478] | Chen, L., A prescription for projectors to compute helicity amplitudes in d dimensions (2019), arXiv:1904.00705 |
| [479] | Peraro, T.; Tancredi, L., Physical projectors for multi-leg helicity amplitudes, J. High Energy Phys., 07, 114 (2019), arXiv:1906.03298 |
| [480] | Anastasiou, C.; Lazopoulos, A., Automatic integral reduction for higher order perturbative calculations, J. High Energy Phys., 07, 046 (2004), arXiv:hep-ph/0404258 |
| [481] | Studerus, C., Reduze-Feynman integral reduction in C++, Comput. Phys. Comm., 181, 1293-1300 (2010), arXiv:0912.2546 · Zbl 1219.81133 |
| [482] | Smirnov, A. V., Algorithm FIRE - Feynman integral reduction, J. High Energy Phys., 10, 107 (2008), arXiv:0807.3243 · Zbl 1245.81033 |
| [483] | Smirnov, A. V., FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Comm., 189, 182-191 (2015), arXiv:1408.2372 · Zbl 1344.81030 |
| [484] | Smirnov, A. V.; Chuharev, F. S., FIRE6: Feynman integral reduction with modular arithmetic (2019), arXiv:1901.07808 |
| [485] | Lee, R. N., Presenting LiteRed: a tool for the Loop InTEgrals REDuction (2012), arXiv:1212.2685 |
| [486] | Lee, R. N., LiteRed 1.4: a powerful tool for reduction of multiloop integrals, Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013): Beijing, China, May 16-21, 2013. Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013): Beijing, China, May 16-21, 2013, J. Phys. Conf. Ser., 523, Article 012059 pp. (2014), arXiv:1310.1145 |
| [487] | Maierhöfer, P.; Usovitsch, J., Kira 1.2 release notes (2018), arXiv:1812.01491 |
| [488] | Klappert, J.; Lange, F.; Maierhöfer, P.; Usovitsch, J., Integral reduction with kira 2.0 and finite field methods (2020), arXiv:2008.06494 |
| [489] | von Manteuffel, A.; Schabinger, R. M., A novel approach to integration by parts reduction, Phys. Lett. B, 744, 101-104 (2015), arXiv:1406.4513 · Zbl 1330.81151 |
| [490] | Peraro, T., FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs, J. High Energy Phys., 07, 031 (2019), arXiv:1905.08019 |
| [491] | Klappert, J.; Lange, F., Reconstructing rational functions with, Comput. Phys. Comm., 247, Article 106951 pp. (2020), arXiv:1904.00009 · Zbl 1509.68342 |
| [492] | Klappert, J.; Klein, S. Y.; Lange, F., Interpolation of dense and sparse rational functions and other improvements in (2020), arXiv:2004.01463 |
| [493] | Heller, M.; von Manteuffel, A., Multivariateapart: Generalized partial fractions (2021), arXiv:2101.08283 |
| [494] | Steinhauser, M., MATAD: A Program package for the computation of MAssive TADpoles, Comput. Phys. Comm., 134, 335-364 (2001), arXiv:hep-ph/0009029 · Zbl 0978.81058 |
| [495] | Gorishnii, S. G.; Larin, S. A.; Surguladze, L. R.; Tkachov, F. V., Mincer: Program for multiloop calculations in quantum field theory for the schoonschip system, Comput. Phys. Comm., 55, 381-408 (1989) |
| [496] | Ruijl, B.; Ueda, T.; Vermaseren, J., Forcer, a FORM program for the parametric reduction of four-loop massless propagator diagrams, Comput. Phys. Comm., 253, Article 107198 pp. (2020), arXiv:1704.06650 · Zbl 1535.81008 |
| [497] | Usovitsch, J., Factorization of denominators in integration-by-parts reductions (2020), arXiv:2002.08173 |
| [498] | Smirnov, A. V.; Smirnov, V. A., How to choose master integrals, Nucl. Phys. B, 960, 115213 (2020), arXiv:2002.08042 · Zbl 1472.81102 |
| [499] | von Manteuffel, A.; Panzer, E.; Schabinger, R. M., A quasi-finite basis for multi-loop Feynman integrals, J. High Energy Phys., 02, 120 (2015), arXiv:1411.7392 · Zbl 1388.81378 |
| [500] | von Manteuffel, A.; Panzer, E.; Schabinger, R. M., On the computation of form factors in massless QCD with finite master integrals, Phys. Rev. D, 93, 12, Article 125014 pp. (2016), arXiv:1510.06758 |
| [501] | Tarasov, O. V., Connection between feynman integrals having different values of the space-time dimension, Phys. Rev. D, 54, 6479-6490 (1996), arXiv:hep-th/9606018 · Zbl 0925.81121 |
| [502] | Lee, R., Space-time dimensionality D as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D, Nuclear Phys. B, 830, 474-492 (2010), arXiv:0911.0252 · Zbl 1203.83051 |
| [503] | Lee, R. N.; Mingulov, K. T., DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications (2017), arXiv:1712.05173 |
| [504] | Heinrich, G.; Huber, T.; Maître, D., Master integrals for fermionic contributions to massless three-loop form-factors, Phys. Lett. B, 662, 344-352 (2008), arXiv:0711.3590 |
| [505] | Arkani-Hamed, N.; Bourjaily, J. L.; Cachazo, F.; Trnka, J., Local integrals for planar scattering amplitudes, J. High Energy Phys., 06, 125 (2012), arXiv:1012.6032 · Zbl 1397.81428 |
| [506] | Henn, J. M., Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett., 110, Article 251601 pp. (2013), arXiv:1304.1806 |
| [507] | Henn, J. M., Lectures on differential equations for Feynman integrals, J. Phys. A, 48, Article 153001 pp. (2015), arXiv:1412.2296 · Zbl 1312.81078 |
| [508] | Schabinger, R. M., Constructing multiloop scattering amplitudes with manifest singularity structure, Phys. Rev. D, 99, 10, Article 105010 pp. (2019), arXiv:1806.05682 |
| [509] | Chicherin, D.; Gehrmann, T.; Henn, J.; Wasser, P.; Zhang, Y.; Zoia, S., All master integrals for three-jet production at next-to-next-to-leading order, Phys. Rev. Lett., 123, 4, Article 041603 pp. (2019), arXiv:1812.11160 |
| [510] | Boehm, J.; Wittmann, M.; Wu, Z.; Xu, Y.; Zhang, Y., IBP reduction coefficients made simple, JHEP, 12, 054 (2020), arXiv:2008.13194 |
| [511] | von Manteuffel, A.; Schabinger, R. M., Numerical multi-loop calculations via finite integrals and one-mass EW-QCD drell-yan master integrals, J. High Energy Phys., 04, 129 (2017), arXiv:1701.06583 |
| [512] | Badger, S.; Bronnum-Hansen, C.; Hartanto, H. B.; Peraro, T., Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case, J. High Energy Phys., 01, 186 (2019), arXiv:1811.11699 · Zbl 1409.81155 |
| [513] | Abreu, S.; Dormans, J.; Febres Cordero, F.; Ita, H.; Page, B., Analytic form of planar two-loop five-gluon scattering amplitudes in QCD, Phys. Rev. Lett., 122, 8, Article 082002 pp. (2019), arXiv:1812.04586 · Zbl 1416.81202 |
| [514] | Abreu, S.; Dixon, L. J.; Herrmann, E.; Page, B.; Zeng, M., The two-loop five-point amplitude in \(\mathcal{N} = 8\) supergravity, J. High Energy Phys., 03, 123 (2019), arXiv:1901.08563 · Zbl 1414.83094 |
| [515] | Badger, S.; Chicherin, D.; Gehrmann, T.; Heinrich, G.; Henn, J.; Peraro, T.; Wasser, P.; Zhang, Y.; Zoia, S., Analytic form of the full two-loop five-gluon all-plus helicity amplitude, Phys. Rev. Lett., 123, 7, Article 071601 pp. (2019), arXiv:1905.03733 |
| [516] | von Manteuffel, A.; Schabinger, R. M., Quark and gluon form factors in four loop QCD: The \(N_f^2\) and \(N_{q \gamma} N_f\) contributions, Phys. Rev. D, 99, 9, Article 094014 pp. (2019), arXiv:1902.08208 |
| [517] | von Manteuffel, A.; Schabinger, R. M., Planar master integrals for four-loop form factors, J. High Energy Phys., 05, 073 (2019), arXiv:1903.06171 · Zbl 1416.81207 |
| [518] | Huber, T.; von Manteuffel, A.; Panzer, E.; Schabinger, R. M.; Yang, G., The four-loop cusp anomalous dimension from the \(N = 4\) Sudakov form factor, Phys. Lett. B, 807, Article 135543 pp. (2020), arXiv:1912.13459 · Zbl 1473.81114 |
| [519] | von Manteuffel, A.; Panzer, E.; Schabinger, R. M., Cusp and collinear anomalous dimensions in four-loop QCD from form factors, Phys. Rev. Lett., 124, 16, Article 162001 pp. (2020), arXiv:2002.04617 |
| [520] | Mastrolia, P.; Mirabella, E.; Ossola, G.; Peraro, T., Scattering amplitudes from multivariate polynomial division, Phys. Lett. B, 718, 173-177 (2012), arXiv:1205.7087 |
| [521] | Georgoudis, A.; Larsen, K. J.; Zhang, Y., Cristal and Azurite: new tools for integration-by-parts reductions, Proceedings, 13th International Symposium on Radiative Corrections: Application of Quantum Field Theory To Phenomenology (RADCOR2017): St. Gilgen, Austria, September 24-29, 2017. Proceedings, 13th International Symposium on Radiative Corrections: Application of Quantum Field Theory To Phenomenology (RADCOR2017): St. Gilgen, Austria, September 24-29, 2017, PoS, RADCOR2017, 020 (2017), arXiv:1712.07510 |
| [522] | Bendle, D.; Böhm, J.; Decker, W.; Georgoudis, A.; Pfreundt, F.-J.; Rahn, M.; Wasser, P.; Zhang, Y., Integration-by-parts reductions of feynman integrals using singular and GPI-space, J. High Energy Phys., 02, 079 (2020), arXiv:1908.04301 · Zbl 1435.81076 |
| [523] | Böhm, J.; Georgoudis, A.; Larsen, K. J.; Schönemann, H.; Zhang, Y., Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections, J. High Energy Phys., 09, 024 (2018), arXiv:1805.01873 · Zbl 1398.81264 |
| [524] | Böhm, J.; Georgoudis, A.; Larsen, K. J.; Schulze, M.; Zhang, Y., Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals, Phys. Rev. D, 98, 2, Article 025023 pp. (2018), arXiv:1712.09737 |
| [525] | Abreu, S.; Febres Cordero, F.; Ita, H.; Page, B.; Sotnikov, V., Planar two-loop five-parton amplitudes from numerical unitarity, J. High Energy Phys., 11, 116 (2018), arXiv:1809.09067 |
| [526] | Abreu, S.; Dormans, J.; Febres Cordero, F.; Ita, H.; Page, B.; Sotnikov, V., Analytic form of the planar two-loop five-parton scattering amplitudes in QCD, J. High Energy Phys., 05, 084 (2019), arXiv:1904.00945 · Zbl 1416.81202 |
| [527] | Dixon, L. J.; Drummond, J. M.; Henn, J. M., Bootstrapping the three-loop hexagon, J. High Energy Phys., 11, 023 (2011), arXiv:1108.4461 · Zbl 1306.81092 |
| [528] | Dixon, L. J.; Drummond, J. M.; von Hippel, M.; Pennington, J., Hexagon functions and the three-loop remainder function, J. High Energy Phys., 12, 049 (2013), arXiv:1308.2276 · Zbl 1342.81159 |
| [529] | Dixon, L. J.; von Hippel, M., Bootstrapping an NMHV amplitude through three loops, J. High Energy Phys., 10, 065 (2014), arXiv:1408.1505 |
| [530] | Dixon, L. J.; von Hippel, M.; McLeod, A. J., The four-loop six-gluon NMHV ratio function, J. High Energy Phys., 01, 053 (2016), arXiv:1509.08127 |
| [531] | Caron-Huot, S.; Dixon, L. J.; McLeod, A.; von Hippel, M., Bootstrapping a five-loop amplitude using Steinmann relations, Phys. Rev. Lett., 117, 24, Article 241601 pp. (2016), arXiv:1609.00669 |
| [532] | Dixon, L. J.; Drummond, J.; Harrington, T.; McLeod, A. J.; Papathanasiou, G.; Spradlin, M., Heptagons from the Steinmann cluster bootstrap, J. High Energy Phys., 02, 137 (2017), arXiv:1612.08976 · Zbl 1377.81197 |
| [533] | Almelid, O.; Duhr, C.; Gardi, E.; McLeod, A.; White, C. D., Bootstrapping the QCD soft anomalous dimension, J. High Energy Phys., 09, 073 (2017), arXiv:1706.10162 · Zbl 1382.81196 |
| [534] | Chicherin, D.; Henn, J.; Mitev, V., Bootstrapping pentagon functions, J. High Energy Phys., 05, 164 (2018), arXiv:1712.09610 |
| [535] | Caron-Huot, S.; Dixon, L. J.; Dulat, F.; von Hippel, M.; McLeod, A. J.; Papathanasiou, G., Six-Gluon amplitudes in planar \(\mathcal{N} = 4\) super-Yang-Mills theory at six and seven loops, J. High Energy Phys., 08, 016 (2019), arXiv:1903.10890 · Zbl 1421.81136 |
| [536] | Caron-Huot, S.; Dixon, L. J.; Dulat, F.; Von Hippel, M.; McLeod, A. J.; Papathanasiou, G., The cosmic galois group and extended Steinmann relations for planar \(\mathcal{N} = 4\) SYM amplitudes, J. High Energy Phys., 09, 061 (2019), arXiv:1906.07116 · Zbl 1423.81174 |
| [537] | Guan, X.; Liu, X.; Ma, Y.-Q., Complete reduction of two-loop five-light-parton scattering amplitudes (2019), arXiv:1912.09294 |
| [538] | Liu, X.; Ma, Y.-Q., Determining arbitrary Feynman integrals by vacuum integrals, Phys. Rev. D, 99, 7, Article 071501 pp. (2019), arXiv:1801.10523 |
| [539] | Liu, X.; Ma, Y.-Q.; Wang, C.-Y., A systematic and efficient method to compute multi-loop master integrals, Phys. Lett. B, 779, 353-357 (2018), arXiv:1711.09572 |
| [540] | Wang, Y.; Li, Z.; Ul Basat, N., Direct reduction of multiloop multiscale scattering amplitudes, Phys. Rev. D, 101, 7, Article 076023 pp. (2020), arXiv:1901.09390 |
| [541] | Mizera, S., Scattering amplitudes from intersection theory, Phys. Rev. Lett., 120, 14, Article 141602 pp. (2018), arXiv:1711.00469 |
| [542] | Mastrolia, P.; Mizera, S., Feynman integrals and intersection theory, J. High Energy Phys., 02, 139 (2019), arXiv:1810.03818 · Zbl 1411.81093 |
| [543] | Frellesvig, H.; Gasparotto, F.; Laporta, S.; Mandal, M. K.; Mastrolia, P.; Mattiazzi, L.; Mizera, S., Decomposition of Feynman integrals on the maximal cut by intersection numbers, J. High Energy Phys., 05, 153 (2019), arXiv:1901.11510 · Zbl 1416.81198 |
| [544] | Frellesvig, H.; Gasparotto, F.; Mandal, M. K.; Mastrolia, P.; Mattiazzi, L.; Mizera, S., Vector space of Feynman integrals and multivariate intersection numbers, Phys. Rev. Lett., 123, 20, Article 201602 pp. (2019), arXiv:1907.02000 |
| [545] | Chen, J.; Jiang, X.; Xu, X.; Yang, L. L., Constructing canonical Feynman integrals with intersection theory, Phys. Lett. B, 814, 136085 (2021), arXiv:2008.03045 · Zbl 1509.81477 |
| [546] | Frellesvig, H.; Gasparotto, F.; Laporta, S.; Mandal, M. K.; Mastrolia, P.; Mattiazzi, L., Decomposition of feynman integrals by multivariate intersection numbers, JHEP, 03, 027 (2021), arXiv:2008.04823 · Zbl 1461.81044 |
| [547] | Baikov, P.; Werlen, M.; Perret-Gallix, D., Explicit solutions of the multiloop integral recurrence relations and its application, Nucl. Instrum. Methods A, 389, 347-349 (1997), arXiv:hep-ph/9611449 |
| [548] | Lee, R. N.; Pomeransky, A. A., Critical points and number of master integrals, J. High Energy Phys., 11, 165 (2013), arXiv:1308.6676 · Zbl 1342.81139 |
| [549] | Frellesvig, H. A., Intersection theory and Higgs physics, PoS, RADCOR2019, 066 (2019) |
| [550] | Primo, A.; Tancredi, L., On the maximal cut of feynman integrals and the solution of their differential equations, Nuclear Phys. B, 916, 94-116 (2017), arXiv:1610.08397 · Zbl 1356.81136 |
| [551] | Chawdhry, H. A.; Czakon, M. L.; Mitov, A.; Poncelet, R., NNLO QCD corrections to three-photon production at the LHC, J. High Energy Phys., 02, 057 (2020), arXiv:1911.00479 |
| [552] | Gehrmann, T.; Henn, J. M.; Lo Presti, N. A., Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 116, 18, 189903 (2016), (erratum) · Zbl 1356.81169 |
| [553] | Chawdhry, H. A.; Lim, M. A.; Mitov, A., Two-loop five-point massless QCD amplitudes within the integration-by-parts approach, Phys. Rev. D, 99, 7, Article 076011 pp. (2019), arXiv:1805.09182 |
| [554] | Aaboud, M., Measurement of the production cross section of three isolated photons in \(p p\) collisions at \(\sqrt{ s} = 8\) TeV using the ATLAS detector, Phys. Lett. B, 781, 55-76 (2018), arXiv:1712.07291 |
| [555] | Abreu, S.; Page, B.; Pascual, E.; Sotnikov, V., Leading-color two-loop QCD corrections for three-photon production at hadron colliders, J. High Energy Phys., 21, 078 (2020), arXiv:2010.15834 |
