One loop QCD corrections to \(gg\rightarrow t\bar{t}H\) at \(\mathcal{O}(\epsilon^2)\). (English) Zbl 07862092
Summary: We compute the one-loop corrections to \(gg\rightarrow t\overline{t}H\) up to order \(\mathcal{O}(\epsilon^2)\) in the dimensional-regularization parameter. We apply the projector method to compute polarized amplitudes, which generalize massless helicity amplitudes to the massive case. We employ a semi-numerical strategy to evaluate the scattering amplitudes. We express the form factors through scalar integrals analytically, and obtain separately integration by parts reduction identities in compact form. We integrate numerically the corresponding master integrals with an enhanced implementation of the Auxiliary Mass Flow algorithm. Using a numerical fit method, we concatenate the analytic and the numeric results to obtain fast and reliable evaluation of the scattering amplitude. This approach improves numerical stability and evaluation time. Our results are implemented in the Mathematica package TTH.
MSC:
| 81-XX | Quantum theory |
Software:
pySecDec; TTH; FORM; FIRE; MultivariateApart; Fermat; FiniteFlow; OpenLoops; SINGULAR; AMFlow; Reduze; Kira; Mathematica; Ratracer; LiteRed; FireFlyReferences:
| [1] | ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B716 (2012) 1 [arXiv:1207.7214] [INSPIRE]. |
| [2] | CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B716 (2012) 30 [arXiv:1207.7235] [INSPIRE]. |
| [3] | H. Yukawa, On the interaction of elementary particles I, Proc. Phys. Math. Soc. Jap.17 (1935) 48 [INSPIRE]. · JFM 61.1592.09 |
| [4] | ATLAS collaboration, Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector, Phys. Lett. B784 (2018) 173 [arXiv:1806.00425] [INSPIRE]. |
| [5] | CMS collaboration, Observation of \(t\overline{t }H\) production, Phys. Rev. Lett.120 (2018) 231801 [arXiv:1804.02610] [INSPIRE]. |
| [6] | ATLAS collaboration, CP properties of Higgs boson interactions with top quarks in the \(t\overline{t }H\) and tH processes using H → γγ with the ATLAS detector, Phys. Rev. Lett.125 (2020) 061802 [arXiv:2004.04545] [INSPIRE]. |
| [7] | CMS collaboration, Measurements of \(t\overline{t }H\) 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 (2020) 061801 [arXiv:2003.10866] [INSPIRE]. |
| [8] | Cepeda, M., Report from working group 2: Higgs physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr., 7, 221, 2019 |
| [9] | LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922 [doi:10.23731/CYRM-2017-002] [INSPIRE]. |
| [10] | J.N. Ng and P. Zakarauskas, A QCD parton calculation of conjoined production of Higgs bosons and heavy flavors in \(p\overline{p }\) collision, Phys. Rev. D29 (1984) 876 [INSPIRE]. |
| [11] | Z. Kunszt, Associated production of heavy Higgs boson with top quarks, Nucl. Phys. B247 (1984) 339 [INSPIRE]. |
| [12] | W. Beenakker et al., Higgs radiation off top quarks at the Tevatron and the LHC, Phys. Rev. Lett.87 (2001) 201805 [hep-ph/0107081] [INSPIRE]. |
| [13] | L. Reina and S. Dawson, Next-to-leading order results for \(t\overline{t }h\) production at the Tevatron, Phys. Rev. Lett.87 (2001) 201804 [hep-ph/0107101] [INSPIRE]. |
| [14] | L. Reina, S. Dawson and D. Wackeroth, QCD corrections to associated \(t\overline{t }h\) production at the Tevatron, Phys. Rev. D65 (2002) 053017 [hep-ph/0109066] [INSPIRE]. |
| [15] | W. Beenakker et al., NLO QCD corrections to \(t\overline{t }H\) production in hadron collisions, Nucl. Phys. B653 (2003) 151 [hep-ph/0211352] [INSPIRE]. |
