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The colourful antenna subtraction method. (English) Zbl 07862113

Summary: We present a general subtraction scheme for NNLO calculations in massless QCD: the colourful antenna subtraction method. It is a reformulation of the antenna subtraction approach designed to address some of the limitations of the traditional framework, especially aiming at high-multiplicity processes. In the context of the new formalism, structures needed to locally subtract the infrared-divergent behaviour of real emission corrections are systematically inferred from virtual subtraction terms, relying on the cancellation of infrared singularities and on the correspondence between integrated and unintegrated antenna functions. We illustrate in detail how the colourful antenna subtraction method works up to NNLO. The algorithm is particularly suited to be fully automated for the generation of NNLO subtraction terms for generic processes. We employ the new formalism to assemble the subtraction terms required for the calculation of the NNLO correction to hadronic three-jet production and describe their validation procedure.

MSC:

81-XX Quantum theory

References:

[1] S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett. B378 (1996) 287 [hep-ph/9602277] [INSPIRE].
[2] S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B467 (1996) 399 [hep-ph/9512328] [INSPIRE].
[3] Alwall, J., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP, 07, 079, 2014 · Zbl 1402.81011 · doi:10.1007/JHEP07(2014)079
[4] Sherpa collaboration, Event Generation with Sherpa 2.2, SciPost Phys.7 (2019) 034 [arXiv:1905.09127] [INSPIRE].
[5] J. Bellm et al., Herwig 7.2 release note, Eur. Phys. J. C80 (2020) 452 [arXiv:1912.06509] [INSPIRE].
[6] Alioli, S.; Nason, P.; Oleari, C.; Re, E., A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP, 06, 043, 2010 · Zbl 1290.81155 · doi:10.1007/JHEP06(2010)043
[7] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP09 (2005) 056 [hep-ph/0505111] [INSPIRE].
[8] Currie, J.; Glover, EWN; Wells, S., Infrared Structure at NNLO Using Antenna Subtraction, JHEP, 04, 066, 2013 · doi:10.1007/JHEP04(2013)066
[9] Del Duca, V., Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions, Phys. Rev. D, 94, 2016 · doi:10.1103/PhysRevD.94.074019
[10] S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett.98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
[11] Czakon, M., A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B, 693, 259, 2010 · doi:10.1016/j.physletb.2010.08.036
[12] Czakon, M.; Heymes, D., Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys. B, 890, 152, 2014 · Zbl 1326.81237 · doi:10.1016/j.nuclphysb.2014.11.006
[13] Gaunt, J.; Stahlhofen, M.; Tackmann, FJ; Walsh, JR, N-jettiness Subtractions for NNLO QCD Calculations, JHEP, 09, 058, 2015 · doi:10.1007/JHEP09(2015)058
[14] M. Cacciari et al., Fully Differential Vector-Boson-Fusion Higgs Production at Next-to-Next-to-Leading Order, Phys. Rev. Lett.115 (2015) 082002 [Erratum ibid.120 (2018) 139901] [arXiv:1506.02660] [INSPIRE].
[15] Caola, F.; Melnikov, K.; Röntsch, R., Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J. C, 77, 248, 2017 · doi:10.1140/epjc/s10052-017-4774-0
[16] L. Magnea et al., Local analytic sector subtraction at NNLO, JHEP12 (2018) 107 [Erratum ibid.06 (2019) 013] [arXiv:1806.09570] [INSPIRE].
[17] Bertolotti, G., NNLO subtraction for any massless final state: a complete analytic expression, JHEP, 07, 140, 2023 · Zbl 07744285 · doi:10.1007/JHEP07(2023)140
[18] F. Devoto et al., A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to N-gluon final states in \(q\overline{q }\) annihilation, JHEP02 (2024) 016 [arXiv:2310.17598] [INSPIRE].