| [556] | Kallweit, S.; Sotnikov, V.; Wiesemann, M., Triphoton production at hadron colliders in NNLO QCD, Phys. Lett. B, 812, Article 136013 pp. (2021), arXiv:2010.04681 |
| [557] | Chawdhry, H. A.; Czakon, M.; Mitov, A.; Poncelet, R., Two-loop leading-color helicity amplitudes for three-photon production at the LHC (2020), arXiv:2012.13553 |
| [558] | Agarwal, B.; Buccioni, F.; von Manteuffel, A.; Tancredi, L., Two-loop leading colour QCD corrections to \(q \overline{q} \to \gamma \gamma g\) and \(q g \to \gamma \gamma q (2021)\), arXiv:2102.01820 |
| [559] | Chawdhry, H. A.; Czakon, M.; Mitov, A.; Poncelet, R., Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC (2021), arXiv:2103.04319 |
| [560] | Abreu, S.; Cordero, F. F.; Ita, H.; Page, B.; Sotnikov, V., Leading-color two-loop QCD corrections for three-jet production at hadron colliders (2021), arXiv:2102.13609 |
| [561] | Badger, S.; Hartanto, H. B.; Zoia, S., Two-loop QCD corrections to \(W b \overline{b}\) production at hadron colliders (2021), arXiv:2102.02516 |
| [562] | Dunbar, D. C.; Godwin, J. H.; Perkins, W. B.; Strong, J. M.W., Color dressed unitarity and recursion for Yang-Mills two-loop all-plus amplitudes, Phys. Rev. D, 101, 1, Article 016009 pp. (2020), arXiv:1911.06547 |
| [563] | Chicherin, D.; Sotnikov, V., Pentagon functions for scattering of five massless particles, J. High Energy Phys., 12, 167 (2020), arXiv:2009.07803 · Zbl 1457.81126 |
| [564] | Abreu, S.; Dormans, J.; Febres Cordero, F.; Ita, H.; Kraus, M.; Page, B.; Pascual, E.; Ruf, R. S.; Sotnikov, V., Caravel: A c++ framework for the computation of multi-loop amplitudes with numerical unitarity (2020), arXiv:2009.11957 |
| [565] | Papadopoulos, C. G.; Tommasini, D.; Wever, C., The pentabox master integrals with the simplified differential equations approach, J. High Energy Phys., 04, 078 (2016), arXiv:1511.09404 |
| [566] | Gehrmann, T.; Henn, J.; Lo Presti, N., Pentagon functions for massless planar scattering amplitudes, J. High Energy Phys., 10, 103 (2018), arXiv:1807.09812 · Zbl 1402.81256 |
| [567] | Abreu, S.; Dixon, L. J.; Herrmann, E.; Page, B.; Zeng, M., The two-loop five-point amplitude in \(\mathcal{N} = 4\) super-Yang-Mills theory, Phys. Rev. Lett., 122, 12, Article 121603 pp. (2019), arXiv:1812.08941 |
| [568] | Chicherin, D.; Gehrmann, T.; Henn, J.; Lo Presti, N.; Mitev, V.; Wasser, P., Analytic result for the nonplanar hexa-box integrals, J. High Energy Phys., 03, 042 (2019), arXiv:1809.06240 · Zbl 1414.81255 |
| [569] | Badger, S.; Frellesvig, H.; Zhang, Y., A two-loop five-gluon helicity amplitude in QCD, J. High Energy Phys., 12, 045 (2013), arXiv:1310.1051 |
| [570] | Dunbar, D. C.; Perkins, W. B., Two-loop five-point all plus helicity Yang-Mills amplitude, Phys. Rev. D, 93, 8, Article 085029 pp. (2016), arXiv:1603.07514 |
| [571] | Badger, S.; Bronnum-Hansen, C.; Hartanto, H. B.; Peraro, T., First look at two-loop five-gluon scattering in QCD, Phys. Rev. Lett., 120, 9, Article 092001 pp. (2018), arXiv:1712.02229 |
| [572] | Abreu, S.; Febres Cordero, F.; Ita, H.; Page, B.; Zeng, M., Planar two-loop five-gluon amplitudes from numerical unitarity, Phys. Rev. D, 97, 11, Article 116014 pp. (2018), arXiv:1712.03946 |
| [573] | Badger, S.; Bronnum-Hansen, C.; Gehrmann, T.; Hartanto, H. B.; Henn, J.; Lo Presti, N. A.; Peraro, T., Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD, PoS, LL2018, 006 (2018), arXiv:1807.09709 |
| [574] | Chicherin, D.; Gehrmann, T.; Henn, J.; Wasser, P.; Zhang, Y.; Zoia, S., Analytic result for a two-loop five-particle amplitude, Phys. Rev. Lett., 122, 12, Article 121602 pp. (2019), arXiv:1812.11057 |
| [575] | Bourjaily, J. L.; Herrmann, E.; Langer, C.; McLeod, A. J.; Trnka, J., All-multiplicity non-planar MHV amplitudes in sYM at two loops, Phys. Rev. Lett., 124, 11, Article 111603 pp. (2020), arXiv:1911.09106 |
| [576] | Chicherin, D.; Gehrmann, T.; Henn, J. M.; Wasser, P.; Zhang, Y.; Zoia, S., The two-loop five-particle amplitude in \(\mathcal{N} = 8\) supergravity, J. High Energy Phys., 03, 115 (2019), arXiv:1901.05932 · Zbl 1414.83096 |
| [577] | Papadopoulos, C. G.; Wever, C., Internal reduction method for computing Feynman integrals, J. High Energy Phys., 02, 112 (2020), arXiv:1910.06275 |
| [578] | Canko, D. D.; Papadopoulos, C. G.; Syrrakos, N., Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg, J. High Energy Phys., 01, 199 (2021), arXiv:2009.13917 |
| [579] | Dalgleish, A. R.; Dunbar, D. C.; Perkins, W. B.; Strong, J. M., Full color two-loop six-gluon all-plus helicity amplitude, Phys. Rev. D, 101, 7, Article 076024 pp. (2020), arXiv:2003.00897 |
| [580] | Dunbar, D. C.; Perkins, W. B.; Strong, J. M., \(n\)-Point QCD two-loop amplitude, Phys. Rev. D, 101, 7, Article 076001 pp. (2020), arXiv:2001.11347 |
| [581] | Dunbar, D. C.; Jehu, G. R.; Perkins, W. B., Two-loop six gluon all plus helicity amplitude, Phys. Rev. Lett., 117, 6, Article 061602 pp. (2016), arXiv:1605.06351 |
| [582] | Dunbar, D. C.; Godwin, J. H.; Jehu, G. R.; Perkins, W. B., Analytic all-plus-helicity gluon amplitudes in QCD, Phys. Rev. D, 96, 11, Article 116013 pp. (2017), arXiv:1710.10071 |
| [583] | Bourjaily, J. L.; Herrmann, E.; Langer, C.; McLeod, A. J.; Trnka, J., Prescriptive unitarity for non-planar six-particle amplitudes at two loops, J. High Energy Phys., 12, 073 (2019), arXiv:1909.09131 · Zbl 1431.83177 |
| [584] | Jin, Q.; Yang, G., Two-loop QCD corrections to the Higgs plus three-parton amplitudes with top mass correction, J. High Energy Phys., 02, 169 (2020), arXiv:1910.09384 |
| [585] | Weinzierl, S.; Binder, I.; Kreimer, D., The art of computing loop integrals, Fields Inst. Commun., 50, 345-395 (2007), arXiv:hep-ph/0604068 · Zbl 1122.81069 |
| [586] | Duhr, C., Mathematical aspects of scattering amplitudes, (Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders (TASI 2014): Boulder, Colorado, June 2-27, 2014 (2014)), 419-476, arXiv:1411.7538 · Zbl 1334.81100 |
| [587] | Freitas, A., Numerical multi-loop integrals and applications, Prog. Part. Nucl. Phys., 90, 201-240 (2016), arXiv:1604.00406 |
| [588] | Kotikov, A. V.; Teber, S., Multi-loop techniques for massless Feynman diagram calculations, Phys. Part. Nucl., 50, 1, 1-41 (2019), arXiv:1805.05109 |
| [589] | Blümlein, J., Large scale analytic calculations in quantum field theories (2019), arXiv:1905.02148 |
| [590] | Kotikov, A. V., Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett. B, 254, 158-164 (1991) |
| [591] | Remiddi, E., Differential equations for Feynman graph amplitudes, Nuovo Cimento A, 110, 1435-1452 (1997), arXiv:hep-th/9711188 |
| [592] | Argeri, M.; Mastrolia, P., Feynman diagrams and differential equations, Internat. J. Modern Phys. A, 22, 4375-4436 (2007), arXiv:0707.4037 · Zbl 1141.81325 |
| [593] | Kummer, E. E., Über die Transcendenten, welche aus wiederholten Integrationen rationaler Formeln entstehen, J. Reine Angew. Math., 21, 74 (1840) · ERAM 021.0659cj |
| [594] | Nielsen, N., Der Eulersche Dilogarithmus und seine Verallgemeinerungen, Nova Acta Leopoldina (Halle), 90 (1909) · JFM 40.0478.01 |
| [595] | Goncharov, A. B., Multiple polylogarithms, cyclotomy and modular complexes, Math Res. Lett., 5, 497-516 (1998), arXiv:1105.2076 · Zbl 0961.11040 |
| [596] | Goncharov, A. B.; Spradlin, M.; Vergu, C.; Volovich, A., Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett., 105, Article 151605 pp. (2010), arXiv:1006.5703 |
| [597] | Duhr, C.; Gangl, H.; Rhodes, J. R., From polygons and symbols to polylogarithmic functions, J. High Energy Phys., 10, 075 (2012), arXiv:1110.0458 · Zbl 1397.81355 |
| [598] | Duhr, C., Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, J. High Energy Phys., 08, 043 (2012), arXiv:1203.0454 · Zbl 1397.16028 |
| [599] | Gehrmann, T.; Remiddi, E., Numerical evaluation of harmonic polylogarithms, Comput. Phys. Comm., 141, 296-312 (2001), arXiv:hep-ph/0107173 · Zbl 0991.65022 |
| [600] | Gehrmann, T.; Remiddi, E., Numerical evaluation of two-dimensional harmonic polylogarithms, Comput. Phys. Comm., 144, 200-223 (2002), arXiv:hep-ph/0111255 · Zbl 1001.65020 |
| [601] | Vollinga, J.; Weinzierl, S., Numerical evaluation of multiple polylogarithms, Comput. Phys. Comm., 167, 177 (2005), arXiv:hep-ph/0410259 · Zbl 1196.65045 |
| [602] | Buehler, S.; Duhr, C., CHAPLIN - COmplex harmonic polylogarithms in Fortran, Comput. Phys. Comm., 185, 2703-2713 (2014), arXiv:1106.5739 · Zbl 1360.33002 |
| [603] | Bogner, C., MPL—A program for computations with iterated integrals on moduli spaces of curves of genus zero, Comput. Phys. Comm., 203, 339-353 (2016), arXiv:1510.04562 · Zbl 1375.81164 |
| [604] | Frellesvig, H.; Tommasini, D.; Wever, C., On the reduction of generalized polylogarithms to \(\text{Li}_n\) and \(\text{Li}_{2 , 2}\) and on the evaluation thereof, J. High Energy Phys., 03, 189 (2016), arXiv:1601.02649 · Zbl 1388.33001 |
| [605] | Ablinger, J.; Blümlein, J.; Round, M.; Schneider, C., Numerical implementation of harmonic polylogarithms to weight w = 8, Comput. Phys. Comm., 240, 189-201 (2019), arXiv:1809.07084 · Zbl 07674773 |
| [606] | Duhr, C.; Dulat, F., PolyLogTools — polylogs for the masses, J. High Energy Phys., 08, 135 (2019), arXiv:1904.07279 |
| [607] | Remiddi, E.; Tancredi, L., An elliptic generalization of multiple polylogarithms, Nuclear Phys. B, 925, 212-251 (2017), arXiv:1709.03622 · Zbl 1375.81109 |
| [608] | Adams, L.; Weinzierl, S., Feynman integrals and iterated integrals of modular forms, Commun. Number Theory Phys., 12, 193-251 (2018), arXiv:1704.08895 · Zbl 1393.81015 |
| [609] | Broedel, J.; Duhr, C.; Dulat, F.; Penante, B.; Tancredi, L., From modular forms to differential equations for feynman integrals, (KMPB Conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory (2019)), 107-131, https://doi.org/10.1007/978-3-030-04480-0_6. arXiv:1807.00842 |
| [610] | Duhr, C.; Tancredi, L., Algorithms and tools for iterated eisenstein integrals, J. High Energy Phys., 02, 105 (2020), arXiv:1912.00077 · Zbl 1435.81077 |
| [611] | Argeri, M.; Di Vita, S.; Mastrolia, P.; Mirabella, E.; Schlenk, J.; Schubert, U.; Tancredi, L., Magnus and dyson series for master integrals, J. High Energy Phys., 03, 082 (2014), arXiv:1401.2979 · Zbl 1333.81379 |
| [612] | Meyer, C., Transforming differential equations of multi-loop Feynman integrals into canonical form, J. High Energy Phys., 04, 006 (2017), arXiv:1611.01087 · Zbl 1378.81064 |
| [613] | Georgoudis, A.; Larsen, K. J.; Zhang, Y., Azurite: An algebraic geometry based package for finding bases of loop integrals, Comput. Phys. Comm., 221, 203-215 (2017), arXiv:1612.04252 · Zbl 1498.81007 |
| [614] | Gituliar, O.; Magerya, V., Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form, Comput. Phys. Comm., 219, 329-338 (2017), arXiv:1701.04269 · Zbl 1411.81015 |
| [615] | Prausa, M., Epsilon: A tool to find a canonical basis of master integrals, Comput. Phys. Comm., 219, 361-376 (2017), arXiv:1701.00725 · Zbl 1411.81019 |
| [616] | Henn, J.; Mistlberger, B.; Smirnov, V. A.; Wasser, P., Constructing d-log integrands and computing master integrals for three-loop four-particle scattering, J. High Energy Phys., 04, 167 (2020), arXiv:2002.09492 |
| [617] | Dlapa, C.; Henn, J.; Yan, K., Deriving canonical differential equations for Feynman integrals from a single uniform weight integral, J. High Energy Phys., 05, 025 (2020), arXiv:2002.02340 |
| [618] | Hidding, M., DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions (2020), arXiv:2006.05510 |
| [619] | Brown, F.; Duhr, C., A double integral of dlog forms which is not polylogarithmic (2020), arXiv:2006.09413 |
| [620] | Adams, L.; Weinzierl, S., The \(\varepsilon \)-form of the differential equations for Feynman integrals in the elliptic case, Phys. Lett. B, 781, 270-278 (2018), arXiv:1802.05020 · Zbl 1398.81097 |
| [621] | Bogner, C.; Müller-Stach, S.; Weinzierl, S., The unequal mass sunrise integral expressed through iterated integrals on \(\overline{\mathcal{M}}_{1 , 3} \), Nuclear Phys. B, 954, Article 114991 pp. (2020), arXiv:1907.01251 · Zbl 1503.81031 |
| [622] | Caola, F.; Henn, J. M.; Melnikov, K.; Smirnov, A. V.; Smirnov, V. A., Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in quark-antiquark collisions, J. High Energy Phys., 11, 041 (2014), arXiv:1408.6409 |
| [623] | von Manteuffel, A.; Tancredi, L., The two-loop helicity amplitudes for \(g g \to V_1 V_2 \to 4 \operatorname{leptons} \), J. High Energy Phys., 06, 197 (2015), arXiv:1503.08835 |
| [624] | Caola, F.; Henn, J. M.; Melnikov, K.; Smirnov, A. V.; Smirnov, V. A., Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion, J. High Energy Phys., 06, 129 (2015), arXiv:1503.08759 |
| [625] | Gehrmann, T.; von Manteuffel, A.; Tancredi, L., The two-loop helicity amplitudes for \(q \overline{q}^\prime \to V_1 V_2 \to 4\) leptons, J. High Energy Phys., 09, 128 (2015), arXiv:1503.04812 |
| [626] | Walden, M.; Weinzierl, S., Numerical evaluation of iterated integrals related to elliptic Feynman integrals (2020), arXiv:2010.05271 |
| [627] | Sabry, A., Fourth order spectral functions for the electron propagator, Nuclear Phys., 33, 401-430 (1962), http://www.sciencedirect.com/science/article/pii/0029558262905357 · Zbl 0107.22904 |
| [628] | Y. Manin, Iterated integrals of modular forms and noncommutative modular symbols, arXiv:math/0502576. · Zbl 1184.11019 |
| [629] | A. Levin, G. Racinet, Towards Multiple Elliptic Polylogarithms, arXiv:math/0703237. |
| [630] | Zagier, D., The 1-2-3 of Modular Forms (2008), Springer · Zbl 1197.11047 |
| [631] | F. Brown, A. Levin, Multiple elliptic polylogarithms, arXiv:1110.6917. |
| [632] | Broadhurst, D. J., The master two loop diagram with masses, Z. Phys. C, 47, 115-124 (1990) |
| [633] | Broadhurst, D. J.; Fleischer, J.; Tarasov, O., Two loop two point functions with masses: Asymptotic expansions and taylor series, in any dimension, Z. Phys. C, 60, 287-302 (1993), arXiv:hep-ph/9304303 |
| [634] | Bauberger, S.; Berends, F. A.; Böhm, M.; Buza, M., Analytical and numerical methods for massive two loop selfenergy diagrams, Nuclear Phys. B, 434, 383-407 (1995), arXiv:hep-ph/9409388 |
| [635] | Bauberger, S.; Böhm, M., Simple one-dimensional integral representations for two loop selfenergies: The master diagram, Nuclear Phys. B, 445, 25-48 (1995), arXiv:hep-ph/9501201 |
| [636] | Caffo, M.; Czyz, H.; Laporta, S.; Remiddi, E., The master differential equations for the two loop sunrise selfmass amplitudes, Nuovo Cimento A, 111, 365-389 (1998), arXiv:hep-th/9805118 |