| [16] | S. Dawson et al., Associated Higgs production with top quarks at the Large Hadron Collider: NLO QCD corrections, Phys. Rev. D68 (2003) 034022 [hep-ph/0305087] [INSPIRE]. |
| [17] | Frixione, S., Weak corrections to Higgs hadroproduction in association with a top-quark pair, JHEP, 09, 065, 2014 · doi:10.1007/JHEP09(2014)065 |
| [18] | Zhang, Y., QCD NLO and EW NLO corrections to ttH production with top quark decays at hadron collider, Phys. Lett. B, 738, 1, 2014 · doi:10.1016/j.physletb.2014.09.022 |
| [19] | Frixione, S., Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons, JHEP, 06, 184, 2015 · doi:10.1007/JHEP06(2015)184 |
| [20] | 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, JHEP, 02, 053, 2017 · doi:10.1007/JHEP02(2017)053 |
| [21] | Catani, S.; Fabre, I.; Grazzini, M.; Kallweit, S., ttH production at NNLO: the flavour off-diagonal channels, Eur. Phys. J. C, 81, 491, 2021 · doi:10.1140/epjc/s10052-021-09247-w |
| [22] | Catani, S., Higgs boson production in association with a top-antitop quark pair in next-to-next-to-leading order QCD, Phys. Rev. Lett., 130, 2023 · doi:10.1103/PhysRevLett.130.111902 |
| [23] | Agarwal, B.; Buccioni, F.; von Manteuffel, A.; Tancredi, L., Two-loop helicity amplitudes for diphoton plus jet production in full color, Phys. Rev. Lett., 127, 2021 · doi:10.1103/PhysRevLett.127.262001 |
| [24] | Badger, S., Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders, JHEP, 11, 083, 2021 · doi:10.1007/JHEP11(2021)083 |
| [25] | Abreu, S., Two-loop QCD corrections for three-photon production at hadron colliders, SciPost Phys., 15, 157, 2023 · Zbl 07906166 · doi:10.21468/SciPostPhys.15.4.157 |
| [26] | Badger, S., Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD, JHEP, 10, 071, 2023 · doi:10.1007/JHEP10(2023)071 |
| [27] | B. Agarwal et al., Five-parton scattering in QCD at two loops, arXiv:2311.09870 [INSPIRE]. |
| [28] | G. De Laurentis, H. Ita, M. Klinkert and V. Sotnikov, Double-virtual NNLO QCD corrections for five-parton scattering: the gluon channel, arXiv:2311.10086 [INSPIRE]. |
| [29] | G. De Laurentis, H. Ita and V. Sotnikov, Double-virtual NNLO QCD corrections for five-parton scattering: the quark channels, arXiv:2311.18752 [INSPIRE]. |
| [30] | Badger, S.; Hartanto, HB; Zoia, S., Two-loop QCD corrections to Wbb production at hadron colliders, Phys. Rev. Lett., 127, 2021 · doi:10.1103/PhysRevLett.127.012001 |
| [31] | Abreu, S., Leading-color two-loop amplitudes for four partons and a W boson in QCD, JHEP, 04, 042, 2022 · doi:10.1007/JHEP04(2022)042 |
| [32] | Badger, S.; Hartanto, HB; Kryś, J.; Zoia, S., Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC, JHEP, 11, 012, 2021 · doi:10.1007/JHEP11(2021)012 |
| [33] | Badger, S.; Hartanto, HB; Kryś, J.; Zoia, S., Two-loop leading colour helicity amplitudes for W^±γ + j production at the LHC, JHEP, 05, 035, 2022 · doi:10.1007/JHEP05(2022)035 |
| [34] | S. Abreu et al., All two-loop Feynman integrals for five-point one-mass scattering, arXiv:2306.15431 [INSPIRE]. |
| [35] | Badger, S., One-loop QCD helicity amplitudes for pp → ttj to O(ε2), JHEP, 06, 066, 2022 · Zbl 1522.81705 · doi:10.1007/JHEP06(2022)066 |
| [36] | Badger, S.; Becchetti, M.; Chaubey, E.; Marzucca, R., Two-loop master integrals for a planar topology contributing to pp → ttj, JHEP, 01, 156, 2023 · Zbl 1540.81098 · doi:10.1007/JHEP01(2023)156 |
| [37] | F. Febres Cordero et al., Two-loop master integrals for leading-color pp \(t\overline{t }H\) amplitudes with a light-quark loop, arXiv:2312.08131 [INSPIRE]. |
