Abstract
Within the framework of local analytic sector subtraction, we present the subtraction of next-to-leading-order QCD singularities for processes featuring massless coloured particles in the initial as well as in the final state. The features of the method are explained in detail, including the introduction of an optimisation procedure aiming at improving numerical stability at the cost of no extra analytic complexity. A numerical validation is provided for a variety of processes relevant to lepton as well as hadron colliders. This work constitutes a relevant step in view of the application of our subtraction method to processes involving initial-state radiation at next-to-next-to-leading order in QCD.
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S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys. B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
S. Frixione, A General approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
S. Catani and M.H. Seymour, A General algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys. B 485 (1997) 291 [Erratum ibid. 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
Z. Nagy and D.E. Soper, General subtraction method for numerical calculation of one loop QCD matrix elements, JHEP 09 (2003) 055 [hep-ph/0308127] [INSPIRE].
G. Bevilacqua, M. Czakon, M. Kubocz and M. Worek, Complete Nagy-Soper subtraction for next-to-leading order calculations in QCD, JHEP 10 (2013) 204 [arXiv:1308.5605] [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
T.D. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP 06 (2005) 024 [hep-ph/0502226] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev. D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE].
F. Caola, K. Melnikov and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J. C 77 (2017) 248 [arXiv:1702.01352] [INSPIRE].
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].
R. Boughezal, C. Focke, X. Liu and F. Petriello, W-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, Phys. Rev. Lett. 115 (2015) 062002 [arXiv:1504.02131] [INSPIRE].
M. Cacciari, F.A. Dreyer, A. Karlberg, G.P. Salam and G. Zanderighi, 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].
G.F.R. Sborlini, F. Driencourt-Mangin and G. Rodrigo, Four-dimensional unsubtraction with massive particles, JHEP 10 (2016) 162 [arXiv:1608.01584] [INSPIRE].
F. Herzog, Geometric IR subtraction for final state real radiation, JHEP 08 (2018) 006 [arXiv:1804.07949] [INSPIRE].
Z. Capatti, V. Hirschi, D. Kermanschah and B. Ruijl, Loop-Tree Duality for Multiloop Numerical Integration, Phys. Rev. Lett. 123 (2019) 151602 [arXiv:1906.06138] [INSPIRE].
L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Local analytic sector subtraction at NNLO, JHEP 12 (2018) 107 [Erratum JHEP 06 (2019) 013] [arXiv:1806.09570] [INSPIRE].
L. Magnea, E. Maina, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Factorisation and Subtraction beyond NLO, JHEP 12 (2018) 062 [arXiv:1809.05444] [INSPIRE].
L. Magnea, G. Pelliccioli, C. Signorile-Signorile, P. Torrielli and S. Uccirati, Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO, JHEP 02 (2021) 037 [arXiv:2010.14493] [INSPIRE].
G. Bertolotti et al., NNLO subtraction for massless final states: a complete analytic expression, in preparation.
Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].
V.N. Gribov and L.N. Lipatov, Deep inelastic e p scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [Yad. Fiz. 15 (1972) 781] [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [Zh. Eksp. Teor. Fiz. 73 (1977) 1216] [INSPIRE].
S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
S. Lionetti, Subtraction of Infrared Singularities at Higher Orders in QCD, Ph.D. Thesis, ETH Zürich (2018) [https://doi.org/10.3929/ethz-b-000332748].
V. Hirschi, S. Lionetti and A. Schweitzer, One-loop weak corrections to Higgs production, JHEP 05 (2019) 002 [arXiv:1902.10167] [INSPIRE].
M. Becchetti, R. Bonciani, V. Del Duca, V. Hirschi, F. Moriello and A. Schweitzer, Next-to-leading order corrections to light-quark mixed QCD-EW contributions to Higgs boson production, Phys. Rev. D 103 (2021) 054037 [arXiv:2010.09451] [INSPIRE].
R. Bonciani et al., Next-to-leading-order QCD Corrections to Higgs Production in association with a Jet, arXiv:2206.10490 [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H.S. Shao and M. Zaro, The automation of next-to-leading order electroweak calculations, JHEP 07 (2018) 185 [Erratum JHEP 11 (2021) 085] [arXiv:1804.10017] [INSPIRE].
V. Hirschi, R. Frederix, S. Frixione, M.V. Garzelli, F. Maltoni and R. Pittau, Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].
G.P. Lepage, VEGAS: An adaptive multidimensional integration program, CLNS-80/447 (1980).
G.P. Lepage, Adaptive multidimensional integration: VEGAS enhanced, J. Comput. Phys. 439 (2021) 110386 [arXiv:2009.05112] [INSPIRE].
J. Butterworth et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43 (2016) 023001 [arXiv:1510.03865] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, The anti-kt jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
S. Catani, Y.L. Dokshitzer, M.H. Seymour and B.R. Webber, Longitudinally invariant k⊥ clustering algorithms for hadron hadron collisions, Nucl. Phys. B 406 (1993) 187 [INSPIRE].
S.D. Ellis and D.E. Soper, Successive combination jet algorithm for hadron collisions, Phys. Rev. D 48 (1993) 3160 [hep-ph/9305266] [INSPIRE].
R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: The FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].
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Bertolotti, G., Torrielli, P., Uccirati, S. et al. Local analytic sector subtraction for initial- and final-state radiation at NLO in massless QCD. J. High Energ. Phys. 2022, 42 (2022). https://doi.org/10.1007/JHEP12(2022)042
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DOI: https://doi.org/10.1007/JHEP12(2022)042