| [637] | Laporta, S.; Remiddi, E., Analytic treatment of the two loop equal mass sunrise graph, Nuclear Phys. B, 704, 349-386 (2005), arXiv:hep-ph/0406160 · Zbl 1119.81356 |
| [638] | Kniehl, B.; Kotikov, A.; Onishchenko, A.; Veretin, O., Two-loop sunset diagrams with three massive lines, Nuclear Phys. B, 738, 306-316 (2006), arXiv:hep-ph/0510235 · Zbl 1109.81331 |
| [639] | Aglietti, U.; Bonciani, R.; Grassi, L.; Remiddi, E., The two loop crossed ladder vertex diagram with two massive exchanges, Nuclear Phys. B, 789, 45-83 (2008), arXiv:0705.2616 · Zbl 1151.81364 |
| [640] | Czakon, M.; Mitov, A., Inclusive heavy flavor hadroproduction in NLO QCD: The exact analytic result, Nuclear Phys. B, 824, 111-135 (2010), arXiv:0811.4119 · Zbl 1196.81231 |
| [641] | Müller-Stach, S.; Weinzierl, S.; Zayadeh, R., A second-order differential equation for the two-loop sunrise graph with arbitrary masses, Commun. Number Theory Phys., 6, 203-222 (2012), arXiv:1112.4360 · Zbl 1275.81069 |
| [642] | Caron-Huot, S.; Larsen, K. J., Uniqueness of two-loop master contours, J. High Energy Phys., 10, 026 (2012), arXiv:1205.0801 |
| [643] | Adams, L.; Bogner, C.; Weinzierl, S., The two-loop sunrise graph with arbitrary masses, J. Math. Phys., 54, Article 052303 pp. (2013), arXiv:1302.7004 · Zbl 1282.81193 |
| [644] | Bloch, S.; Vanhove, P., The elliptic dilogarithm for the sunset graph, J. Number Theory, 148, 328-364 (2015), arXiv:1309.5865 · Zbl 1319.81044 |
| [645] | Remiddi, E.; Tancredi, L., Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph, Nuclear Phys. B, 880, 343-377 (2014), arXiv:1311.3342 · Zbl 1284.81139 |
| [646] | Adams, L.; Bogner, C.; Weinzierl, S., The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms, J. Math. Phys., 55, 10, Article 102301 pp. (2014), arXiv:1405.5640 · Zbl 1298.81204 |
| [647] | Adams, L.; Bogner, C.; Weinzierl, S., The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case, J. Math. Phys., 56, 7, Article 072303 pp. (2015), arXiv:1504.03255 · Zbl 1320.81059 |
| [648] | Adams, L.; Bogner, C.; Weinzierl, S., The iterated structure of the all-order result for the two-loop sunrise integral, J. Math. Phys., 57, 3, Article 032304 pp. (2016), arXiv:1512.05630 · Zbl 1333.81283 |
| [649] | Bloch, S.; Kerr, M.; Vanhove, P., Local mirror symmetry and the sunset Feynman integral, Adv. Theor. Math. Phys., 21, 1373-1453 (2017), arXiv:1601.08181 · Zbl 1390.14123 |
| [650] | Remiddi, E.; Tancredi, L., Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral, Nuclear Phys. B, 907, 400-444 (2016), arXiv:1602.01481 · Zbl 1336.81038 |
| [651] | von Manteuffel, A.; Tancredi, L., A non-planar two-loop three-point function beyond multiple polylogarithms, J. High Energy Phys., 06, 127 (2017), arXiv:1701.05905 |
| [652] | Bogner, C.; Schweitzer, A.; Weinzierl, S., Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral, Nuclear Phys. B, 922, 528-550 (2017), arXiv:1705.08952 · Zbl 1373.81293 |
| [653] | Ablinger, J.; Blümlein, J.; De Freitas, A.; van Hoeij, M.; Imamoglu, E.; Raab, C. G.; Radu, C. S.; Schneider, C., Iterated elliptic and hypergeometric integrals for Feynman diagrams, J. Math. Phys., 59, 6, Article 062305 pp. (2018), arXiv:1706.01299 · Zbl 1394.81164 |
| [654] | Groote, S.; Körner, J., Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated bessel integral identities, Nuclear Phys. B, 938, 416-425 (2019), arXiv:1804.10570 · Zbl 1405.81081 |
| [655] | (Blümlein, J.; Schneider, C.; Paule, P., Proceedings, KMPB Conference: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory: Zeuthen, Germany, October 23-26, 2017 (2017)), https://doi.org/10.1007/978-3-030-04480-0 |
| [656] | Broedel, J.; Duhr, C.; Dulat, F.; Marzucca, R.; Penante, B.; Tancredi, L., An analytic solution for the equal-mass banana graph, J. High Energy Phys., 09, 112 (2019), arXiv:1907.03787 |
| [657] | Broedel, J.; Mafra, C. R.; Matthes, N.; Schlotterer, O., Elliptic multiple zeta values and one-loop superstring amplitudes, J. High Energy Phys., 07, 112 (2015), arXiv:1412.5535 · Zbl 1388.83190 |
| [658] | Broedel, J.; Matthes, N.; Schlotterer, O., Relations between elliptic multiple zeta values and a special derivation algebra, J. Phys. A, 49, 15, Article 155203 pp. (2016), arXiv:1507.02254 · Zbl 1354.81045 |
| [659] | Broedel, J.; Matthes, N.; Richter, G.; Schlotterer, O., Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes, J. Phys. A, 51, 28, Article 285401 pp. (2018), arXiv:1704.03449 · Zbl 1401.81071 |
| [660] | Broedel, J.; Schlotterer, O.; Zerbini, F., From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop, J. High Energy Phys., 01, 155 (2019), arXiv:1803.00527 · Zbl 1409.83178 |
| [661] | Broedel, J.; Duhr, C.; Dulat, F.; Tancredi, L., Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism, J. High Energy Phys., 05, 093 (2018), arXiv:1712.07089 |
| [662] | Broedel, J.; Duhr, C.; Dulat, F.; Tancredi, L., Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral, Phys. Rev. D, 97, 11, Article 116009 pp. (2018), arXiv:1712.07095 |
| [663] | Broedel, J.; Duhr, C.; Dulat, F.; Penante, B.; Tancredi, L., Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series, J. High Energy Phys., 08, 014 (2018), arXiv:1803.10256 |
| [664] | Broedel, J.; Duhr, C.; Dulat, F.; Penante, B.; Tancredi, L., Elliptic Feynman integrals and pure functions, J. High Energy Phys., 01, 023 (2019), arXiv:1809.10698 · Zbl 1409.81162 |
| [665] | Broedel, J.; Duhr, C.; Dulat, F.; Penante, B.; Tancredi, L., Elliptic polylogarithms and feynman parameter integrals, J. High Energy Phys., 05, 120 (2019), arXiv:1902.09971 |
| [666] | Bonciani, R.; Del Duca, V.; Frellesvig, H.; Henn, J. M.; Moriello, F.; Smirnov, V. A., Two-loop planar master integrals for Higgs \(\to 3\) partons with full heavy-quark mass dependence, J. High Energy Phys., 12, 096 (2016), arXiv:1609.06685 |
| [667] | Bonciani, R.; Del Duca, V.; Frellesvig, H.; Henn, J.; Hidding, M.; Maestri, L.; Moriello, F.; Salvatori, G.; Smirnov, V., Evaluating a family of two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence, J. High Energy Phys., 01, 132 (2020), arXiv:1907.13156 |
| [668] | Grigo, J.; Hoff, J.; Marquard, P.; Steinhauser, M., Moments of heavy quark correlators with two masses: exact mass dependence to three loops, Nuclear Phys. B, 864, 580-596 (2012), arXiv:1206.3418 · Zbl 1262.81200 |
| [669] | Blümlein, J.; De Freitas, A.; Van Hoeij, M.; Imamoglu, E.; Marquard, P.; Schneider, C., The \(\rho\) parameter at three loops and elliptic integrals, PoS, LL2018, 017 (2018), arXiv:1807.05287 |
| [670] | Abreu, S.; Becchetti, M.; Duhr, C.; Marzucca, R., Three-loop contributions to the \(\rho\) parameter and iterated integrals of modular forms, J. High Energy Phys., 02, 050 (2020), arXiv:1912.02747 · Zbl 1435.81232 |
| [671] | Ablinger, J.; Blümlein, J.; De Freitas, A.; Hasselhuhn, A.; Schneider, C.; Wissbrock, F., Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses, Nuclear Phys. B, 921, 585-688 (2017), arXiv:1705.07030 · Zbl 1370.81170 |
| [672] | Ablinger, J.; Blümlein, J.; Marquard, P.; Rana, N.; Schneider, C., Heavy quark form factors at three loops in the planar limit, Phys. Lett. B, 782, 528-532 (2018), arXiv:1804.07313 |
| [673] | Blümlein, J.; Marquard, P.; Rana, N.; Schneider, C., The heavy Fermion contributions to the massive three loop form factors, Nuclear Phys. B, 949, Article 114751 pp. (2019), arXiv:1908.00357 · Zbl 1448.81470 |
| [674] | Ablinger, J.; Blümlein, J.; De Freitas, A.; Saragnese, M.; Schneider, C.; Schönwald, K., The three-loop polarized pure singlet operator matrix element with two different masses, Nuclear Phys. B, 952, Article 114916 pp. (2020), arXiv:1911.11630 · Zbl 1472.81263 |
| [675] | Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.; Schönwald, K., The three-loop single mass polarized pure singlet operator matrix element, Nuclear Phys. B, 953, Article 114945 pp. (2020), arXiv:1912.02536 · Zbl 1473.81177 |
| [676] | Ablinger, J.; Blümlein, J.; De Freitas, A.; Goedicke, A.; Saragnese, M.; Schneider, C.; Schönwald, K., The two-mass contribution to the three-loop polarized gluonic operator matrix element \(A_{g g , Q}^{( 3 )}\), Nuclear Phys. B, 955, Article 115059 pp. (2020), arXiv:2004.08916 · Zbl 1473.81191 |
| [677] | Blümlein, J.; Schneider, C., Analytic computing methods for precision calculations in quantum field theory, Internat. J. Modern Phys. A, 33, 17, Article 1830015 pp. (2018), arXiv:1809.02889 · Zbl 1392.81192 |
| [678] | Duhr, C., Function theory for multiloop Feynman integrals, Ann. Rev. Nucl. Part. Sci., 69, 15-39 (2019) |
| [679] | Fael, M.; Schönwald, K.; Steinhauser, M., Exact results for \(Z_m^{\operatorname{OS}}\) and \(Z_2^{\operatorname{OS}}\) with two mass scales and up to three loops, JHEP, 10, 087 (2020), arXiv:2008.01102 |
| [680] | Davies, J.; Vogt, A.; Ruijl, B.; Ueda, T.; Vermaseren, J., Large-\( n_f\) contributions to the four-loop splitting functions in QCD, Nuclear Phys. B, 915, 335-362 (2017), arXiv:1610.07477 · Zbl 1354.81052 |
| [681] | Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., Five-loop quark mass and field anomalous dimensions for a general gauge group, J. High Energy Phys., 01, 081 (2017), arXiv:1612.05512 · Zbl 1373.81391 |
| [682] | von Manteuffel, A.; Schabinger, R. M., Quark and gluon form factors to four-loop order in QCD: the \(N_f^3\) contributions, Phys. Rev. D, 95, 3, Article 034030 pp. (2017), arXiv:1611.00795 |
| [683] | Henn, J.; Smirnov, A. V.; Smirnov, V. A.; Steinhauser, M.; Lee, R. N., Four-loop photon quark form factor and cusp anomalous dimension in the large-\( N_c\) limit of QCD, J. High Energy Phys., 03, 139 (2017), arXiv:1612.04389 |
| [684] | Ruijl, B.; Ueda, T.; Vermaseren, J.; Vogt, A., Four-loop QCD propagators and vertices with one vanishing external momentum, J. High Energy Phys., 06, 040 (2017), arXiv:1703.08532 · Zbl 1380.81238 |
| [685] | Lee, R. N.; Smirnov, A. V.; Smirnov, V. A.; Steinhauser, M., The \(n_f^2\) contributions to fermionic four-loop form factors, Phys. Rev. D, 96, 1, Article 014008 pp. (2017), arXiv:1705.06862 |
| [686] | Moch, S.; Ruijl, B.; Ueda, T.; Vermaseren, J.; Vogt, A., Four-loop non-singlet splitting functions in the planar limit and beyond, J. High Energy Phys., 10, 041 (2017), arXiv:1707.08315 · Zbl 1383.81344 |
| [687] | Moch, S.; Ruijl, B.; Ueda, T.; Vermaseren, J. M.; Vogt, A., On quartic colour factors in splitting functions and the gluon cusp anomalous dimension, Phys. Lett. B, 782, 627-632 (2018), arXiv:1805.09638 |
| [688] | Grozin, A., Four-loop cusp anomalous dimension in QED, J. High Energy Phys.. J. High Energy Phys., J. High Energy Phys., 01, 134 (2019), (addendum) |
| [689] | Herzog, F.; Moch, S.; Ruijl, B.; Ueda, T.; Vermaseren, J.; Vogt, A., Five-loop contributions to low-n non-singlet anomalous dimensions in QCD, Phys. Lett. B, 790, 436-443 (2019), arXiv:1812.11818 |
| [690] | Henn, J.; Peraro, T.; Stahlhofen, M.; Wasser, P., Matter dependence of the four-loop cusp anomalous dimension, Phys. Rev. Lett., 122, 20, Article 201602 pp. (2019), arXiv:1901.03693 |
| [691] | Brüser, R.; Grozin, A.; Henn, J. M.; Stahlhofen, M., Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles, J. High Energy Phys., 05, 186 (2019), arXiv:1902.05076 |
| [692] | Becher, T.; Neubert, M., Infrared singularities of scattering amplitudes and \(N{}^3\) LL resummation for \(n\)-jet processes, J. High Energy Phys., 01, 025 (2020), arXiv:1908.11379 · Zbl 1434.81135 |
| [693] | Lee, R. N.; Smirnov, A. V.; Smirnov, V. A.; Steinhauser, M., Four-loop quark form factor with quartic fundamental colour factor, J. High Energy Phys., 02, 172 (2019), arXiv:1901.02898 |
| [694] | Catani, S.; De Florian, D.; Grazzini, M., Soft-gluon effective coupling and cusp anomalous dimension, Eur. Phys. J. C, 79, 8, 685 (2019), arXiv:1904.10365 |
| [695] | Henn, J. M.; Korchemsky, G. P.; Mistlberger, B., The full four-loop cusp anomalous dimension in \(\mathcal{N} = 4\) super Yang-Mills and QCD, J. High Energy Phys., 04, 018 (2020), arXiv:1911.10174 · Zbl 1436.81136 |
| [696] | Das, G.; Moch, S.-O.; Vogt, A., Soft corrections to inclusive deep-inelastic scattering at four loops and beyond, J. High Energy Phys., 03, 116 (2020), arXiv:1912.12920 |
| [697] | Agarwal, N.; Danish, A.; Magnea, L.; Pal, S.; Tripathi, A., Multiparton webs beyond three loops, J. High Energy Phys., 05, 128 (2020), arXiv:2003.09714 |
| [698] | Grozin, A. G.; Marquard, P.; Smirnov, A. V.; Smirnov, V. A.; Steinhauser, M., Matching the heavy-quark fields in QCD and HQET at four loops, Phys. Rev. D, 102, 5, 054008 (2020), arXiv:2005.14047 |
| [699] | Brüser, R.; Dlapa, C.; Henn, J. M.; Yan, K., The full angle-dependence of the four-loop cusp anomalous dimension in QED (2020), arXiv:2007.04851 |
| [700] | Fael, M.; Schönwald, K.; Steinhauser, M., Relation between the \(\overline{\operatorname{MS}}\) and the kinetic mass of heavy quarks, Phys. Rev. D, 103, 1, Article 014005 pp. (2021), arXiv:2011.11655 |
| [701] | Fael, M.; Schönwald, K.; Steinhauser, M., Third order corrections to the semi-leptonic \(b \to c\) and the muon decays (2020), arXiv:2011.13654 |
| [702] | Grozin, A. G.; Marquard, P.; Smirnov, A. V.; Smirnov, V. A.; Steinhauser, M., Matching heavy-quark fields in QCD and HQET at 4 loops, Phys. Atom. Nucl., 83, 6, 994-996 (2020) |
| [703] | Baikov, P.; Chetyrkin, K.; Kühn, J., Five-loop running of the QCD coupling constant, Phys. Rev. Lett., 118, 8, Article 082002 pp. (2017), arXiv:1606.08659 |
| [704] | Herzog, F.; Ruijl, B.; Ueda, T.; Vermaseren, J. A.M.; Vogt, A., The five-loop beta function of yang-mills theory with fermions, J. High Energy Phys., 02, 090 (2017), arXiv:1701.01404 · Zbl 1377.81103 |
| [705] | Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge, J. High Energy Phys., 10, 166 (2017), arXiv:1709.07718 · Zbl 1383.81343 |
| [706] | Chetyrkin, K. G.; Falcioni, G.; Herzog, F.; Vermaseren, J. A.M., Five-loop renormalisation of QCD in covariant gauges, J. High Energy Phys.. J. High Energy Phys., J. High Energy Phys., 12, 006 (2017), (addendum) · Zbl 1383.81336 |
| [707] | Kompaniets, M.; Pikelner, A., Critical exponents from five-loop scalar theory renormalization near six-dimensions (2021), arXiv:2101.10018 |
| [708] | Aoyama, T.; Hayakawa, M.; Kinoshita, T.; Nio, M., Tenth-order QED contribution to the electron g-2 and an improved value of the fine structure constant, Phys. Rev. Lett., 109, Article 111807 pp. (2012), arXiv:1205.5368 |
| [709] | Aoyama, T.; Hayakawa, M.; Kinoshita, T.; Nio, M., Tenth-order electron anomalous magnetic moment — Contribution of diagrams without closed lepton loops, Phys. Rev. D. Phys. Rev. D, Phys. Rev. D, 96, 3, 019901 (2017), (erratum) |