| [38] | Chen, J., Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair, JHEP, 04, 025, 2022 |
| [39] | Henn, JM, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett., 110, 2013 · doi:10.1103/PhysRevLett.110.251601 |
| [40] | F.V. Tkachov, A theorem on analytical calculability of 4-loop renormalization group functions, Phys. Lett. B100 (1981) 65 [INSPIRE]. |
| [41] | K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B192 (1981) 159 [INSPIRE]. |
| [42] | N. Byers and C.N. Yang, Physical regions in invariant variables for n particles and the phase-space volume element, Rev. Mod. Phys.36 (1964) 595 [INSPIRE]. |
| [43] | G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B44 (1972) 189 [INSPIRE]. |
| [44] | Peraro, T.; Tancredi, L., Physical projectors for multi-leg helicity amplitudes, JHEP, 07, 114, 2019 · doi:10.1007/JHEP07(2019)114 |
| [45] | Peraro, T.; Tancredi, L., Tensor decomposition for bosonic and fermionic scattering amplitudes, Phys. Rev. D, 103, 2021 · doi:10.1103/PhysRevD.103.054042 |
| [46] | L.J. Dixon, Calculating scattering amplitudes efficiently, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 95), (1996) [hep-ph/9601359] [INSPIRE]. |
| [47] | Arkani-Hamed, N.; Huang, T-C; Huang, Y-T, Scattering amplitudes for all masses and spins, JHEP, 11, 070, 2021 · Zbl 1521.81418 · doi:10.1007/JHEP11(2021)070 |
| [48] | Badger, S.; Chaubey, E.; Hartanto, HB; Marzucca, R., Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel, JHEP, 06, 163, 2021 · doi:10.1007/JHEP06(2021)163 |
| [49] | Denner, A.; Dittmaier, S., Electroweak radiative corrections for collider physics, Phys. Rept., 864, 1, 2020 · Zbl 1476.81155 · doi:10.1016/j.physrep.2020.04.001 |
| [50] | K. Melnikov and T. van Ritbergen, The three loop on-shell renormalization of QCD and QED, Nucl. Phys. B591 (2000) 515 [hep-ph/0005131] [INSPIRE]. |
| [51] | S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B427 (1998) 161 [hep-ph/9802439] [INSPIRE]. |
| [52] | S. Catani, S. Dittmaier, M.H. Seymour and Z. Trocsanyi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B627 (2002) 189 [hep-ph/0201036] [INSPIRE]. · Zbl 0990.81140 |
| [53] | T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.102 (2009) 162001 [Erratum ibid.111 (2013) 199905] [arXiv:0901.0722] [INSPIRE]. |
| [54] | T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev. D79 (2009) 125004 [Erratum ibid.80 (2009) 109901] [arXiv:0904.1021] [INSPIRE]. |
| [55] | P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys.105 (1993) 279 [INSPIRE]. · Zbl 0782.68091 |
| [56] | B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE]. |
| [57] | Studerus, C., Reduze-Feynman integral reduction in C++, Comput. Phys. Commun., 181, 1293, 2010 · Zbl 1219.81133 · doi:10.1016/j.cpc.2010.03.012 |
| [58] | Maierhöfer, P.; Usovitsch, J.; Uwer, P., Kira — a Feynman integral reduction program, Comput. Phys. Commun., 230, 99, 2018 · Zbl 1498.81004 · doi:10.1016/j.cpc.2018.04.012 |
| [59] | J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods, Comput. Phys. Commun.266 (2021) 108024 [arXiv:2008.06494] [INSPIRE]. · Zbl 1523.81078 |
| [60] | Liu, X.; Ma, Y-Q, AMFlow: a Mathematica package for Feynman integrals computation via auxiliary mass flow, Comput. Phys. Commun., 283, 2023 · Zbl 07693415 · doi:10.1016/j.cpc.2022.108565 |
| [61] | H. Ferguson and D. Bailey, A polynomial time, numerically stable integer relation algorithm, RNR technical report RNR-91-032 (1992). |
| [62] | Bogner, C.; Weinzierl, S., Feynman graph polynomials, Int. J. Mod. Phys. A, 25, 2585, 2010 · Zbl 1193.81072 · doi:10.1142/S0217751X10049438 |
