Abstract
We present the computation of the double real and real-virtual contributions to top-antitop pair production in the quark-antiquark channel at leading colour. The \( q\overline{q} \) → \( t\overline{t} g \) amplitudes contributing to the real-virtual part are computed with OpenLoops, and their numerical stability in the soft and collinear regions is found to be sufficiently high to perform a realistic NNLO calculation in double precision. The subtraction terms required at real-real and real-virtual levels are constructed within the antenna subtraction formalism extended to deal with the presence of coloured massive final state particles. We show that those subtraction terms approximate the real-real and real-virtual matrix elements in all their singular limits.
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References
ATLAS collaboration, Measurements of top quark pair relative differential cross-sections with ATLAS in pp collisions at \( \sqrt{s} \) = 7 TeV, Eur. Phys. J. C 73 (2013) 2261 [arXiv:1207.5644] [INSPIRE].
CMS collaboration, Measurement of differential top-quark pair production cross sections in the lepton + jets channel in pp collisions at 8 TeV, CMS-PAS-TOP-12-027.
CMS collaboration, Measurement of the differential ttbar cross section in the dilepton channel at 8 TeV, CMS-PAS-TOP-12-028.
G. Abelof and A. Gehrmann-De Ridder, Double real radiation corrections to \( t\overline{t} \) production at the LHC: the all-fermion processes, JHEP 04 (2012) 076 [arXiv:1112.4736] [INSPIRE].
C. Anastasiou and S.M. Aybat, The one-loop gluon amplitude for heavy-quark production at NNLO, Phys. Rev. D 78 (2008) 114006 [arXiv:0809.1355] [INSPIRE].
P. Bärnreuther, M. Czakon and A. Mitov, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to \( q\overline{q} \) → \( t\overline{t} \) + X, Phys. Rev. Lett. 109 (2012) 132001 [arXiv:1204.5201] [INSPIRE].
I. Bierenbaum, M. Czakon and A. Mitov, The singular behavior of one-loop massive QCD amplitudes with one external soft gluon, Nucl. Phys. B 856 (2012) 228 [arXiv:1107.4384] [INSPIRE].
R. Bonciani, A. Ferroglia, T. Gehrmann, D. Maître and C. Studerus, Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: The Quark-Antiquark Channel, JHEP 07 (2008)129 [arXiv:0806.2301] [INSPIRE].
R. Bonciani, A. Ferroglia, T. Gehrmann and C. Studerus, Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel, JHEP 08 (2009) 067 [arXiv:0906.3671] [INSPIRE].
R. Bonciani, A. Ferroglia, T. Gehrmann, A. von Manteuffel and C. Studerus, Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel, JHEP 01 (2011) 102 [arXiv:1011.6661] [INSPIRE].
M. Czakon, Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD, Phys. Lett. B 664 (2008) 307 [arXiv:0803.1400] [INSPIRE].
M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys. B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE].
M. Czakon and A. Mitov, NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels, JHEP 12 (2012) 054 [arXiv:1207.0236] [INSPIRE].
B. Kniehl, Z. Merebashvili, J.G. Korner and M. Rogal, Heavy quark pair production in gluon fusion at next-to-next-to-leading O(α 4 s ) order: One-loop squared contributions, Phys. Rev. D 78 (2008) 094013 [arXiv:0809.3980] [INSPIRE].
J.G. Korner, Z. Merebashvili and M. Rogal, NNLO O(α 4 s ) results for heavy quark pair production in quark-antiquark collisions: The one-loop squared contributions, Phys. Rev. D 77 (2008) 094011 [Erratum ibid. D 85 (2012) 119904] [arXiv:0802.0106] [INSPIRE].
M. Czakon, P. Fiedler and A. Mitov, Total Top-Quark Pair-Production Cross section at Hadron Colliders Through \( \mathcal{O}\left({\alpha}_s^4\right) \), Phys. Rev. Lett. 110 (2013) 252004 [arXiv:1303.6254] [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].
T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265] [INSPIRE].
C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, JHEP 03 (2011) 038 [arXiv:1011.4867] [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].
A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
R. Boughezal, K. Melnikov and F. Petriello, A subtraction scheme for NNLO computations, Phys. Rev. D 85 (2012) 034025 [arXiv:1111.7041] [INSPIRE].
S. Frixione, A general approach to jet cross-sections in QCD, Nucl. Phys. B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Double real radiation corrections to \( t\overline{t} \) production at the LHC: the gg → t \( \overline{t} \) q \( \overline{q} \) channel, JHEP 11 (2012) 074 [arXiv:1207.6546] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Antenna subtraction for the production of heavy particles at hadron colliders, JHEP 04 (2011) 063 [arXiv:1102.2443] [INSPIRE].
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
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, JHEP 01 (2014) 110 [arXiv:1310.3993] [INSPIRE].
J. Currie, E.W.N. Glover and S. Wells, Infrared Structure at NNLO Using Antenna Subtraction, JHEP 04 (2013) 066 [arXiv:1301.4693] [INSPIRE].
A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, Real-Virtual corrections for gluon scattering at NNLO, JHEP 02 (2012) 141 [arXiv:1112.3613] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires, Double Virtual corrections for gluon scattering at NNLO, JHEP 02 (2013) 026 [arXiv:1211.2710] [INSPIRE].
W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna function for S → Q \( \overline{Q} \) q \( \overline{q} \) at NNLO QCD, JHEP 06 (2011) 032 [arXiv:1105.0530] [INSPIRE].