| [710] | Aoyama, T.; Kinoshita, T.; Nio, M., Revised and improved value of the QED tenth-order electron anomalous magnetic moment, Phys. Rev. D, 97, 3, Article 036001 pp. (2018), arXiv:1712.06060 |
| [711] | Volkov, S., Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops, Phys. Rev. D, 100, 9, Article 096004 pp. (2019), arXiv:1909.08015 |
| [712] | Broadhurst, D. J.; Kreimer, D., Combinatoric explosion of renormalization tamed by Hopf algebra: Thirty loop Pade-Borel resummation, Phys. Lett. B, 475, 63-70 (2000), arXiv:hep-th/9912093 · Zbl 1049.81569 |
| [713] | Panzer, E., On the analytic computation of massless propagators in dimensional regularization, Nuclear Phys. B, 874, 567-593 (2013), arXiv:1305.2161 · Zbl 1282.81091 |
| [714] | Batkovich, D.; Chetyrkin, K.; Kompaniets, M., Six loop analytical calculation of the field anomalous dimension and the critical exponent \(\eta\) in \(O ( n )\)-symmetric \(\varphi^4\) model, Nuclear Phys. B, 906, 147-167 (2016), arXiv:1601.01960 · Zbl 1334.81061 |
| [715] | Kompaniets, M. V.; Panzer, E., Minimally subtracted six loop renormalization of \(O ( n )\)-symmetric \(\phi^4\) theory and critical exponents, Phys. Rev. D, 96, 3, Article 036016 pp. (2017), arXiv:1705.06483 |
| [716] | Panzer, E., Hepp’s bound for feynman graphs and matroids (2019), arXiv:1908.09820 |
| [717] | Borinsky, M., Tropical Monte Carlo quadrature for feynman integrals (2020), arXiv:2008.12310 |
| [718] | Maclagan, D.; Sturmfels, B., Introduction to Tropical Geometry (2015), American Mathematical Society · Zbl 1321.14048 |
| [719] | Drummond, J.; Foster, J.; Gürdogan, O.; Kalousios, C., Algebraic singularities of scattering amplitudes from tropical geometry (2019), arXiv:1912.08217 |
| [720] | Ueda, T.; Fujimoto, J., New implementation of the sector decomposition on FORM, PoS, ACAT08, 120 (2008), arXiv:0902.2656 |
| [721] | Kaneko, T.; Ueda, T., A geometric method of sector decomposition, Comput. Phys. Comm., 181, 1352-1361 (2010), arXiv:0908.2897 · Zbl 1219.65014 |
| [722] | Kaneko, T.; Ueda, T., Sector decomposition via computational geometry, PoS, ACAT2010, 082 (2010), arXiv:1004.5490 |
| [723] | Schlenk, J.; Zirke, T., Calculation of multi-loop integrals with SecDec-3.0, PoS, RADCOR2015, 106 (2016), arXiv:1601.03982 |
| [724] | Bogner, C.; Borowka, S.; Hahn, T.; Heinrich, G.; Jones, S.; Kerner, M.; von Manteuffel, A.; Michel, M.; Panzer, E.; Papara, V., Loopedia, a database for loop integrals, Comput. Phys. Comm., 225, 1-9 (2018), arXiv:1709.01266 · Zbl 1515.81114 |
| [725] | https://loopedia.mpp.mpg.de/. |
| [726] | Beneke, M.; Smirnov, V. A., Asymptotic expansion of Feynman integrals near threshold, Nuclear Phys. B, 522, 321-344 (1998), arXiv:hep-ph/9711391 |
| [727] | de la Cruz, L., Feynman integrals as A-hypergeometric functions, J. High Energy Phys., 12, 123 (2019), arXiv:1907.00507 · Zbl 1431.81061 |
| [728] | Klausen, R. P., Hypergeometric series representations of feynman integrals by GKZ hypergeometric systems, J. High Energy Phys., 04, 121 (2020), arXiv:1910.08651 · Zbl 1436.81049 |
| [729] | Feng, T.-F.; Chang, C.-H.; Chen, J.-B.; Zhang, H.-B., GKZ-hypergeometric systems for Feynman integrals, Nuclear Phys. B, 953, Article 114952 pp. (2020), arXiv:1912.01726 · Zbl 1473.81066 |
| [730] | Reichelt, T.; Schulze, M.; Sevenheck, C.; Walther, U., Algebraic aspects of hypergeometric differential equations (2020), arXiv:2004.07262 |
| [731] | Bönisch, K.; Fischbach, F.; Klemm, A.; Nega, C.; Safari, R., Analytic structure of all loop banana amplitudes (2020), arXiv:2008.10574 |
| [732] | Lee, R.; Blümlein, J.; Moch, S.-O.; Riemann, T., Calculating multiloop integrals using dimensional recurrence relation and \(D\)-analyticity, Nuclear Phys. B, 205-206, 135-140 (2010), arXiv:1007.2256 |
| [733] | Nakanishi, N., Graph Theory and Feynman Integrals (1971), Gordon and Breach, New York · Zbl 0212.29203 |
| [734] | Smirnov, V. A., Analytical result for dimensionally regularized massless on-shell double box, Phys. Lett. B, 460, 397-404 (1999), arXiv:hep-ph/9905323 |
| [735] | Smirnov, V. A.; Veretin, O., Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators, Nuclear Phys. B, 566, 469-485 (2000), arXiv:hep-ph/9907385 · Zbl 0956.81055 |
| [736] | Tausk, J., Nonplanar massless two loop feynman diagrams with four on-shell legs, Phys. Lett. B, 469, 225-234 (1999), arXiv:hep-ph/9909506 · Zbl 0987.81500 |
| [737] | Heinrich, G.; Smirnov, V. A., Analytical evaluation of dimensionally regularized massive on-shell double boxes, Phys. Lett. B, 598, 55-66 (2004), arXiv:hep-ph/0406053 |
| [738] | Czakon, M.; Gluza, J.; Riemann, T.; Czakon, M.; Gluza, J.; Syska, J., On the massive two-loop corrections to bhabha scattering, Acta Phys. Polon. B, 36, 3319-3326 (2005), arXiv:hep-ph/0511187 |
| [739] | Bonciani, R.; Ferroglia, A.; Mastrolia, P.; Remiddi, E.; van der Bij, J., Two-loop N(F)=1 QED Bhabha scattering differential cross section, Nuclear Phys. B, 701, 121-179 (2004), arXiv:hep-ph/0405275 |
| [740] | Henn, J. M.; Smirnov, V. A., Analytic results for two-loop master integrals for Bhabha scattering I, J. High Energy Phys., 11, 041 (2013), arXiv:1307.4083 |
| [741] | Mastrolia, P.; Passera, M.; Primo, A.; Schubert, U., Master integrals for the NNLO virtual corrections to \(\mu e\) scattering in QED: the planar graphs, J. High Energy Phys., 11, 198 (2017), arXiv:1709.07435 |
| [742] | Di Vita, S.; Laporta, S.; Mastrolia, P.; Primo, A.; Schubert, U., Master integrals for the NNLO virtual corrections to \(\mu e\) scattering in QED: the non-planar graphs, J. High Energy Phys., 09, 016 (2018), arXiv:1806.08241 |
| [743] | Becchetti, M.; Bonciani, R.; Casconi, V.; Ferroglia, A.; Lavacca, S.; von Manteuffel, A., Master integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel, J. High Energy Phys., 08, 071 (2019), arXiv:1904.10834 |
| [744] | Di Vita, S.; Gehrmann, T.; Laporta, S.; Mastrolia, P.; Primo, A.; Schubert, U., Master integrals for the NNLO virtual corrections to \(q \overline{q} \to t \overline{t}\) scattering in QCD: the non-planar graphs, J. High Energy Phys., 06, 117 (2019), arXiv:1904.10964 |
| [745] | Czakon, M., Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Comm., 175, 559-571 (2006), arXiv:hep-ph/0511200 · Zbl 1196.81054 |
| [746] | Gluza, J.; Kajda, K.; Riemann, T., AMBRE: A Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals, Comput. Phys. Comm., 177, 879-893 (2007), arXiv:0704.2423 · Zbl 1196.81131 |
| [747] | Smirnov, A.; Smirnov, V., On the resolution of singularities of multiple Mellin-Barnes integrals, Eur. Phys. J. C, 62, 445-449 (2009), arXiv:0901.0386 · Zbl 1188.81090 |
| [748] | Moch, S.; Uwer, P.; Weinzierl, S., Nested sums, expansion of transcendental functions and multiscale multiloop integrals, J. Math. Phys., 43, 3363-3386 (2002), arXiv:hep-ph/0110083 · Zbl 1060.33007 |
| [749] | Davydychev, A. I.; Kalmykov, M., Massive Feynman diagrams and inverse binomial sums, Nuclear Phys. B, 699, 3-64 (2004), arXiv:hep-th/0303162 · Zbl 1123.81388 |
| [750] | Weinzierl, S., Expansion around half integer values, binomial sums and inverse binomial sums, J. Math. Phys., 45, 2656-2673 (2004), arXiv:hep-ph/0402131 · Zbl 1071.33018 |
| [751] | Kalmykov, M.; Ward, B.; Yost, S., Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter, J. High Energy Phys., 10, 048 (2007), arXiv:0707.3654 |
| [752] | McLeod, A. J.; Munch, H.; Papathanasiou, G.; von Hippel, M., A novel algorithm for nested summation and hypergeometric expansions, JHEP, 11, 122 (2020), arXiv:2005.05612 |
| [753] | Kotikov, A., About calculation of massless and massive feynman integrals, Particles, 3, 2, 394-443 (2020), arXiv:2004.06625 |
| [754] | Vermaseren, J., Harmonic sums, Mellin transforms and integrals, Internat. J. Modern Phys. A, 14, 2037-2076 (1999), arXiv:hep-ph/9806280 · Zbl 0939.65032 |
| [755] | Weinzierl, S., Symbolic expansion of transcendental functions, Comput. Phys. Comm., 145, 357-370 (2002), arXiv:math-ph/0201011 · Zbl 1001.65025 |
| [756] | Moch, S.; Uwer, P., XSummer: Transcendental functions and symbolic summation in form, Comput. Phys. Comm., 174, 759-770 (2006), arXiv:math-ph/0508008 · Zbl 1196.68332 |
| [757] | Ablinger, J.; Blümlein, J.; Schneider, C., Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms, J. Math. Phys., 54, Article 082301 pp. (2013), arXiv:1302.0378 · Zbl 1295.81071 |
| [758] | Schneider, C.; Wang, J., Modern summation methods for loop integrals in quantum field theory: The packages sigma, evaluatemultisums and sumproduction, J. Phys. Conf. Ser., 523, Article 012037 pp. (2014), arXiv:1310.0160 |
| [759] | Ablinger, J.; Blümlein, J.; Schneider, C.; Wang, J., Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers, J. Phys. Conf. Ser., 523, Article 012060 pp. (2014), arXiv:1310.5645 |
| [760] | Moch, S.; Schneider, C., Feynman integrals and difference equations, PoS, ACAT, 083 (2007), arXiv:0709.1769 |
| [761] | Kalmykov, M. Y.; Kniehl, B. A., Mellin-Barnes representations of feynman diagrams, linear systems of differential equations, and polynomial solutions, Phys. Lett. B, 714, 103-109 (2012), arXiv:1205.1697 |
| [762] | Kalmykov, M. Y.; Kniehl, B. A., Counting master integrals: Integration by parts versus differential reduction, Phys. Lett. B, 702, 268-271 (2011), arXiv:1105.5319 |
| [763] | Kalmykov, M. Y.; Kniehl, B. A., Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation, J. High Energy Phys., 07, 031 (2017), arXiv:1612.06637 · Zbl 1380.81423 |
| [764] | Bitoun, T.; Bogner, C.; Klausen, R. P.; Panzer, E., Feynman integral relations from parametric annihilators, Lett. Math. Phys., 109, 3, 497-564 (2019), arXiv:1712.09215 · Zbl 1412.81141 |
| [765] | Bitoun, T.; Bogner, C.; Klausen, R. P.; Panzer, E., The number of master integrals as Euler characteristic, PoS, LL2018, 065 (2018), arXiv:1809.03399 |
| [766] | Lee, R. N.; Pomeransky, A. A., Differential equations, recurrence relations, and quadratic constraints for \(L\)-loop two-point massive tadpoles and propagators, J. High Energy Phys., 08, 027 (2019), arXiv:1904.12496 |
| [767] | Slater, L. J., Generalised Hypergeometric Functions (1966), Cambridge University Press · Zbl 0135.28101 |
| [768] | Brown, F. C., On the periods of some feynman integrals (2009), arXiv:0910.0114 |
| [769] | Panzer, E., Feynman Integrals and Hyperlogarithms (2015), Humboldt U., arXiv:1506.07243 · Zbl 1344.81024 |
| [770] | Panzer, E., Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals, Comput. Phys. Comm., 188, 148-166 (2015), arXiv:1403.3385 · Zbl 1344.81024 |
| [771] | Hidding, M.; Moriello, F., All orders structure and efficient computation of linearly reducible elliptic Feynman integrals, J. High Energy Phys., 01, 169 (2019), arXiv:1712.04441 · Zbl 1409.81048 |
| [772] | Heller, M.; von Manteuffel, A.; Schabinger, R. M., Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals, Phys. Rev. D, 102, 1, Article 016025 pp. (2020), arXiv:1907.00491 |
| [773] | Bonciani, R.; Di Vita, S.; Mastrolia, P.; Schubert, U., Two-Loop Master Integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering, J. High Energy Phys., 09, 091 (2016), arXiv:1604.08581 |
| [774] | Besier, M.; Wasser, P.; Weinzierl, S., RationalizeRoots: Software package for the rationalization of square roots, Comput. Phys. Comm., 253, Article 107197 pp. (2020), arXiv:1910.13251 · Zbl 1535.65031 |
| [775] | Besier, M.; Festi, D., Rationalizability of square roots (2020), arXiv:2006.07121 · Zbl 1465.81075 |
| [776] | Brown, F., Feynman amplitudes, coaction principle, and cosmic Galois group, Commun. Number Theory Phys., 11, 453-556 (2017), arXiv:1512.06409 · Zbl 1395.81117 |
| [777] | Abreu, S.; Britto, R.; Duhr, C.; Gardi, E., Algebraic structure of cut eynman integrals and the diagrammatic coaction, Phys. Rev. Lett., 119, 5, Article 051601 pp. (2017), arXiv:1703.05064 |
| [778] | Abreu, S.; Britto, R.; Duhr, C.; Gardi, E., Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case, J. High Energy Phys., 12, 090 (2017), arXiv:1704.07931 · Zbl 1383.81321 |
| [779] | Abreu, S.; Britto, R.; Duhr, C.; Gardi, E.; Matthew, J., From positive geometries to a coaction on hypergeometric functions, J. High Energy Phys., 02, 122 (2020), arXiv:1910.08358 · Zbl 1435.81075 |
| [780] | Smirnov, V. A., Problems of the strategy of regions, Phys. Lett. B, 465, 226-234 (1999), arXiv:hep-ph/9907471 |
| [781] | Pak, A.; Smirnov, A., Geometric approach to asymptotic expansion of Feynman integrals, Eur. Phys. J. C, 71, 1626 (2011), arXiv:1011.4863 |
| [782] | Ananthanarayan, B.; Pal, A.; Ramanan, S.; Sarkar, R., Unveiling regions in multi-scale feynman integrals using singularities and power geometry, Eur. Phys. J. C, 79, 1, 57 (2019), arXiv:1810.06270 |
| [783] | Ananthanarayan, B.; Das, A. B.; Sarkar, R., Asymptotic analysis of Feynman diagrams and their maximal cuts, Eur. Phys. J. C, 80, 12, 1131 (2020), arXiv:2003.02451 |
| [784] | Jantzen, B., Foundation and generalization of the expansion by regions, J. High Energy Phys., 12, 076 (2011), arXiv:1111.2589 · Zbl 1306.81420 |
| [785] | Jantzen, B.; Smirnov, A. V.; Smirnov, V. A., Expansion by regions: revealing potential and Glauber regions automatically, Eur. Phys. J. C, 72, 2139 (2012), arXiv:1206.0546 |
| [786] | Smirnov, V. A., Analytic tools for Feynman integrals, Springer Tracts Mod. Phys., 250, 1-296 (2012) · Zbl 1268.81004 |
| [787] | Semenova, T. Y.; Smirnov, A. V.; Smirnov, V. A., On the status of expansion by regions, Eur. Phys. J. C, 79, 2, 136 (2019), arXiv:1809.04325 |
| [788] | Smirnov, A. V., FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions, Comput. Phys. Comm., 185, 2090-2100 (2014), arXiv:1312.3186 · Zbl 1351.81078 |
| [789] | Smirnov, A. V., FIESTA4: Optimized feynman integral calculations with GPU support, Comput. Phys. Comm., 204, 189-199 (2016), arXiv:1511.03614 · Zbl 1378.65075 |
| [790] | Becher, T.; Broggio, A.; Ferroglia, A., Introduction to Soft-Collinear Effective Theory, vol. 896 (2015), Springer, arXiv:1410.1892 |
| [791] | Becher, T.; Davidson, S.; Gambino, P.; Laine, M.; Neubert, M.; Salomon, C., Soft-collinear effective theory, Les Houches Lect. Notes, 108 (2020), arXiv:1803.04310 |
| [792] | Ochman, M.; Riemann, T., MBsums - a Mathematica package for the representation of Mellin-Barnes integrals by multiple sums, Proceedings, 39th International Conference of Theoretical Physics: Matter to the Deepest, Recent Developments in Physics of Fundamental Interactions: Ustron, Poland, September 13-18, 2015. Proceedings, 39th International Conference of Theoretical Physics: Matter to the Deepest, Recent Developments in Physics of Fundamental Interactions: Ustron, Poland, September 13-18, 2015, Acta Phys. Polon. B, 46, 11, 2117 (2015), arXiv:1511.01323 · Zbl 1372.65073 |