[19] Chawdhry, HA; Czakon, ML; Mitov, A.; Poncelet, R., NNLO QCD corrections to three-photon production at the LHC, JHEP, 02, 057, 2020 · doi:10.1007/JHEP02(2020)057
[20] Kallweit, S.; Sotnikov, V.; Wiesemann, M., Triphoton production at hadron colliders in NNLO QCD, Phys. Lett. B, 812, 2021 · doi:10.1016/j.physletb.2020.136013
[21] Chawdhry, HA; Czakon, M.; Mitov, A.; Poncelet, R., NNLO QCD corrections to diphoton production with an additional jet at the LHC, JHEP, 09, 093, 2021 · doi:10.1007/JHEP09(2021)093
[22] M. Czakon, A. Mitov and R. Poncelet, Next-to-Next-to-Leading Order Study of Three-Jet Production at the LHC, Phys. Rev. Lett.127 (2021) 152001 [Erratum ibid.129 (2022) 119901] [arXiv:2106.05331] [INSPIRE].
[23] Chen, X., Automation of antenna subtraction in colour space: gluonic processes, JHEP, 10, 099, 2022 · doi:10.1007/JHEP10(2022)099
[24] H.B. Hartanto, R. Poncelet, A. Popescu and S. Zoia, Next-to-next-to-leading order QCD corrections to \(W\overline{b }b\) production at the LHC, Phys. Rev. D106 (2022) 074016 [arXiv:2205.01687] [INSPIRE].
[25] Alvarez, M., NNLO QCD corrections to event shapes at the LHC, JHEP, 03, 129, 2023 · doi:10.1007/JHEP03(2023)129
[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] 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
[28] Buonocore, L., Associated production of a W boson and massive bottom quarks at next-to-next-to-leading order in QCD, Phys. Rev. D, 107, 2023 · doi:10.1103/PhysRevD.107.074032
[29] Buonocore, L., Precise Predictions for the Associated Production of a W Boson with a Top-Antitop Quark Pair at the LHC, Phys. Rev. Lett., 131, 2023 · doi:10.1103/PhysRevLett.131.231901
[30] Chicherin, D.; Henn, J.; Mitev, V., Bootstrapping pentagon functions, JHEP, 05, 164, 2018 · doi:10.1007/JHEP05(2018)164
[31] T. Gehrmann, J.M. Henn and N.A. Lo Presti, Pentagon functions for massless planar scattering amplitudes, JHEP10 (2018) 103 [arXiv:1807.09812] [INSPIRE]. · Zbl 1402.81256
[32] Chicherin, D.; Sotnikov, V., Pentagon Functions for Scattering of Five Massless Particles, JHEP, 12, 167, 2020 · Zbl 1457.81126 · doi:10.1007/JHEP12(2020)167
[33] Abreu, S.; Page, B.; Pascual, E.; Sotnikov, V., Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders, JHEP, 01, 078, 2021 · doi:10.1007/JHEP01(2021)078
[34] Abreu, S., Leading-color two-loop QCD corrections for three-jet production at hadron colliders, JHEP, 07, 095, 2021 · doi:10.1007/JHEP07(2021)095
[35] 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
[36] 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
[37] 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
[38] S. Abreu et al., All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering, arXiv:2306.15431 [INSPIRE].
[39] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Infrared structure of e^+e^− → 2 jets at NNLO, Nucl. Phys. B691 (2004) 195 [hep-ph/0403057] [INSPIRE].
[40] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett. B612 (2005) 49 [hep-ph/0502110] [INSPIRE].
[41] A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Quark-gluon antenna functions from neutralino decay, Phys. Lett. B612 (2005) 36 [hep-ph/0501291] [INSPIRE].
[42] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e^+e^− → 3 jets at NNLO, JHEP11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
[43] J. Currie, T. Gehrmann, A. Huss and J. Niehues, NNLO QCD corrections to jet production in deep inelastic scattering, JHEP07 (2017) 018 [Erratum ibid.12 (2020) 042] [arXiv:1703.05977] [INSPIRE].