| [63] | Adams, L.; Chaubey, E.; Weinzierl, S., Planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularization parameter, Phys. Rev. Lett., 121, 2018 · doi:10.1103/PhysRevLett.121.142001 |
| [64] | R.H. Lewis, Fermat computer algebra system, Mathematics Department, Fordham University, http://home.bway.net/lewis/, New York, NY, U.S.A. (2008) |
| [65] | Klappert, J.; Lange, F., Reconstructing rational functions with FireFly, Comput. Phys. Commun., 247, 2020 · Zbl 1509.68342 · doi:10.1016/j.cpc.2019.106951 |
| [66] | Klappert, J.; Klein, SY; Lange, F., Interpolation of dense and sparse rational functions and other improvements in FireFly, Comput. Phys. Commun., 264, 2021 · Zbl 1524.65056 · doi:10.1016/j.cpc.2021.107968 |
| [67] | von Manteuffel, A.; Schabinger, RM, A novel approach to integration by parts reduction, Phys. Lett. B, 744, 101, 2015 · Zbl 1330.81151 · doi:10.1016/j.physletb.2015.03.029 |
| [68] | Peraro, T., FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs, JHEP, 07, 031, 2019 · doi:10.1007/JHEP07(2019)031 |
| [69] | Heller, M.; von Manteuffel, A., MultivariateApart: generalized partial fractions, Comput. Phys. Commun., 271, 2022 · Zbl 1524.26024 · doi:10.1016/j.cpc.2021.108174 |
| [70] | W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann, Singular 4-2-0 — a computer algebra system for polynomial computations webpage, http://www.singular.uni-kl.de (2020) |
| [71] | V. Magerya, Rational tracer: a tool for faster rational function reconstruction, arXiv:2211.03572 [INSPIRE]. |
| [72] | Zippel, R., Interpolating polynomials from their values, J. Symb. Comput., 9, 375, 1990 · Zbl 0702.65011 · doi:10.1016/S0747-7171(08)80018-1 |
| [73] | Laurentis, G.; Maître, D., Extracting analytical one-loop amplitudes from numerical evaluations, JHEP, 07, 123, 2019 · Zbl 1418.81089 · doi:10.1007/JHEP07(2019)123 |
| [74] | De Laurentis, G.; Page, B., Ansätze for scattering amplitudes from p-adic numbers and algebraic geometry, JHEP, 12, 140, 2022 · Zbl 1536.81130 · doi:10.1007/JHEP12(2022)140 |
| [75] | H.A. Chawdhry, p-adic reconstruction of rational functions in multi-loop amplitudes, arXiv:2312.03672 [INSPIRE]. |
| [76] | Kreer, PA; Weinzierl, S., The H-graph with equal masses in terms of multiple polylogarithms, Phys. Lett. B, 819, 2021 · Zbl 07409702 · doi:10.1016/j.physletb.2021.136405 |
| [77] | Liu, X.; Ma, Y-Q; Wang, C-Y, A systematic and efficient method to compute multi-loop master integrals, Phys. Lett. B, 779, 353, 2018 · doi:10.1016/j.physletb.2018.02.026 |
| [78] | R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser.523 (2014) 012059 [arXiv:1310.1145] [INSPIRE]. |
| [79] | Smirnov, AV; Chuharev, FS, FIRE6: Feynman Integral REduction with modular arithmetic, Comput. Phys. Commun., 247, 2020 · Zbl 1510.81007 · doi:10.1016/j.cpc.2019.106877 |
| [80] | G. Duplancic and B. Nizic, Reduction method for dimensionally regulated one loop N point Feynman integrals, Eur. Phys. J. C35 (2004) 105 [hep-ph/0303184] [INSPIRE]. · Zbl 1191.81116 |
| [81] | Ellis, RK; Zanderighi, G., Scalar one-loop integrals for QCD, JHEP, 02, 002, 2008 · doi:10.1088/1126-6708/2008/02/002 |
| [82] | Buccioni, F., OpenLoops 2, Eur. Phys. J. C, 79, 866, 2019 · doi:10.1140/epjc/s10052-019-7306-2 |
| [83] | Borowka, S., pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, Comput. Phys. Commun., 222, 313, 2018 · Zbl 07693053 · doi:10.1016/j.cpc.2017.09.015 |
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.