| [793] | M. Czakon, A.V. Smirnov, https://mbtools.hepforge.org. |
| [794] | Gluza, J.; Kajda, K.; Riemann, T.; Yundin, V., Numerical evaluation of tensor feynman integrals in Euclidean kinematics, Eur. Phys. J. C, 71, 1516 (2011), arXiv:1010.1667 |
| [795] | Blümlein, J.; Dubovyk, I.; Gluza, J.; Ochman, M.; Raab, C. G.; Riemann, T.; Schneider, C.; Mende, M., Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums, PoS, LL2014, 052 (2014), arXiv:1407.7832 |
| [796] | Dubovyk, I.; Gluza, J.; Riemann, T.; Usovitsch, J., Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions, PoS, LL2016, 034 (2016), arXiv:1607.07538 |
| [797] | Gluza, J.; Jelinski, T.; Kosower, D. A., Efficient evaluation of massive Mellin-Barnes integrals, Phys. Rev. D, 95, 7, Article 076016 pp. (2017), arXiv:1609.09111 |
| [798] | Anastasiou, C.; Daleo, A., Numerical evaluation of loop integrals, J. High Energy Phys., 10, 031 (2006), arXiv:hep-ph/0511176 |
| [799] | Dubovyk, I.; Gluza, J.; Jelinski, T.; Riemann, T.; Usovitsch, J., New prospects for the numerical calculation of Mellin-Barnes integrals in Minkowskian kinematics, Proceedings, 23rd Cracow Epiphany Conference on Particle Theory Meets the First Data from LHC Run 2: Cracow, Poland, January 9-12, 2017. Proceedings, 23rd Cracow Epiphany Conference on Particle Theory Meets the First Data from LHC Run 2: Cracow, Poland, January 9-12, 2017, Acta Phys. Polon. B, 48, 995 (2017), arXiv:1704.02288 |
| [800] | Usovitsch, J.; Dubovyk, I.; Riemann, T., MBnumerics: Numerical integration of Mellin-Barnes integrals in physical regions, Proceedings, 14th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2018 (LL2018): St. Goar, Germany, April 29-May 04, 2018. Proceedings, 14th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory 2018 (LL2018): St. Goar, Germany, April 29-May 04, 2018, PoS, LL2018, 046 (2018), arXiv:1810.04580 |
| [801] | Usovitsch, J., Numerical Evaluation of Mellin-Barnes Integrals in Minkowskian Regions and their Application to Two-Loop Bosonic Electroweak Contributions to the Weak Mixing Angle of the \(\operatorname{Z} \overline{\operatorname{b}} \operatorname{b} \)-Vertex (2018), Humboldt U., Berlin (main), https://doi.org/10.3204/PUBDB-2018-05160 |
| [802] | Dubovyk, I.; Freitas, A.; Gluza, J.; Riemann, T.; Usovitsch, J., The two-loop electroweak bosonic corrections to \(\sin^2 \theta_{\text{eff}}^b\), Phys. Lett. B, 762, 184-189 (2016), arXiv:1607.08375 |
| [803] | Dubovyk, I.; Freitas, A.; Gluza, J.; Riemann, T.; Usovitsch, J., Complete electroweak two-loop corrections to Z boson production and decay, Phys. Lett. B, 783, 86-94 (2018), arXiv:1804.10236 |
| [804] | Dubovyk, I.; Freitas, A.; Gluza, J.; Riemann, T.; Usovitsch, J., Electroweak pseudo-observables and Z-boson form factors at two-loop accuracy, J. High Energy Phys., 08, 113 (2019), arXiv:1906.08815 |
| [805] | Prausa, M., Mellin-Barnes meets Method of Brackets: a novel approach to Mellin-Barnes representations of Feynman integrals, Eur. Phys. J. C, 77, 9, 594 (2017), arXiv:1706.09852 |
| [806] | Gonzalez, I.; Blümlein, J.; Moch, S.-O.; Riemann, T., Method of brackets and feynman diagrams evaluation, Nuclear Phys. B, 205-206, 141-146 (2010), arXiv:1008.2148 |
| [807] | Caffo, M.; Czyz, H.; Remiddi, E., Numerical evaluation of the general massive 2 loop sunrise selfmass master integrals from differential equations, Nuclear Phys. B, 634, 309-325 (2002), arXiv:hep-ph/0203256 · Zbl 0995.81079 |
| [808] | Caffo, M.; Czyz, H.; Grzelinska, A.; Remiddi, E., Numerical evaluation of the general massive 2 loop 4 denominator selfmass master integral from differential equations, Nuclear Phys. B, 681, 230-246 (2004), arXiv:hep-ph/0312189 · Zbl 1044.81679 |
| [809] | Martin, S. P., Evaluation of two loop selfenergy basis integrals using differential equations, Phys. Rev. D, 68, Article 075002 pp. (2003), arXiv:hep-ph/0307101 |
| [810] | Pozzorini, S.; Remiddi, E., Precise numerical evaluation of the two loop sunrise graph master integrals in the equal mass case, Comput. Phys. Comm., 175, 381-387 (2006), arXiv:hep-ph/0505041 · Zbl 1196.81075 |
| [811] | Martin, S. P.; Robertson, D. G., TSIL: A program for the calculation of two-loop self-energy integrals, Comput. Phys. Comm., 174, 133-151 (2006), arXiv:hep-ph/0501132 · Zbl 1196.81070 |
| [812] | Caffo, M.; Czyz, H.; Gunia, M.; Remiddi, E., BOKASUN: A Fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams, Comput. Phys. Comm., 180, 427-430 (2009), arXiv:0807.1959 · Zbl 1198.81011 |
| [813] | Bauberger, S.; Freitas, A.; Wiegand, D., TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses (2019), arXiv:1908.09887 |
| [814] | Bauberger, S.; Freitas, A., TVID: Three-loop vacuum integrals from dispersion relations (2017), arXiv:1702.02996 |
| [815] | Freitas, A., Three-loop vacuum integrals with arbitrary masses, J. High Energy Phys., 11, 145 (2016), arXiv:1609.09159 · Zbl 1390.81282 |
| [816] | Martin, S. P.; Robertson, D. G., Evaluation of the general 3-loop vacuum Feynman integral, Phys. Rev. D, 95, 1, Article 016008 pp. (2017), arXiv:1610.07720 |
| [817] | Ghinculov, A., On the evaluation of three loop scalar integrals in the massive case, Phys. Lett. B, 385, 279-283 (1996), arXiv:hep-ph/9604333 |
| [818] | Boughezal, R.; Czakon, M.; Schutzmeier, T., NNLO fermionic corrections to the charm quark mass dependent matrix elements in \(\overline{B} \to X_s \gamma \), J. High Energy Phys., 09, 072 (2007), arXiv:0707.3090 |
| [819] | Czakon, M.; Schutzmeier, T., Double fermionic contributions to the heavy-quark vacuum polarization, J. High Energy Phys., 07, 001 (2008), arXiv:0712.2762 |
| [820] | Czakon, M., Tops from light quarks: Full mass dependence at two-loops in QCD, Phys. Lett. B, 664, 307-314 (2008), arXiv:0803.1400 |
| [821] | Czakon, M.; Fiedler, P.; Mitov, A., Total top-quark pair-production cross section at hadron colliders through \(O ( \alpha_s^4 )\), Phys. Rev. Lett., 110, Article 252004 pp. (2013), arXiv:1303.6254 |
| [822] | Lee, R. N.; Smirnov, A. V.; Smirnov, V. A., Solving differential equations for Feynman integrals by expansions near singular points, J. High Energy Phys., 03, 008 (2018), arXiv:1709.07525 · Zbl 1388.81927 |
| [823] | Lee, R. N.; Smirnov, A. V.; Smirnov, V. A., Evaluating ‘elliptic’ master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points, J. High Energy Phys., 07, 102 (2018), arXiv:1805.00227 · Zbl 1395.81288 |
| [824] | Bonciani, R.; Degrassi, G.; Giardino, P. P.; Gröber, R., A numerical routine for the crossed vertex diagram with a massive-particle loop, Comput. Phys. Comm., 241, 122-131 (2019), arXiv:1812.02698 · Zbl 07674789 |
| [825] | Mandal, M. K.; Zhao, X., Evaluating multi-loop Feynman integrals numerically through differential equations, J. High Energy Phys., 03, 190 (2019), arXiv:1812.03060 |
| [826] | Gnendiger, C., To \(d\), or not to \(d\): recent developments and comparisons of regularization schemes, Eur. Phys. J. C, 77, 7, 471 (2017), arXiv:1705.01827 |
| [827] | Bruque, A.; Cherchiglia, A.; Perez-Victoria, M., Dimensional regularization vs methods in fixed dimension with and without \(\gamma_5\), J. High Energy Phys., 08, 109 (2018), arXiv:1803.09764 · Zbl 1396.83046 |
| [828] | Gnendiger, C.; Signer, A., Dimensional schemes for cross sections at NNLO, Eur. Phys. J. C, 80, 3, 215 (2020), arXiv:1912.09974 |
| [829] | Soper, D. E., QCD calculations by numerical integration, Phys. Rev. Lett., 81, 2638-2641 (1998), arXiv:hep-ph/9804454 |
| [830] | Soper, D. E., Techniques for QCD calculations by numerical integration, Phys. Rev. D, 62, Article 014009 pp. (2000), arXiv:hep-ph/9910292 |
| [831] | Catani, S.; Gleisberg, T.; Krauss, F.; Rodrigo, G.; Winter, J.-C., From loops to trees by-passing Feynman’s theorem, J. High Energy Phys., 09, 065 (2008), arXiv:0804.3170 · Zbl 1245.81117 |
| [832] | Gong, W.; Nagy, Z.; Soper, D. E., Direct numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev. D, 79, Article 033005 pp. (2009), arXiv:0812.3686 |
| [833] | Kilian, W.; Kleinschmidt, T., Numerical evaluation of feynman loop integrals by reduction to tree graphs (2009), arXiv:0912.3495 |
| [834] | Becker, S.; Reuschle, C.; Weinzierl, S., Numerical NLO QCD calculations, J. High Energy Phys., 1012, 013 (2010), arXiv:1010.4187 · Zbl 1294.81267 |
| [835] | Becker, S.; Goetz, D.; Reuschle, C.; Schwan, C.; Weinzierl, S., NLO results for five, six and seven jets in electron-positron annihilation, Phys. Rev. Lett., 108, Article 032005 pp. (2012), 5 pages, arXiv:1111.1733 |
| [836] | Becker, S.; Reuschle, C.; Weinzierl, S., Efficiency improvements for the numerical computation of NLO corrections, J. High Energy Phys., 07, 090 (2012), arXiv:1205.2096 |
| [837] | Becker, S.; Weinzierl, S., Direct contour deformation with arbitrary masses in the loop, Phys. Rev. D, 86, Article 074009 pp. (2012), arXiv:1208.4088 |
| [838] | Duplancic, G.; Klajn, B., Direct numerical approach to one-loop amplitudes, Phys. Rev. D, 95, 1, Article 016002 pp. (2017), arXiv:1604.07022 |
| [839] | Passarino, G.; Uccirati, S., Algebraic numerical evaluation of feynman diagrams: Two loop selfenergies, Nuclear Phys. B, 629, 97-187 (2002), arXiv:hep-ph/0112004 · Zbl 1039.81539 |
| [840] | Binoth, T.; Heinrich, G.; Kauer, N., A numerical evaluation of the scalar hexagon integral in the physical region, Nuclear Phys. B, 654, 277-300 (2003), arXiv:hep-ph/0210023 · Zbl 1010.81060 |
| [841] | Kurihara, Y.; Kaneko, T., Numerical contour integration for loop integrals, Comput. Phys. Comm., 174, 530-539 (2006), arXiv:hep-ph/0503003 · Zbl 1196.81066 |
| [842] | Binoth, T.; Guillet, J. P.; Heinrich, G.; Pilon, E.; Schubert, C., An algebraic / numerical formalism for one-loop multi-leg amplitudes, J. High Energy Phys., 10, 015 (2005), arXiv:hep-ph/0504267 |
| [843] | Kurihara, Y.; Fujimoto, J.; Ishikawa, T.; Kaneko, T.; Kawabata, S.; Kato, Y.; Tanaka, H.; Shimizu, Y.; Fujimoto, J.; Kodaira, J.; Uematsu, T., NLO-QCD calculation in GRACE, Nuclear Phys. B, 157, 231-235 (2006) |
| [844] | Nagy, Z.; Soper, D. E., Numerical integration of one-loop feynman diagrams for N-photon amplitudes, Phys. Rev. D, 74, Article 093006 pp. (2006), arXiv:hep-ph/0610028 |
| [845] | Lazopoulos, A.; Melnikov, K.; Petriello, F., QCD corrections to tri-boson production, Phys. Rev. D, 76, Article 014001 pp. (2007), arXiv:hep-ph/0703273 |
| [846] | Yuasa, F.; Ishikawa, T.; Fujimoto, J.; Hamaguchi, N.; de Doncker, E.; Shimizu, Y., Numerical evaluation of Feynman integrals by a direct computation method, Proceedings, 12th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2008): Erice, Italy, November 3-7, 2008. Proceedings, 12th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2008): Erice, Italy, November 3-7, 2008, PoS, ACAT08, 122 (2008), arXiv:0904.2823 |
| [847] | Yuasa, F.; Ishikawa, T.; Kurihara, Y.; Fujimoto, J.; Shimizu, Y.; Hamaguchi, N.; de Doncker, E.; Kato, K., Numerical approach to calculation of Feynman loop integrals, PoS, CPP2010, 017 (2010), arXiv:1109.4213 |
| [848] | Binoth, T.; Heinrich, G., An automatized algorithm to compute infrared divergent multi-loop integrals, Nuclear Phys. B, 585, 741-759 (2000), arXiv:hep-ph/0004013 · Zbl 1042.81565 |
| [849] | Binoth, T.; Heinrich, G., Numerical evaluation of multi-loop integrals by sector decomposition, Nuclear Phys. B, 680, 375-388 (2004), arXiv:hep-ph/0305234 · Zbl 1043.81630 |
| [850] | Anastasiou, C.; Beerli, S.; Daleo, A., Evaluating multi-loop feynman diagrams with infrared and threshold singularities numerically, J. High Energy Phys., 05, 071 (2007), arXiv:hep-ph/0703282 |
| [851] | Bierenbaum, I.; Catani, S.; Draggiotis, P.; Rodrigo, G., A tree-loop duality relation at two loops and beyond, J. High Energy Phys., 10, 073 (2010), arXiv:1007.0194 · Zbl 1291.81381 |
| [852] | Yuasa, F.; de Doncker, E.; Hamaguchi, N.; Ishikawa, T.; Kato, K., Numerical computation of two-loop box diagrams with masses (2011), arXiv:1112.0637 · Zbl 1296.81117 |
| [853] | Becker, S.; Weinzierl, S., Direct numerical integration for multi-loop integrals, Eur. Phys. J. C, 73, 2, 2321 (2013), arXiv:1211.0509 |
| [854] | Anastasiou, C.; Sterman, G., Removing infrared divergences from two-loop integrals, J. High Energy Phys., 07, 056 (2019), arXiv:1812.03753 |
| [855] | Anastasiou, C.; Haindl, R.; Sterman, G.; Yang, Z.; Zeng, M., Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation (2020), arXiv:2008.12293 |
| [856] | Bierenbaum, I.; Buchta, S.; Draggiotis, P.; Malamos, I.; Rodrigo, G., Tree-loop duality relation beyond simple poles, J. High Energy Phys., 03, 025 (2013), arXiv:1211.5048 |
| [857] | Buchta, S.; Chachamis, G.; Draggiotis, P.; Malamos, I.; Rodrigo, G., On the singular behaviour of scattering amplitudes in quantum field theory, J. High Energy Phys., 11, 014 (2014), arXiv:1405.7850 · Zbl 1333.81149 |
| [858] | Hernandez-Pinto, R. J.; Sborlini, G. F.R.; Rodrigo, G., Towards gauge theories in four dimensions, J. High Energy Phys., 02, 044 (2016), arXiv:1506.04617 · Zbl 1388.81329 |
| [859] | Buchta, S.; Chachamis, G.; Draggiotis, P.; Rodrigo, G., Numerical implementation of the loop-tree duality method, Eur. Phys. J. C, 77, 5, 274 (2017), arXiv:1510.00187 |
| [860] | Sborlini, G. F.R.; Driencourt-Mangin, F.; Hernandez-Pinto, R.; Rodrigo, G., Four-dimensional unsubtraction from the loop-tree duality, J. High Energy Phys., 08, 160 (2016), arXiv:1604.06699 |
| [861] | Sborlini, G. F.R.; Driencourt-Mangin, F.; Rodrigo, G., Four-dimensional unsubtraction with massive particles, J. High Energy Phys., 10, 162 (2016), arXiv:1608.01584 |
| [862] | Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, G. F.R., Universal dual amplitudes and asymptotic expansions for \(g g \to H\) and \(H \to \gamma \gamma\) in four dimensions, Eur. Phys. J. C, 78, 3, 231 (2018), arXiv:1702.07581 |
| [863] | Aguilera-Verdugo, J. J.; Hernandez-Pinto, R. J.; Rodrigo, G.; Sborlini, G. F.R.; Torres Bobadilla, W. J., Causal representation of multi-loop feynman integrands within the loop-tree duality, J. High Energy Phys., 01, 069 (2021), arXiv:2006.11217 · Zbl 1459.81044 |
| [864] | Driencourt-Mangin, F.; Rodrigo, G.; Sborlini, G. F.R.; Torres Bobadilla, W. J., Universal four-dimensional representation of \(H \to \gamma \gamma\) at two loops through the Loop-Tree Duality, J. High Energy Phys., 02, 143 (2019), arXiv:1901.09853 |
| [865] | Driencourt-Mangin, F., Four-Dimensional Representation of Scattering Amplitudes and Physical Observables Through the Application of the Loop-Tree Duality Theorem (2019), U. Valencia (main), arXiv:1907.12450 |