[44] Currie, J., Precise predictions for dijet production at the LHC, Phys. Rev. Lett., 119, 2017 · doi:10.1103/PhysRevLett.119.152001
[45] Chen, X.; Gehrmann, T.; Glover, EWN; Mo, J., Antenna subtraction for jet production observables in full colour at NNLO, JHEP, 10, 040, 2022 · doi:10.1007/JHEP10(2022)040
[46] Chen, X., Isolated photon and photon+jet production at NNLO QCD accuracy, JHEP, 04, 166, 2020
[47] Gehrmann, T.; Glover, N.; Huss, A.; Whitehead, J., Scale and isolation sensitivity of diphoton distributions at the LHC, JHEP, 01, 108, 2021 · doi:10.1007/JHEP01(2021)108
[48] A. Gehrmann-De Ridder et al., Precise QCD predictions for the production of a Z boson in association with a hadronic jet, Phys. Rev. Lett.117 (2016) 022001 [arXiv:1507.02850] [INSPIRE].
[49] A. Gehrmann-De Ridder et al., The NNLO QCD corrections to Z boson production at large transverse momentum, JHEP07 (2016) 133 [arXiv:1605.04295] [INSPIRE].
[50] A. Gehrmann-De Ridder et al., Next-to-Next-to-Leading-Order QCD Corrections to the Transverse Momentum Distribution of Weak Gauge Bosons, Phys. Rev. Lett.120 (2018) 122001 [arXiv:1712.07543] [INSPIRE].
[51] R. Gauld et al., Predictions for Z -Boson Production in Association with a b-Jet at \(\mathcal{O}({\alpha }_s^3 )\), Phys. Rev. Lett.125 (2020) 222002 [arXiv:2005.03016] [INSPIRE].
[52] Gauld, R., NNLO QCD predictions for Z-boson production in association with a charm jet within the LHCb fiducial region, Eur. Phys. J. C, 83, 336, 2023 · doi:10.1140/epjc/s10052-023-11530-x
[53] Chen, X., NNLO QCD corrections to Higgs boson production at large transverse momentum, JHEP, 10, 066, 2016 · doi:10.1007/JHEP10(2016)066
[54] Cruz-Martinez, J.; Gehrmann, T.; Glover, EWN; Huss, A., Second-order QCD effects in Higgs boson production through vector boson fusion, Phys. Lett. B, 781, 672, 2018 · doi:10.1016/j.physletb.2018.04.046
[55] Gauld, R., Associated production of a Higgs boson decaying into bottom quarks and a weak vector boson decaying leptonically at NNLO in QCD, JHEP, 10, 002, 2019 · doi:10.1007/JHEP10(2019)002
[56] R. Gauld et al., VH + jet production in hadron-hadron collisions up to order \({\alpha }_s^3\) in perturbative QCD, JHEP03 (2022) 008 [arXiv:2110.12992] [INSPIRE].
[57] Magnea, L., Factorisation and Subtraction beyond NLO, JHEP, 12, 062, 2018 · doi:10.1007/JHEP12(2018)062
[58] Braun-White, O.; Glover, N.; Preuss, CT, A general algorithm to build real-radiation antenna functions for higher-order calculations, JHEP, 06, 065, 2023 · doi:10.1007/JHEP06(2023)065
[59] Braun-White, O.; Glover, N.; Preuss, CT, A general algorithm to build mixed real and virtual antenna functions for higher-order calculations, JHEP, 11, 179, 2023 · doi:10.1007/JHEP11(2023)179
[60] Fox, E.; Glover, N., Initial-final and initial-initial antenna functions for real radiation at next-to-leading order, JHEP, 12, 171, 2023 · doi:10.1007/JHEP12(2023)171
[61] A. Daleo, T. Gehrmann and D. Maitre, Antenna subtraction with hadronic initial states, JHEP04 (2007) 016 [hep-ph/0612257] [INSPIRE].
[62] A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP01 (2010) 118 [arXiv:0912.0374] [INSPIRE]. · Zbl 1269.81194
[63] R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP02 (2011) 098 [arXiv:1011.6631] [INSPIRE]. · Zbl 1294.81270
[64] A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, JHEP10 (2012) 047 [arXiv:1207.5779] [INSPIRE].