W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna functions for S → Q \( \overline{Q} \) gg at NNLO QCD, JHEP 10 (2013) 161 [arXiv:1309.6887] [INSPIRE].
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, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].
A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].
T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e + e − → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
A. Gehrmann-De Ridder and M. Ritzmann, NLO Antenna Subtraction with Massive Fermions, JHEP 07 (2009) 041 [arXiv:0904.3297] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations, JHEP 10 (2012) 047 [arXiv:1207.5779] [INSPIRE].
E.W. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP 06 (2010) 096 [arXiv:1003.2824] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires, Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution, Phys. Rev. Lett. 110 (2013) 162003 [arXiv:1301.7310] [INSPIRE].
G. Abelof, O. Dekkers and A. Gehrmann-De Ridder, Antenna subtraction with massive fermions at NNLO: Double real initial-final configurations, JHEP 12 (2012) 107 [arXiv:1210.5059] [INSPIRE].
F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering Amplitudes with Open Loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: A program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596] [INSPIRE].
S. Badger, R. Sattler and V. Yundin, One-Loop Helicity Amplitudes for \( t\overline{t} \) Production at Hadron Colliders, Phys. Rev. D 83 (2011) 074020 [arXiv:1101.5947] [INSPIRE].
W. Beenakker, H. Kuijf, W.L. van Neerven and J. Smith, QCD Corrections to Heavy Quark Production in \( p\overline{p} \) Collisions, Phys. Rev. D 40 (1989) 54 [INSPIRE].
P. Nason, S. Dawson and R.K. Ellis, The One Particle Inclusive Differential Cross-Section for Heavy Quark Production in Hadronic Collisions, Nucl. Phys. B 327 (1989) 49 [Erratum ibid. B 335 (1990) 260] [INSPIRE].
S. Catani, S. Dittmaier and Z. Trócsányi, One loop singular behavior of QCD and SUSY QCD amplitudes with massive partons, Phys. Lett. B 500 (2001) 149 [hep-ph/0011222] [INSPIRE].
G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].
F.A. Berends and W.T. Giele, Multiple Soft Gluon Radiation in Parton Processes, Nucl. Phys. B 313 (1989) 595 [INSPIRE].
J.M. Campbell and E.W.N. Glover, Double unresolved approximations to multiparton scattering amplitudes, Nucl. Phys. B 527 (1998) 264 [hep-ph/9710255] [INSPIRE].
D. de Florian and M. Grazzini, The structure of large logarithmic corrections at small transverse momentum in hadronic collisions, Nucl. Phys. B 616 (2001) 247 [hep-ph/0108273] [INSPIRE].
S. Weinzierl, Subtraction terms for one loop amplitudes with one unresolved parton, JHEP 07 (2003) 052 [hep-ph/0306248] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, V. Del Duca and C.R. Schmidt, The infrared behavior of one loop gluon amplitudes at next-to-next-to-leading order, Phys. Lett. B 445 (1998) 168 [hep-ph/9810409] [INSPIRE].
D.A. Kosower, All order collinear behavior in gauge theories, Nucl. Phys. B 552 (1999) 319 [hep-ph/9901201] [INSPIRE].
D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [INSPIRE].
Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order, Phys. Rev. D 60 (1999) 116001 [hep-ph/9903516] [INSPIRE].
S. Catani and M. Grazzini, The soft gluon current at one loop order, Nucl. Phys. B 591 (2000) 435 [hep-ph/0007142] [INSPIRE].
D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D 67 (2003) 116003 [hep-ph/0212097] [INSPIRE].
D.A. Kosower, All orders singular emission in gauge theories, Phys. Rev. Lett. 91 (2003) 061602 [hep-ph/0301069] [INSPIRE].
S. Catani, D. de Florian and G. Rodrigo, The triple collinear limit of one loop QCD amplitudes, Phys. Lett. B 586 (2004) 323 [hep-ph/0312067] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [INSPIRE].
S.D. Badger and E.W.N. Glover, Two loop splitting functions in QCD, JHEP 07 (2004) 040 [hep-ph/0405236] [INSPIRE].
A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].
A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].
P. Mastrolia, G. Ossola, T. Reiter and F. Tramontano, Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level, JHEP 08 (2010) 080 [arXiv:1006.0710] [INSPIRE].
M. Grazzini, S. Kallweit, D. Rathlev and A. Torre, Zγ production at hadron colliders in NNLO QCD, Phys. Lett. B 731 (2014) 204 [arXiv:1309.7000] [INSPIRE].
A. Denner, S. Dittmaier and L. Hofer, COLLIER: a fortran-based complex one-loop library in extended regularizations, in preparation.
A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].
S. Hoeche et al., Next-to-leading order QCD predictions for top-quark pair production with up to two jets merged with a parton shower, arXiv:1402.6293 [INSPIRE].
P. Draggiotis, M.V. Garzelli, C.G. Papadopoulos and R. Pittau, Feynman Rules for the Rational Part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [INSPIRE].
R. Kleiss, W.J. Stirling and S.D. Ellis, A New Monte Carlo Treatment of Multiparticle Phase Space at High-energies, Comput. Phys. Commun. 40 (1986) 359 [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: Going Beyond, JHEP 06 (2011) 128 [arXiv:1106.0522] [INSPIRE].
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Abelof, G., Ridder, A.GD., Maierhöfer, P. et al. NNLO QCD subtraction for top-antitop production in the \( q\overline{q} \) channel. J. High Energ. Phys. 2014, 35 (2014). https://doi.org/10.1007/JHEP08(2014)035
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DOI: https://doi.org/10.1007/JHEP08(2014)035