| [866] | Runkel, R.; Szor, Z.; Vesga, J. P.; Weinzierl, S., Integrands of loop amplitudes within loop-tree duality, Phys. Rev. D, 101, 11, Article 116014 pp. (2020), arXiv:1906.02218 |
| [867] | Capatti, Z.; Hirschi, V.; Kermanschah, D.; Ruijl, B., Loop tree duality for multi-loop numerical integration, Phys. Rev. Lett., 123, 15, Article 151602 pp. (2019), arXiv:1906.06138 |
| [868] | Capatti, Z.; Hirschi, V.; Kermanschah, D.; Pelloni, A.; Ruijl, B., Numerical loop-tree duality: contour deformation and subtraction, J. High Energy Phys., 04, 096 (2020), arXiv:1912.09291 · Zbl 1436.81144 |
| [869] | Aguilera-Verdugo, J. J.; Driencourt-Mangin, F.; Plenter, J.; Ramirez-Uribe, S.; Rodrigo, G.; Sborlini, G. F.R.; Torres Bobadilla, W. J.; Tracz, S., Causality, unitarity thresholds, anomalous thresholds and infrared singularities from the loop-tree duality at higher orders (2019), arXiv:1904.08389 · Zbl 1431.81156 |
| [870] | Baumeister, R.; Mediger, D.; Pecovnik, J.; Weinzierl, S., Vanishing of certain cuts or residues of loop integrals with higher powers of the propagators, Phys. Rev. D, 99, 9, Article 096023 pp. (2019), arXiv:1903.02286 |
| [871] | Runkel, R.; Szor, Z.; Vesga, J. P.; Weinzierl, S., Causality and loop-tree duality at higher loops, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 123, 5, 059902 (2019), (erratum) |
| [872] | Aguilera-Verdugo, J. J.; Driencourt-Mangin, F.; Hernandez Pinto, R. J.; Plenter, J.; Ramirez-Uribe, S.; Renteria Olivo, A. E.; Rodrigo, G.; Sborlini, G. F.; Torres Bobadilla, W. J.; Tracz, S., Open loop amplitudes and causality to all orders and powers from the loop-tree duality, Phys. Rev. Lett., 124, 21, Article 211602 pp. (2020), arXiv:2001.03564 |
| [873] | Ramírez-Uribe, S.; Hernández-Pinto, R. J.; Rodrigo, G.; Sborlini, G. F.; Torres Bobadilla, W. J., Universal opening of four-loop scattering amplitudes to trees (2020), arXiv:2006.13818 |
| [874] | Plenter, J.; Rodrigo, G., Asymptotic expansions through the loop-tree duality (2020), arXiv:2005.02119 |
| [875] | Capatti, Z.; Hirschi, V.; Kermanschah, D.; Pelloni, A.; Ruijl, B., Manifestly causal loop-tree duality (2020), arXiv:2009.05509 |
| [876] | Capatti, Z.; Hirschi, V.; Pelloni, A.; Ruijl, B., Local unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order (2020), arXiv:2010.01068 |
| [877] | Aguilera-Verdugo, J. J.; Hernandez-Pinto, R. J.; Rodrigo, G.; Sborlini, G. F.R.; Torres Bobadilla, W. J., Mathematical properties of nested residues and their application to multi-loop scattering amplitudes, J. High Energy Phys., 02, 112 (2021), arXiv:2010.12971 |
| [878] | Sborlini, G. F.R., A geometrical approach to causality in multi-loop amplitudes (2021), arXiv:2102.05062 |
| [879] | Bobadilla, W. J.T., Loop-tree duality from cusps and edges (2021), arXiv:2102.05048 |
| [880] | Pittau, R., A four-dimensional approach to quantum field theories, J. High Energy Phys., 11, 151 (2012), arXiv:1208.5457 · Zbl 1397.81177 |
| [881] | Donati, A. M.; Pittau, R., FDR, an easier way to NNLO calculations: a two-loop case study, Eur. Phys. J. C, 74, 2864 (2014), arXiv:1311.3551 |
| [882] | Zirke, T. J., Numerical evaluation of two-loop integrals in FDR, J. High Energy Phys., 02, 029 (2016), arXiv:1512.04920 |
| [883] | Page, B.; Pittau, R., Two-loop off-shell QCD amplitudes in FDR, J. High Energy Phys., 11, 183 (2015), arXiv:1506.09093 · Zbl 1388.81595 |
| [884] | Page, B.; Pittau, R., NNLO final-state quark-pair corrections in four dimensions, Eur. Phys. J. C, 79, 4, 361 (2019), arXiv:1810.00234 |
| [885] | Pittau, R.; Blondel, A.; Gluza, J.; Jadach, S.; Janot, P.; Riemann, T., NNLO corrections in 4 dimensions, CERN Yellow Rep.: Monogr., 3, 163-169 (2020) |
| [886] | Fazio, R. A.; Mastrolia, P.; Mirabella, E.; Torres Bobadilla, W. J., On the four-dimensional formulation of dimensionally regulated amplitudes, Eur. Phys. J. C, 74, 12, 3197 (2014), arXiv:1404.4783 |
| [887] | Pozzorini, S.; Zhang, H.; Zoller, M. F., Rational terms of UV origin at two loops, J. High Energy Phys., 05, 077 (2020), arXiv:2001.11388 |
| [888] | Lang, J.-N.; Pozzorini, S.; Zhang, H.; Zoller, M. F., Two-loop rational terms in Yang-Mills theories, J. High Energy Phys., 10, 016 (2020), arXiv:2007.03713 |
| [889] | Bernshtein, L., The analytic continuation of generalized functions with respect to a parameter, Funct. Anal. Appl., 6, 273-285 (1972) · Zbl 0282.46038 |
| [890] | Tkachov, F. V., Algebraic algorithms for multiloop calculations. The First 15 years. What’s next?, Nucl. Instrum. Methods A, 389, 309-313 (1997), arXiv:hep-ph/9609429 |
| [891] | Sato, M.; Shintani, T.; Muro, M., Theory of prehomogeneous vector spaces (algebraic part), Nagoya Math. J., 120, 1-34 (1990) · Zbl 0715.22014 |
| [892] | Ferroglia, A.; Passera, M.; Passarino, G.; Uccirati, S., All purpose numerical evaluation of one loop multileg Feynman diagrams, Nuclear Phys. B, 650, 162-228 (2003), arXiv:hep-ph/0209219 · Zbl 1005.81059 |
| [893] | Ferroglia, A.; Passarino, G.; Uccirati, S.; Passera, M.; Ilyin, V.; Korenkov, V.; Perret-Gallix, D., A frontier in multi-scale multi-loop integrals: The algebraic-numerical method, Nucl. Instrum. Methods A, 502, 391-395 (2003) |
| [894] | Ferroglia, A.; Passera, M.; Passarino, G.; Uccirati, S., Two loop vertices in quantum field theory: Infrared convergent scalar configurations, Nuclear Phys. B, 680, 199-270 (2004), arXiv:hep-ph/0311186 · Zbl 1042.81060 |
| [895] | Passarino, G.; Uccirati, S., Two-loop vertices in quantum field theory: Infrared and collinear divergent configurations, Nuclear Phys. B, 747, 113-189 (2006), 62 pages, 15 figures, 16 tables, arXiv:hep-ph/0603121 · Zbl 1178.81203 |
| [896] | Actis, S.; Passarino, G.; Sturm, C.; Uccirati, S., NNLO computational techniques: The Cases H to gamma gamma and H to g g, Nuclear Phys. B, 811, 182-273 (2009), LaTeX, 70 pages, 8 eps figures, arXiv:0809.3667 · Zbl 1194.81282 |
| [897] | Passarino, G.; Sturm, C.; Uccirati, S., Higgs pseudo-observables, second Riemann sheet and all that, Nuclear Phys. B, 834, 77-115 (2010), arXiv:1001.3360 · Zbl 1204.81190 |
| [898] | Passarino, G.; Sturm, C.; Uccirati, S., Complete two-loop corrections to \(H \to \gamma \gamma \), Phys. Lett. B, 655, 298-306 (2007), arXiv:0707.1401 |
| [899] | Radionov, A.; Tkachov, F., Partial D-operators for the generalized IBP reduction (2020), arXiv:2003.07808 |
| [900] | Uccirati, S., Numerical evaluation of non-infrared two-loop vertices, Particle Physics Phenomenology At High Energy Colliders. Proceedings, Final Meeting of the European Union Network, Montpellier, France, September 26-27, 2004. Particle Physics Phenomenology At High Energy Colliders. Proceedings, Final Meeting of the European Union Network, Montpellier, France, September 26-27, 2004, Acta Phys. Polon. B, 35, 2573-2586 (2004), arXiv:hep-ph/0410332 |
| [901] | Guillet, J. P.; Pilon, E.; Shimizu, Y.; Zidi, M., Framework for a novel mixed analytical/numerical approach for the computation of two-loop \(N\)-point Feynman diagrams, PTEP, 2020, 4, 043B01 (2020), arXiv:1905.08115 · Zbl 1477.81074 |
| [902] | Guillet, J.; Pilon, E.; Shimizu, Y.; Zidi, M., Towards an efficient method to compute two-loop scalar amplitudes, J. Phys. Conf. Ser., 1525, 1, Article 012016 pp. (2020) |
| [903] | Borowka, S.; Gehrmann, T.; Hulme, D., Systematic approximation of multi-scale feynman integrals, J. High Energy Phys., 08, 111 (2018), arXiv:1804.06824 · Zbl 1396.81095 |
| [904] | Plenter, J., Asymptotic expansions through the loop-tree duality, Acta Phys. Polon. B, 50, 1983-1992 (2019) · Zbl 07913420 |
| [905] | Moriello, F., Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops, J. High Energy Phys., 01, 150 (2020), arXiv:1907.13234 |
| [906] | de Doncker, E.; Shimizu, Y.; Fujimoto, J.; Yuasa, F., Computation of loop integrals using extrapolation, Comput. Phys. Comm., 159, 145-156 (2004) · Zbl 1196.81014 |
| [907] | de Doncker, E.; Yuasa, F., Distributed and multi-core computation of 2-loop integrals, Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013): Beijing, China, May 16-21, 2013. Proceedings, 15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2013): Beijing, China, May 16-21, 2013, J. Phys. Conf. Ser., 523, Article 012052 pp. (2014) |
| [908] | de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Kapenga, J.; Olagbemi, O., Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals, Comput. Phys. Comm., 224, 164-185 (2018), arXiv:1702.04904 · Zbl 07694302 |
| [909] | Kato, K.; De Doncker, E.; Ishikawa, T.; Yuasa, F., Direct numerical computation and its application to the higher-order radiative corrections, Proceedings, 18th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2017): Seattle, WA, USA, August 21-25, 2017. Proceedings, 18th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2017): Seattle, WA, USA, August 21-25, 2017, J. Phys. Conf. Ser., 1085, 5, Article 052002 pp. (2018), arXiv:1803.05221 |
| [910] | de Doncker, E.; Almulihi, A.; Yuasa, F., High-speed evaluation of loop integrals using lattice rules, Proceedings, 18th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2017): Seattle, WA, USA, August 21-25, 2017. Proceedings, 18th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2017): Seattle, WA, USA, August 21-25, 2017, J. Phys. Conf. Ser., 1085, 5, Article 052005 pp. (2018) |
| [911] | de Doncker, E.; Yuasa, F.; Kurihara, Y., Regularization of IR divergent loop integrals, Proceedings, 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2011): Uxbridge, UK, September 5-9, 2011. Proceedings, 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 2011): Uxbridge, UK, September 5-9, 2011, J. Phys. Conf. Ser., 368, Article 012060 pp. (2012) |
| [912] | L.F. Richardson, J.A. Gaunt, The deferred approach to the limit, https://doi.org/10.1098/rsta.1927.0008. · JFM 53.0432.02 |
| [913] | Hepp, K., Proof of the Bogolyubov-Parasiuk theorem on renormalization, Comm. Math. Phys., 2, 301-326 (1966) · Zbl 1222.81219 |
| [914] | Speer, E. R., The convergence of BPH renormalization, Comm. Math. Phys., 35, 151-154 (1974) |
| [915] | Speer, E. R., Ultraviolet and infrared singularity structure of generic feynman amplitudes, Ann. Poincare Phys. Theor., 23, 1-21 (1975) |
| [916] | Bogoliubov, N. N.; Parasiuk, O. S., On the multiplication of the causal function in the quantum theory of fields, Acta Math., 97, 227-266 (1957) · Zbl 0081.43302 |
| [917] | Zimmermann, W., Convergence of Bogolyubov’s method of renormalization in momentum space, Comm. Math. Phys., 15, 208-234 (1969) · Zbl 0192.61203 |
| [918] | Ebrahimi-Fard, K.; Kreimer, D., Hopf algebra approach to feynman diagram calculations, J. Phys. A, 38, R385-R406 (2005), arXiv:hep-th/0510202 · Zbl 1092.81051 |
| [919] | Kennedy, A. D.; Binoth, T.; Rippon, T., Automating renormalization of quantum field theories (2007), arXiv:0712.1016 [hep-ph] |
| [920] | Bergbauer, C.; Brunetti, R.; Kreimer, D., Renormalization and resolution of singularities (2009), arXiv:0908.0633 |
| [921] | Breitenlohner, P.; Maison, D., Dimensionally renormalized green’s functions for theories with massless particles. 1, Comm. Math. Phys., 52, 39 (1977) |
| [922] | Breitenlohner, P.; Maison, D., Dimensionally renormalized green’s functions for theories with massless particles. 2, Comm. Math. Phys., 52, 55 (1977) |
| [923] | Speer, E. R., Mass singularities of generic Feynman amplitudes, Ann. Poincare Phys. Theor., 26, 87-105 (1977) |
| [924] | Smirnov, A. V.; Smirnov, V. A., Hepp and speer sectors within modern strategies of sector decomposition, J. High Energy Phys., 05, 004 (2009), arXiv:0812.4700 |
| [925] | Chetyrkin, K. G.; Tkachov, F. V., Infrared R operation and ultraviolet counterterms in the MS scheme, Phys. Lett. B, 114, 340-344 (1982) |
| [926] | Chetyrkin, K. G.; Smirnov, V. A., R* operation corrected, Phys. Lett. B, 144, 419-424 (1984) |
| [927] | Smirnov, V. A.; Chetyrkin, K. G., R* operation in the minimal subtraction scheme, Theoret. Math. Phys., 63, 462-469 (1985), [Teor. Mat. Fiz.63,208(1985)] |
| [928] | Herzog, F.; Ruijl, B., The R \({}^\ast \)-operation for Feynman graphs with generic numerators, J. High Energy Phys., 05, 037 (2017), arXiv:1703.03776 · Zbl 1380.81133 |
| [929] | Beekveldt, R.; Borinsky, M.; Herzog, F., The Hopf algebra structure of the R \({}^\star \)-operation, J. High Energy Phys., 20, 061 (2020), arXiv:2003.04301 |
| [930] | Herzog, F., Zimmermann’s forest formula, infrared divergences and the QCD beta function, Nuclear Phys. B, 926, 370-380 (2018), arXiv:1711.06121 · Zbl 1380.81229 |
| [931] | Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., Towards the five-loop Beta function for a general gauge group, J. High Energy Phys., 07, 127 (2016), arXiv:1606.08662 · Zbl 1390.81644 |
| [932] | Luthe, T.; Maier, A.; Marquard, P.; Schröder, Y., Complete renormalization of QCD at five loops, J. High Energy Phys., 03, 020 (2017), arXiv:1701.07068 · Zbl 1377.81237 |
| [933] | Roth, M.; Denner, A., High-energy approximation of one-loop Feynman integrals, Nuclear Phys. B, 479, 495-514 (1996), arXiv:hep-ph/9605420 |
| [934] | Pozzorini, S., Next to leading mass singularities in two loop electroweak singlet form-factors, Nuclear Phys. B, 692, 135-174 (2004), arXiv:hep-ph/0401087 · Zbl 1151.81412 |
| [935] | Denner, A.; Pozzorini, S., An algorithm for the high-energy expansion of multi-loop diagrams to next-to-leading logarithmic accuracy, Nuclear Phys. B, 717, 48-85 (2005), arXiv:hep-ph/0408068 · Zbl 1207.81089 |
| [936] | Heinrich, G., Sector decomposition, Internat. J. Modern Phys. A, 23, 1457-1486 (2008), arXiv:0803.4177 · Zbl 1153.81522 |
| [937] | Cheng, H.; Wu, T. T., Expanding Protons: Scattering at High Energies, 285 (1987), MIT-PR: MIT-PR Cambridge, USA |
| [938] | Gelfand, I.; Shilov, G., Generalized Functions, vol. 1 (1964), Academic Press, New York · Zbl 0115.33101 |
| [939] | Bogner, C.; Weinzierl, S., Periods and Feynman integrals, J. Math. Phys., 50, Article 042302 pp. (2009), arXiv:0711.4863 · Zbl 1214.81096 |
| [940] | Bogner, C.; Weinzierl, S., Resolution of singularities for multi-loop integrals, Comput. Phys. Comm., 178, 596-610 (2008), arXiv:0709.4092 · Zbl 1196.81010 |
| [941] | Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math., 79, 109 (1964) · Zbl 0122.38603 |
| [942] | Smirnov, A.; Tentyukov, M., Feynman integral evaluation by a sector decomposition approach (FIESTA), Comput. Phys. Comm., 180, 735-746 (2009), arXiv:0807.4129 · Zbl 1198.81044 |
| [943] | Schlenk, J., Techniques for Higher Order Corrections and Their Application to LHC Phenomenology (2016), Technical University Munich, (Ph.D. thesis) |