[65] E.W. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP06 (2010) 096 [arXiv:1003.2824] [INSPIRE]. · Zbl 1288.81147
[66] Gehrmann, T.; Monni, PF, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP, 12, 049, 2011 · Zbl 1306.81339 · doi:10.1007/JHEP12(2011)049
[67] G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B126 (1977) 298 [INSPIRE].
[68] J. Currie, A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, NNLO QCD corrections to jet production at hadron colliders from gluon scattering, JHEP01 (2014) 110 [arXiv:1310.3993] [INSPIRE].
[69] A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, Real-Virtual corrections for gluon scattering at NNLO, JHEP02 (2012) 141 [arXiv:1112.3613] [INSPIRE]. · Zbl 1309.81285
[70] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires, Double Virtual corrections for gluon scattering at NNLO, JHEP02 (2013) 026 [arXiv:1211.2710] [INSPIRE].
[71] G. Curci, W. Furmanski and R. Petronzio, Evolution of Parton Densities Beyond Leading Order: The Nonsinglet Case, Nucl. Phys. B175 (1980) 27 [INSPIRE].
[72] W. Furmanski and R. Petronzio, Singlet Parton Densities Beyond Leading Order, Phys. Lett. B97 (1980) 437 [INSPIRE].
[73] Chen, X., NNLO QCD corrections in full colour for jet production observables at the LHC, JHEP, 09, 025, 2022
[74] A. Bassetto, M. Ciafaloni and G. Marchesini, Jet Structure and Infrared Sensitive Quantities in Perturbative QCD, Phys. Rept.100 (1983) 201 [INSPIRE].
[75] S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B427 (1998) 161 [hep-ph/9802439] [INSPIRE].
[76] S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys. B570 (2000) 287 [hep-ph/9908523] [INSPIRE].
[77] T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP06 (2009) 081 [Erratum ibid.11 (2013) 024] [arXiv:0903.1126] [INSPIRE].
[78] Gardi, E.; Magnea, L., Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP, 03, 079, 2009 · doi:10.1088/1126-6708/2009/03/079
[79] E. Gardi and L. Magnea, Infrared singularities in QCD amplitudes, Nuovo Cim. C32N5-6 (2009) 137 [arXiv:0908.3273] [INSPIRE].
[80] Z. Bern, A. De Freitas and L.J. Dixon, Two loop helicity amplitudes for quark gluon scattering in QCD and gluino gluon scattering in supersymmetric Yang-Mills theory, JHEP06 (2003) 028 [Erratum ibid.04 (2014) 112] [hep-ph/0304168] [INSPIRE].
[81] Seymour, MH; Sjodahl, M., Symmetry of anomalous dimension matrices explained, JHEP, 12, 066, 2008 · doi:10.1088/1126-6708/2008/12/066
[82] Czakon, M.; Fiedler, P., The soft function for color octet production at threshold, Nucl. Phys. B, 879, 236, 2014 · Zbl 1284.81294 · doi:10.1016/j.nuclphysb.2013.12.008
[83] Chen, X.; Jakubčík, P.; Marcoli, M.; Stagnitto, G., Radiation from a gluon-gluino colour-singlet dipole at N^3LO, JHEP, 12, 198, 2023 · doi:10.1007/JHEP12(2023)198
[84] D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D67 (2003) 116003 [hep-ph/0212097] [INSPIRE].
[85] Weinzierl, S., NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett., 101, 2008 · doi:10.1103/PhysRevLett.101.162001
[86] Weinzierl, S., The infrared structure of e^+e^− → 3 jets at NNLO reloaded, JHEP, 07, 009, 2009 · doi:10.1088/1126-6708/2009/07/009
[87] ATLAS collaboration, Measurement of multi-jet cross sections in proton-proton collisions at a 7 TeV center-of-mass energy, Eur. Phys. J. C71 (2011) 1763 [arXiv:1107.2092] [INSPIRE].
[88] ATLAS collaboration, Measurement of hadronic event shapes in high-p_T multijet final states at \(\sqrt{s} = 13\) TeV with the ATLAS detector, JHEP01 (2021) 188 [Erratum ibid.12 (2021) 053] [arXiv:2007.12600] [INSPIRE].