| [944] | Smirnov, A.; Smirnov, V.; Tentyukov, M., FIESTA 2: Parallelizeable multiloop numerical calculations, Comput. Phys. Comm., 182, 790-803 (2011), arXiv:0912.0158 · Zbl 1214.81171 |
| [945] | Carter, J.; Heinrich, G., SecDec: A general program for sector decomposition, Comput. Phys. Comm., 182, 1566-1581 (2011), arXiv:1011.5493 · Zbl 1262.81119 |
| [946] | Beerli, S., A New Method for Evaluating Two-Loop Feynman Integrals and its Application to Higgs Production (2008), ETH Zurich, (Advisor: Zoltan Kunszt) |
| [947] | Borowka, S.; Carter, J.; Heinrich, G., Numerical evaluation of multi-loop integrals for arbitrary kinematics with secdec 2.0, Comput. Phys. Comm., 184, 396-408 (2013), arXiv:1204.4152 |
| [948] | Borowka, S., Evaluation of Multi-Loop Multi-Scale Integrals and Phenomenological Two-Loop Applications (2014), Max Planck Institute for Physics/Technical University Munich, arXiv:1410.7939 |
| [949] | Borowka, S.; Heinrich, G., Massive non-planar two-loop four-point integrals with SecDec 2.1, Comput. Phys. Comm., 184, 2552-2561 (2013), arXiv:1303.1157 · Zbl 1349.81012 |
| [950] | Borowka, S.; Heinrich, G.; Jahn, S.; Jones, S. P.; Kerner, M.; Schlenk, J., A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec, Comput. Phys. Comm., 240, 120-137 (2019), arXiv:1811.11720 · Zbl 07674767 |
| [951] | Landau, L. D., On analytic properties of vertex parts in quantum field theory, Nuclear Phys., 13, 181-192 (1959) · Zbl 0088.22004 |
| [952] | Eden, R. J.; Landshoff, P. V.; Olive, D. I.; Polkinghorne, J. C., The Analytic S-Matrix (1966), Cambridge University Press · Zbl 0139.46204 |
| [953] | Collins, J., A new and complete proof of the Landau condition for pinch singularities of Feynman graphs and other integrals (2020), arXiv:2007.04085 |
| [954] | Denner, A.; Dittmaier, S.; Roth, M.; Wackeroth, D., Predictions for all processes \(e^+ e^- \to 4\) fermions + gamma, Nuclear Phys. B, 560, 33-65 (1999), arXiv:hep-ph/9904472 |
| [955] | Denner, A.; Dittmaier, S.; Roth, M.; Wieders, L. H., Electroweak corrections to charged-current \(e^+ e^- \to 4\) fermion processes: Technical details and further results, Nuclear Phys. B. Nuclear Phys. B, Nuclear Phys. B, 854, 504-294 (2012), (erratum) |
| [956] | Hahn, T., CUBA: A library for multidimensional numerical integration, Comput. Phys. Comm., 168, 78-95 (2005), arXiv:hep-ph/0404043 · Zbl 1196.65052 |
| [957] | Hahn, T., Concurrent Cuba (2014), arXiv:1408.6373 · Zbl 1380.65471 |
| [958] | Dick, J.; Kuo, F. Y.; Sloan, I. H., High-dimensional integration: The quasi-Monte Carlo way, Acta Numer., 22, 133-288 (2013) · Zbl 1296.65004 |
| [959] | Kuo, F. Y.; Nuyens, D., Lecture Notes: A Practical Guide to Quasi-Monte Carlo Methods (2016), National Chiao Tung University & National Taiwan University |
| [960] | Li, Z.; Wang, J.; Yan, Q.-S.; Zhao, X., Efficient numerical evaluation of Feynman integral, Chinese Phys. C, 40, 3, Article 033103 pp. (2016), arXiv:1508.02512 |
| [961] | Doncker, E. D.; Almulihi, A.; Yuasa, F., Transformed lattice rules for Feynman loop integrals on GPUs, J. Phys. Conf. Ser., 1136, Article 012002 pp. (2018) |
| [962] | Nuyens, D.; Cools, R., Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces, Math. Comp., 75, 254, 903-920 (2006) · Zbl 1094.65004 |
| [963] | Korobov, N., Number-theoretic methods in approximate analysis, Fizmatgiz (1963), Moscow · Zbl 0115.11703 |
| [964] | Laurie, D. P., Periodizing transformations for numerical integration, Proceedings of the Sixth International Congress on Computational and Applied Mathematics. Proceedings of the Sixth International Congress on Computational and Applied Mathematics, J. Comput. Appl. Math., 66, 1, 337-344 (1996), http://www.sciencedirect.com/science/article/pii/0377042795001964 · Zbl 0858.65016 |
| [965] | Kuo, F. Y.; Sloan, I. H.; Woźniakowski, H., Periodization strategy may fail in high dimensions, Numer. Algorithms, 46, 4, 369-391 (2007), https://doi.org/10.1007/s11075-007-9145-8 · Zbl 1140.65011 |
| [966] | Hickernell, F. J., Obtaining \(O ( N^{- 2 + \epsilon} )\) convergence for lattice quadrature rules, (Fang, K.-T.; Hickernell, F.; Niederreiter, H., Monte Carlo and Quasi-Monte Carlo Methods 2000 (2002), Springer, Berlin), 274-289 · Zbl 1002.65009 |
| [967] | S.P. Jones, https://github.com/mppmu/qmc. |
| [968] | Catani, S.; Seymour, M. H., A General algorithm for calculating jet cross-sections in NLO QCD, Nuclear Phys. B. Nuclear Phys. B, Nuclear Phys. B, 510, 503-419 (1998), (erratum) |
| [969] | Catani, S.; Dittmaier, S.; Seymour, M. H.; Trocsanyi, Z., The Dipole formalism for next-to-leading order QCD calculations with massive partons, Nuclear Phys. B, 627, 189-265 (2002), arXiv:hep-ph/0201036 · Zbl 0990.81140 |
| [970] | Frixione, S.; Kunszt, Z.; Signer, A., Three jet cross-sections to next-to-leading order, Nuclear Phys. B, 467, 399-442 (1996), arXiv:hep-ph/9512328 |
| [971] | Frixione, S., A general approach to jet cross-sections in QCD, Nuclear Phys. B, 507, 295-314 (1997), arXiv:hep-ph/9706545 |
| [972] | Nagy, Z.; Soper, D. E., General subtraction method for numerical calculation of one loop QCD matrix elements, J. High Energy Phys., 09, 055 (2003), arXiv:hep-ph/0308127 |
| [973] | Nagy, Z.; Soper, D. E., Parton showers with quantum interference, J. High Energy Phys., 09, 114 (2007), arXiv:0706.0017 |
| [974] | Chung, C. H.; Krämer, M.; Robens, T., An alternative subtraction scheme for next-to-leading order QCD calculations, J. High Energy Phys., 06, 144 (2011), arXiv:1012.4948 · Zbl 1298.81374 |
| [975] | Chung, C.-H.; Robens, T., Nagy-soper subtraction scheme for multiparton final states, Phys. Rev. D, 87, Article 074032 pp. (2013), arXiv:1209.1569 |
| [976] | Bevilacqua, G.; Czakon, M.; Kubocz, M.; Worek, M., Complete Nagy-Soper subtraction for next-to-leading order calculations in QCD, J. High Energy Phys., 10, 204 (2013), arXiv:1308.5605 |
| [977] | Gleisberg, T.; Krauss, F., Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C, 53, 501-523 (2008), arXiv:0709.2881 |
| [978] | Frederix, R.; Gehrmann, T.; Greiner, N., Automation of the dipole subtraction method in MadGraph/MadEvent, J. High Energy Phys., 09, 122 (2008), arXiv:0808.2128 |
| [979] | Hasegawa, K.; Moch, S.; Uwer, P., AutoDipole: Automated generation of dipole subtraction terms, Comput. Phys. Comm., 181, 1802-1817 (2010), arXiv:0911.4371 · Zbl 1219.81244 |
| [980] | Bellm, J., Herwig 7.0/Herwig++ 3.0 release note, Eur. Phys. J. C, 76, 4, 196 (2016), arXiv:1512.01178 |
| [981] | Frederix, R.; Frixione, S.; Maltoni, F.; Stelzer, T., Automation of next-to-leading order computations in QCD: The FKS subtraction, J. High Energy Phys., 10, 003 (2009), arXiv:0908.4272 |
| [982] | Alioli, S.; Nason, P.; Oleari, C.; Re, E., A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, J. High Energy Phys., 06, 043 (2010), arXiv:1002.2581 · Zbl 1290.81155 |
| [983] | Stewart, I. W.; Tackmann, F. J.; Waalewijn, W. J., N-Jettiness: An inclusive event shape to veto jets, Phys. Rev. Lett., 105, Article 092002 pp. (2010), arXiv:1004.2489 |
| [984] | Boughezal, R.; Focke, C.; Liu, X.; Petriello, F., \(W\)-Boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett., 115, 6, Article 062002 pp. (2015), arXiv:1504.02131 |
| [985] | Gaunt, J.; Stahlhofen, M.; Tackmann, F. J.; Walsh, J. R., N-jettiness subtractions for NNLO QCD calculations, J. High Energy Phys., 09, 058 (2015), arXiv:1505.04794 |
| [986] | Moult, I.; Rothen, L.; Stewart, I. W.; Tackmann, F. J.; Zhu, H. X., Subleading power corrections for N-Jettiness subtractions, Phys. Rev. D, 95, 7, Article 074023 pp. (2017), arXiv:1612.00450 |
| [987] | Boughezal, R.; Liu, X.; Petriello, F., Power corrections in the N-jettiness subtraction scheme, J. High Energy Phys., 03, 160 (2017), arXiv:1612.02911 · Zbl 1377.81226 |
| [988] | Moult, I.; Rothen, L.; Stewart, I. W.; Tackmann, F. J.; Zhu, H. X., N -jettiness subtractions for \(g g \to H\) at subleading power, Phys. Rev. D, 97, 1, Article 014013 pp. (2018), arXiv:1710.03227 |
| [989] | Boughezal, R.; Isgro, A.; Petriello, F., Next-to-leading-logarithmic power corrections for \(N\)-jettiness subtraction in color-singlet production, Phys. Rev. D, 97, 7, Article 076006 pp. (2018), arXiv:1802.00456 |
| [990] | Ebert, M. A.; Moult, I.; Stewart, I. W.; Tackmann, F. J.; Vita, G.; Zhu, H. X., Power corrections for N-Jettiness subtractions at \(\mathcal{O} ( \alpha_s )\), J. High Energy Phys., 12, 084 (2018), arXiv:1807.10764 |
| [991] | Cieri, L.; Oleari, C.; Rocco, M., Higher-order power corrections in a transverse-momentum cut for colour-singlet production at NLO, Eur. Phys. J. C, 79, 10, 852 (2019), arXiv:1906.09044 |
| [992] | Boughezal, R.; Isgro, A.; Petriello, F., Next-to-leading power corrections to \(V + 1\) jet production in \(N\)-jettiness subtraction, Phys. Rev. D, 101, 1, Article 016005 pp. (2020), arXiv:1907.12213 |
| [993] | Melnikov, K.; Rietkerk, R.; Tancredi, L.; Wever, C., Double-real contribution to the quark beam function at \(N{}^3\) LO QCD, J. High Energy Phys., 02, 159 (2019), arXiv:1809.06300 |
| [994] | Melnikov, K.; Rietkerk, R.; Tancredi, L.; Wever, C., Triple-real contribution to the quark beam function in QCD at next-to-next-to-next-to-leading order, J. High Energy Phys., 06, 033 (2019), arXiv:1904.02433 |
| [995] | Billis, G.; Ebert, M. A.; Michel, J. K.L.; Tackmann, F. J., A toolbox for \(q_T\) and \(0\)-Jettiness subtractions at \(N{}^3\) LO, Eur. Phys. J. Plus, 136, 2, 214 (2021), arXiv:1909.00811 |
| [996] | Behring, A.; Melnikov, K.; Rietkerk, R.; Tancredi, L.; Wever, C., Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-\( N_c\) approximation, Phys. Rev. D, 100, 11, Article 114034 pp. (2019), arXiv:1910.10059 |
| [997] | Luo, M.-x.; Yang, T.-Z.; Zhu, H. X.; Zhu, Y. J., Quark transverse parton distribution at the next-to-next-to-next-to-leading order, Phys. Rev. Lett., 124, 9, Article 092001 pp. (2020), arXiv:1912.05778 |
| [998] | Baranowski, D., NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter \(\epsilon \), Eur. Phys. J. C, 80, 6, 523 (2020), arXiv:2004.03285 |
| [999] | Ebert, M. A.; Michel, J. K.; Stewart, I. W.; Tackmann, F. J., Drell-Yan \(q_T\) resummation of fiducial power corrections at \(N{}^3\) LL (2020), arXiv:2006.11382 |
| [1000] | Chen, H.; Yang, T.-Z.; Zhu, H. X.; Zhu, Y. J., Analytic continuation and reciprocity relation for collinear splitting in QCD, Chin. Phys. C, 45, 4, 043101 (2021), arXiv:2006.10534 |
| [1001] | Ebert, M. A.; Mistlberger, B.; Vita, G., Transverse momentum dependent PDFs at \(N{}^3\) LO, JHEP, 09, 146 (2020), arXiv:2006.05329 |
| [1002] | Ebert, M. A.; Mistlberger, B.; Vita, G., N-jettiness beam functions at \(N{}^3\) LO, JHEP, 09, 143 (2020), arXiv:2006.03056 |
| [1003] | Ebert, M. A.; Mistlberger, B.; Vita, G., Collinear expansion for color singlet cross sections, JHEP, 09, 181 (2020), arXiv:2006.03055 |
| [1004] | Del Duca, V.; Deutschmann, N.; Lionetti, S., Momentum mappings for subtractions at higher orders in QCD, J. High Energy Phys., 12, 129 (2019), arXiv:1910.01024 |
| [1005] | Bonciani, R.; Catani, S.; Grazzini, M.; Sargsyan, H.; Torre, A., The \(q_T\) subtraction method for top quark production at hadron colliders, Eur. Phys. J. C, 75, 12, 581 (2015), arXiv:1508.03585 |
| [1006] | Catani, S.; Devoto, S.; Grazzini, M.; Kallweit, S.; Mazzitelli, J.; Sargsyan, H., Top-quark pair hadroproduction at next-to-next-to-leading order in QCD, Phys. Rev. D, 99, 5, Article 051501 pp. (2019), arXiv:1901.04005 |
| [1007] | Catani, S.; Devoto, S.; Grazzini, M.; Kallweit, S.; Mazzitelli, J., Top-quark pair production at the LHC: Fully differential QCD predictions at NNLO, J. High Energy Phys., 07, 100 (2019), arXiv:1906.06535 |
| [1008] | Catani, S.; Devoto, S.; Grazzini, M.; Kallweit, S.; Mazzitelli, J., Bottom-quark production at hadron colliders: fully differential predictions in NNLO QCD, J. High Energy Phys., 03, 029 (2021), arXiv:2010.11906 |
| [1009] | Cieri, L.; Ferrera, G.; Sborlini, G. F., Combining QED and QCD transverse-momentum resummation for Z boson production at hadron colliders, J. High Energy Phys., 08, 165 (2018), arXiv:1805.11948 |
| [1010] | Buonocore, L.; Grazzini, M.; Tramontano, F., The \(q_T\) subtraction method: electroweak corrections and power suppressed contributions, Eur. Phys. J. C, 80, 3, 254 (2020), arXiv:1911.10166 |
| [1011] | Cieri, L.; de Florian, D.; Der, M.; Mazzitelli, J., Mixed QCD \(\otimes\) QED corrections to exclusive Drell Yan production using the \(q_T\)-subtraction method, JHEP, 09, 155 (2020), arXiv:2005.01315 |
| [1012] | Delto, M.; Jaquier, M.; Melnikov, K.; Röntsch, R., Mixed QCD \(\otimes\) QED corrections to on-shell \(Z\) boson production at the LHC, J. High Energy Phys., 01, 043 (2020), arXiv:1909.08428 |
| [1013] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W.N., Antenna subtraction at NNLO, J. High Energy Phys., 09, 056 (2005), arXiv:hep-ph/0505111 |
| [1014] | Currie, J.; Glover, E. W.N.; Wells, S., Infrared structure at NNLO using antenna subtraction, J. High Energy Phys., 04, 066 (2013), arXiv:1301.4693 |
| [1015] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. W.N.; Heinrich, G., Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett., 99, Article 132002 pp. (2007), arXiv:0707.1285 |
| [1016] | Currie, J.; Gehrmann, T.; Niehues, J., Precise QCD predictions for the production of dijet final states in deep inelastic scattering, Phys. Rev. Lett., 117, 4, Article 042001 pp. (2016), arXiv:1606.03991 |
| [1017] | Czakon, M., A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B, 693, 259-268 (2010), arXiv:1005.0274 |
| [1018] | Czakon, M., Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nuclear Phys. B, 849, 250-295 (2011), 44 pages, 10 figures, arXiv:1101.0642 · Zbl 1215.81117 |
| [1019] | Boughezal, R.; Melnikov, K.; Petriello, F., A subtraction scheme for NNLO computations, Phys. Rev. D, 85, Article 034025 pp. (2012), 13 pages, arXiv:1111.7041 |
| [1020] | Czakon, M.; Heymes, D., Four-dimensional formulation of the sector-improved residue subtraction scheme, Nuclear Phys. B, 890, 152-227 (2014), arXiv:1408.2500 · Zbl 1326.81237 |
| [1021] | Heinrich, G., A numerical method for NNLO calculations, Nuclear Phys. Proc. Suppl., 116, 368-372 (2003), arXiv:hep-ph/0211144 · Zbl 1037.81585 |
| [1022] | Gehrmann-De Ridder, A.; Gehrmann, T.; Heinrich, G., Four-particle phase space integrals in massless QCD, Nuclear Phys. B, 682, 265-288 (2004), arXiv:hep-ph/0311276 · Zbl 1045.81558 |
| [1023] | Anastasiou, C.; Melnikov, K.; Petriello, F., A new method for real radiation at NNLO, Phys. Rev. D, 69, Article 076010 pp. (2004), arXiv:hep-ph/0311311 |
| [1024] | Anastasiou, C.; Melnikov, K.; Petriello, F., Real radiation at NNLO: \( e^+ e^- \to 2\) jets through \(O ( \alpha_s^2 )\), Phys. Rev. Lett., 93, Article 032002 pp. (2004), arXiv:hep-ph/0402280 |
| [1025] | Binoth, T.; Heinrich, G., Numerical evaluation of phase space integrals by sector decomposition, Nuclear Phys. B, 693, 134-148 (2004), arXiv:hep-ph/0402265 · Zbl 1151.81352 |
| [1026] | Anastasiou, C.; Melnikov, K.; Petriello, F., Higgs boson production at hadron colliders: Differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett., 93, Article 262002 pp. (2004), arXiv:hep-ph/0409088 |
| [1027] | Melnikov, K.; Petriello, F., The W boson production cross section at the LHC through \(O ( \alpha_s^2 )\), Phys. Rev. Lett., 96, Article 231803 pp. (2006), arXiv:hep-ph/0603182 |
| [1028] | Czakon, M.; van Hameren, A.; Mitov, A.; Poncelet, R., Single-jet inclusive rates with exact color at \(\mathcal{O} ( \alpha_s^4)\), J. High Energy Phys., 10, 262 (2019), arXiv:1907.12911 |
| [1029] | Caola, F.; Delto, M.; Frellesvig, H.; Melnikov, K., The double-soft integral for an arbitrary angle between hard radiators, Eur. Phys. J. C, 78, 8, 687 (2018), arXiv:1807.05835 |
| [1030] | Caola, F.; Melnikov, K.; Röntsch, R., Analytic results for color-singlet production at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J. C, 79, 5, 386 (2019), arXiv:1902.02081 |
| [1031] | Caola, F.; Melnikov, K.; Röntsch, R., Analytic results for decays of color singlets to \(g g\) and \(q \overline{q}\) final states at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J. C, 79, 12, 1013 (2019), arXiv:1907.05398 |
| [1032] | Delto, M.; Melnikov, K., Integrated triple-collinear counter-terms for the nested soft-collinear subtraction scheme, J. High Energy Phys., 05, 148 (2019), arXiv:1901.05213 |
| [1033] | Asteriadis, K.; Caola, F.; Melnikov, K.; Röntsch, R., Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J. C, 80, 1, 8 (2020), arXiv:1910.13761 |
| [1034] | Bizoń, W.; Delto, M., Analytic double-soft integrated subtraction terms for two massive emitters in a back-to-back kinematics, J. High Energy Phys., 07, 011 (2020), arXiv:2004.01663 |
| [1035] | Magnea, L.; Maina, E.; Pelliccioli, G.; Signorile-Signorile, C.; Torrielli, P.; Uccirati, S., Local analytic sector subtraction at NNLO, J. High Energy Phys.. J. High Energy Phys., J. High Energy Phys., 06, 013 (2019), (erratum) |
| [1036] | Magnea, L.; Maina, E.; Pelliccioli, G.; Signorile-Signorile, C.; Torrielli, P.; Uccirati, S., Factorisation and subtraction beyond NLO, J. High Energy Phys., 12, 062 (2018), arXiv:1809.05444 |
| [1037] | Brucherseifer, M.; Caola, F.; Melnikov, K., On the NNLO QCD corrections to single-top production at the LHC, Phys. Lett. B, 736, 58-63 (2014), arXiv:1404.7116 |
| [1038] | Herzog, F., Geometric IR subtraction for final state real radiation, J. High Energy Phys., 08, 006 (2018), arXiv:1804.07949 |
| [1039] | Ma, Y., A forest formula to subtract infrared singularities in amplitudes for wide-angle scattering, J. High Energy Phys., 05, 012 (2020), arXiv:1910.11304 |
| [1040] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E., Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett. B, 612, 49-60 (2005), arXiv:hep-ph/0502110 |
| [1041] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E., Quark-gluon antenna functions from neutralino decay, Phys. Lett. B, 612, 36-48 (2005), arXiv:hep-ph/0501291 |
| [1042] | Daleo, A.; Gehrmann, T.; Maître, D., Antenna subtraction with hadronic initial states, J. High Energy Phys., 04, 016 (2007), arXiv:hep-ph/0612257 |
| [1043] | Daleo, A.; Gehrmann-De Ridder, A.; Gehrmann, T.; Luisoni, G., Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, J. High Energy Phys., 01, 118 (2010), arXiv:0912.0374 · Zbl 1269.81194 |
| [1044] | Gehrmann, T.; Monni, P. F., Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, J. High Energy Phys., 12, 049 (2011), arXiv:1107.4037 · Zbl 1306.81339 |
| [1045] | Boughezal, R.; Gehrmann-De Ridder, A.; Ritzmann, M., Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, J. High Energy Phys., 02, 098 (2011), arXiv:1011.6631 · Zbl 1294.81270 |
| [1046] | Gehrmann-De Ridder, A.; Gehrmann, T.; Ritzmann, M., Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, J. High Energy Phys., 10, 047 (2012), arXiv:1207.5779 |
| [1047] | Somogyi, G.; Trocsanyi, Z.; Del Duca, V., Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, J. High Energy Phys., 06, 024 (2005), arXiv:hep-ph/0502226 |
| [1048] | Somogyi, G.; Trocsanyi, Z.; Del Duca, V., A Subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of doubly-real emissions, J. High Energy Phys., 01, 070 (2007), arXiv:hep-ph/0609042 |
| [1049] | Somogyi, G.; Trocsanyi, Z., A Subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of real-virtual emission, J. High Energy Phys., 01, 052 (2007), arXiv:hep-ph/0609043 |
| [1050] | Somogyi, G.; Trocsanyi, Z., A Subtraction scheme for computing QCD jet cross sections at NNLO: Integrating the subtraction terms. I, J. High Energy Phys., 08, 042 (2008), arXiv:0807.0509 |
| [1051] | Aglietti, U.; Del Duca, V.; Duhr, C.; Somogyi, G.; Trocsanyi, Z., Analytic integration of real-virtual counterterms in NNLO jet cross sections. I, J. High Energy Phys., 09, 107 (2008), arXiv:0807.0514 |
| [1052] | Somogyi, G., Subtraction with hadronic initial states at NLO: An NNLO-compatible scheme, J. High Energy Phys., 05, 016 (2009), arXiv:0903.1218 |
| [1053] | Bolzoni, P.; Moch, S.-O.; Somogyi, G.; Trocsanyi, Z., Analytic integration of real-virtual counterterms in NNLO jet cross sections. II, J. High Energy Phys., 08, 079 (2009), arXiv:0905.4390 |
| [1054] | Bolzoni, P.; Somogyi, G.; Trocsanyi, Z., A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, J. High Energy Phys., 1101, 059 (2011), 83 pages, one reference added, typos corrected, agrees with published version, arXiv:1011.1909 · Zbl 1214.81293 |
| [1055] | Del Duca, V.; Somogyi, G.; Trocsanyi, Z., Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections, J. High Energy Phys., 06, 079 (2013), arXiv:1301.3504 |
| [1056] | Somogyi, G., A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the doubly unresolved subtraction terms, J. High Energy Phys., 04, 010 (2013), arXiv:1301.3919 · Zbl 1342.81700 |
| [1057] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E.; Heinrich, G., NNLO corrections to event shapes in \(e^+ e^-\) annihilation, J. High Energy Phys., 12, 094 (2007), arXiv:0711.4711 |
| [1058] | Weinzierl, S., NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett., 101, Article 162001 pp. (2008), arXiv:0807.3241 |
| [1059] | Weinzierl, S., Event shapes and jet rates in electron-positron annihilation at NNLO, J. High Energy Phys., 06, 041 (2009), arXiv:0904.1077 |
| [1060] | Gehrmann, T.; Glover, E.; Huss, A.; Niehues, J.; Zhang, H., NNLO QCD corrections to event orientation in \(e^+ e^-\) annihilation, Phys. Lett. B, 775, 185-189 (2017), arXiv:1709.01097 |
| [1061] | Abelof, G.; Gehrmann-De Ridder, A.; Majer, I., Top quark pair production at NNLO in the quark-antiquark channel, J. High Energy Phys., 12, 074 (2015), arXiv:1506.04037 |
| [1062] | Currie, J.; Glover, E.; Gehrmann, T.; Gehrmann-De Ridder, A.; Huss, A.; Pires, J., Single jet inclusive production for the individual jet \(p_{\operatorname{T}}\) scale choice at the LHC, Acta Phys. Polon. B, 48, 955-967 (2017), arXiv:1704.00923 |
| [1063] | Currie, J.; Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E. N.; Huss, A.; Pires, J.a., Infrared sensitivity of single jet inclusive production at hadron colliders, J. High Energy Phys., 10, 155 (2018), arXiv:1807.03692 |
| [1064] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E.; Huss, A.; Pires, J., Triple differential dijet cross section at the LHC, Phys. Rev. Lett., 123, 10, Article 102001 pp. (2019), arXiv:1905.09047 |
| [1065] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E.; Huss, A.; Morgan, T., Precise QCD predictions for the production of a Z boson in association with a hadronic jet, Phys. Rev. Lett., 117, 2, Article 022001 pp. (2016), arXiv:1507.02850 |
| [1066] | Gehrmann-De Ridder, A.; Gehrmann, T.; Glover, E.; Huss, A.; Morgan, T., The NNLO QCD corrections to z boson production at large transverse momentum, J. High Energy Phys., 07, 133 (2016), arXiv:1605.04295 |
| [1067] | Currie, J.; Gehrmann, T.; Huss, A.; Niehues, J., NNLO QCD Corrections to jet production in deep inelastic scattering, J. High Energy Phys., 07, 018 (2017), arXiv:1703.05977 |
| [1068] | Chen, X.; Gehrmann, T.; Glover, N.; Höfer, M.; Huss, A., Isolated photon and photon+jet production at NNLO QCD accuracy, J. High Energy Phys., 04, 166 (2020), arXiv:1904.01044 |
| [1069] | Gauld, R.; Gehrmann-De Ridder, A.; Glover, E. N.; Huss, A.; Majer, I., Predictions for \(\operatorname{Z} \)-boson production in association with a \(\operatorname{b} \)-jet at \(\mathcal{O} ( \alpha_s^3 )\), Phys. Rev. Lett., 125, 22, 222002 (2020), arXiv:2005.03016 |
| [1070] | Abelof, G.; Boughezal, R.; Liu, X.; Petriello, F., Single-inclusive jet production in electron-nucleon collisions through next-to-next-to-leading order in perturbative QCD, Phys. Lett. B, 763, 52-59 (2016), arXiv:1607.04921 |
| [1071] | Britzger, D.; Currie, J.; Gehrmann, T.; Huss, A.; Niehues, J.; Zlebcik, R., Dijet production in diffractive deep-inelastic scattering in next-to-next-to-leading order QCD, Eur. Phys. J. C, 78, 7, 538 (2018), arXiv:1804.05663 |
| [1072] | Niehues, J.; Walker, D., NNLO QCD Corrections to jet production in charged current deep inelastic scattering, Phys. Lett. B, 788, 243-248 (2019), arXiv:1807.02529 |
| [1073] | Gehrmann, T.; Huss, A.; Mo, J.; Niehues, J., Second-order QCD corrections to event shape distributions in deep inelastic scattering, Eur. Phys. J. C, 79, 12, 1022 (2019), arXiv:1909.02760 |
| [1074] | Czakon, M.; Fiedler, P.; Mitov, A., Resolving the tevatron top quark forward-backward asymmetry puzzle: Fully differential next-to-next-to-leading-order calculation, Phys. Rev. Lett., 115, 5, Article 052001 pp. (2015), arXiv:1411.3007 |
| [1075] | Czakon, M.; Fiedler, P.; Heymes, D.; Mitov, A., NNLO QCD Predictions for fully-differential top-quark pair production at the tevatron, J. High Energy Phys., 05, 034 (2016), arXiv:1601.05375 |
| [1076] | Czakon, M.; Heymes, D.; Mitov, A.; Pagani, D.; Tsinikos, I.; Zaro, M., Top-pair production at the LHC through NNLO QCD and NLO EW, J. High Energy Phys., 10, 186 (2017), arXiv:1705.04105 |
| [1077] | Czakon, M.; Mitov, A.; Poncelet, R., NNLO QCD Corrections to leptonic observables in top-quark pair production and decay (2020), arXiv:2008.11133 |
| [1078] | Boughezal, R.; Caola, F.; Melnikov, K.; Petriello, F.; Schulze, M., Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, J. High Energy Phys., 06, 072 (2013), arXiv:1302.6216 |
| [1079] | Brucherseifer, M.; Caola, F.; Melnikov, K., \( \mathcal{O} ( \alpha_s^2 )\) Corrections to fully-differential top quark decays, J. High Energy Phys., 04, 059 (2013), arXiv:1301.7133 |
| [1080] | Del Duca, V.; Duhr, C.; Kardos, A.; Somogyi, G.; Szor, Z.; Trocsanyi, Z.; Tulipant, Z., Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions, Phys. Rev. D, 94, 7, Article 074019 pp. (2016), arXiv:1606.03453 |
| [1081] | Somogyi, G.; Tramontano, F., Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD, JHEP, 11, 142 (2020), arXiv:2007.15015 |
| [1082] | Ferrera, G.; Grazzini, M.; Tramontano, F., Higher-order QCD effects for associated WH production and decay at the LHC, J. High Energy Phys., 04, 039 (2014), arXiv:1312.1669 |
| [1083] | Grazzini, M.; Kallweit, S.; Rathlev, D.; Torre, A., \( Z \gamma\) Production at hadron colliders in NNLO QCD, Phys. Lett. B, 731, 204-207 (2014), arXiv:1309.7000 |
| [1084] | Grazzini, M.; Kallweit, S.; Rathlev, D., \( W \gamma\) And \(Z \gamma\) production at the LHC in NNLO QCD, J. High Energy Phys., 07, 085 (2015), arXiv:1504.01330 |
| [1085] | Cascioli, F.; Gehrmann, T.; Grazzini, M.; Kallweit, S.; Maierhöfer, P.; von Manteuffel, A.; Pozzorini, S.; Rathlev, D.; Tancredi, L.; Weihs, E., ZZ Production at hadron colliders in NNLO QCD, Phys. Lett. B, 735, 311-313 (2014), arXiv:1405.2219 |
| [1086] | Grazzini, M.; Kallweit, S.; Rathlev, D., ZZ production at the LHC: fiducial cross sections and distributions in NNLO QCD, Phys. Lett. B, 750, 407-410 (2015), arXiv:1507.06257 |
| [1087] | Kallweit, S.; Wiesemann, M., \( Z Z\) production at the LHC: NNLO predictions for \(2 \ell 2 \nu\) and \(4 \ell\) signatures, Phys. Lett. B, 786, 382-389 (2018), arXiv:1806.05941 |
| [1088] | Gehrmann, T.; Grazzini, M.; Kallweit, S.; Maierhöfer, P.; von Manteuffel, A.; Pozzorini, S.; Rathlev, D.; Tancredi, L., \( W^+ W^-\) Production at Hadron Colliders in Next to Next to Leading Order QCD, Phys. Rev. Lett., 113, 21, Article 212001 pp. (2014), arXiv:1408.5243 |
| [1089] | Grazzini, M.; Kallweit, S.; Pozzorini, S.; Rathlev, D.; Wiesemann, M., \( W^+ W^-\) production at the LHC: fiducial cross sections and distributions in NNLO QCD, J. High Energy Phys., 08, 140 (2016), arXiv:1605.02716 |
| [1090] | Grazzini, M.; Kallweit, S.; Rathlev, D.; Wiesemann, M., \( W^\pm Z\) production at hadron colliders in NNLO QCD, Phys. Lett. B, 761, 179-183 (2016), arXiv:1604.08576 |
| [1091] | Grazzini, M.; Kallweit, S.; Rathlev, D.; Wiesemann, M., \( W^\pm Z\) production at the LHC: fiducial cross sections and distributions in NNLO QCD, J. High Energy Phys., 05, 139 (2017), arXiv:1703.09065 |
| [1092] | Berger, E. L.; Gao, J.; Yuan, C. P.; Zhu, H. X., NNLO QCD corrections to t-channel single top-quark production and decay, Phys. Rev. D, 94, 7, Article 071501 pp. (2016), arXiv:1606.08463 |
| [1093] | Boughezal, R.; Liu, X.; Petriello, F., W-boson plus jet differential distributions at NNLO in QCD, Phys. Rev. D, 94, 11, Article 113009 pp. (2016), arXiv:1602.06965 |
| [1094] | Heinrich, G.; Jahn, S.; Jones, S.; Kerner, M.; Pires, J., NNLO predictions for Z-boson pair production at the LHC, J. High Energy Phys., 03, 142 (2018), arXiv:1710.06294 |
| [1095] | Boughezal, R.; Campbell, J. M.; Ellis, R.; Focke, C.; Giele, W. T.; Liu, X.; Petriello, F., Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett., 116, 15, Article 152001 pp. (2016), arXiv:1512.01291 |
| [1096] | Boughezal, R.; Liu, X.; Petriello, F., Phenomenology of the Z-boson plus jet process at NNLO, Phys. Rev. D, 94, 7, Article 074015 pp. (2016), arXiv:1602.08140 |
| [1097] | Campbell, J. M.; Ellis, R. K.; Williams, C., Direct photon production at next-to-next-to-leading order, Phys. Rev. Lett.. Phys. Rev. Lett., Phys. Rev. Lett., 124, 22, 259901 (2020), (erratum) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