[89] CMS collaboration, Measurement of the Ratio of the Inclusive 3-Jet Cross Section to the Inclusive 2-Jet Cross Section in pp Collisions at \(\sqrt{s} = 7\) TeV and First Determination of the Strong Coupling Constant in the TeV Range, Eur. Phys. J. C73 (2013) 2604 [arXiv:1304.7498] [INSPIRE].
[90] CMS collaboration, Study of Hadronic Event-Shape Variables in Multijet Final States in pp Collisions at \(\sqrt{s} = 7\) TeV, JHEP10 (2014) 087 [arXiv:1407.2856] [INSPIRE].
[91] CMS collaboration, Event shape variables measured using multijet final states in proton-proton collisions at \(\sqrt{s} = 13\) TeV, JHEP12 (2018) 117 [arXiv:1811.00588] [INSPIRE].
[92] F.A. Berends and W. Giele, The Six Gluon Process as an Example of Weyl-Van Der Waerden Spinor Calculus, Nucl. Phys. B294 (1987) 700 [INSPIRE].
[93] Z. Kunszt, Combined Use of the Calkul Method and N = 1 Supersymmetry to Calculate QCD Six Parton Processes, Nucl. Phys. B271 (1986) 333 [INSPIRE].
[94] J.F. Gunion and Z. Kunszt, Four Jet Processes: Gluon-Gluon Scattering to Nonidentical Quark- Antiquark Pairs, Phys. Lett. B159 (1985) 167 [INSPIRE].
[95] J.F. Gunion and J. Kalinowski, A direct Calculation of the Six Gluon Subprocess, Phys. Rev. D34 (1986) 2119 [INSPIRE].
[96] J.F. Gunion and Z. Kunszt, Six Quark Subprocesses in QCD, Phys. Lett. B176 (1986) 163 [INSPIRE].
[97] Dixon, LJ; Henn, JM; Plefka, J.; Schuster, T., All tree-level amplitudes in massless QCD, JHEP, 01, 035, 2011 · Zbl 1214.81297 · doi:10.1007/JHEP01(2011)035
[98] Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett.70 (1993) 2677 [hep-ph/9302280] [INSPIRE].
[99] Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to two quark three gluon amplitudes, Nucl. Phys. B437 (1995) 259 [hep-ph/9409393] [INSPIRE].
[100] Z. Kunszt, A. Signer and Z. Trócsányi, One loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon, Phys. Lett. B336 (1994) 529 [hep-ph/9405386] [INSPIRE].
[101] A. Signer, Helicity method for next-to-leading order corrections in QCD, Ph.D. thesis, ETH Zürich, CH-8093 Zürich, Switzerland (1995).
[102] Abreu, S., Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD, JHEP, 05, 084, 2019 · Zbl 1416.81202 · doi:10.1007/JHEP05(2019)084
[103] Cascioli, F.; Maierhöfer, P.; Pozzorini, S., Scattering Amplitudes with Open Loops, Phys. Rev. Lett., 108, 2012 · doi:10.1103/PhysRevLett.108.111601
[104] Buccioni, F.; Pozzorini, S.; Zoller, M., On-the-fly reduction of open loops, Eur. Phys. J. C, 78, 70, 2018 · doi:10.1140/epjc/s10052-018-5562-1
[105] Buccioni, F., OpenLoops 2, Eur. Phys. J. C, 79, 866, 2019 · doi:10.1140/epjc/s10052-019-7306-2
[106] Gehrmann, T.; Schürmann, R., Photon fragmentation in the antenna subtraction formalism, JHEP, 04, 031, 2022 · Zbl 1522.81720 · doi:10.1007/JHEP04(2022)031
[107] Gehrmann, T.; Stagnitto, G., Antenna subtraction at NNLO with identified hadrons, JHEP, 10, 136, 2022 · doi:10.1007/JHEP10(2022)136
[108] A. Gehrmann-De Ridder and M. Ritzmann, NLO Antenna Subtraction with Massive Fermions, JHEP07 (2009) 041 [arXiv:0904.3297] [INSPIRE].
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.