Abstract
We present the two-loop virtual amplitudes for heavy-quark pair production in light quark-antiquark annihilation and gluon fusion channels, including full spin and color dependence. We use expansions around kinematical limits and numerical integration to obtain results for the involved master integrals. From these, we determine the renormalised infrared finite remainders of the coefficients of amplitude decompositions in terms of color and spin structures. The remainders are given in form of numerical interpolation grids supported by expansions around the production threshold and the high energy limit. Finally, we provide the spin density matrix, which encodes the heavy-quark spin correlations and is sufficient for phenomenological applications. Our results are necessary for the derivation of top-quark pair production cross sections in hadron collisions in the narrow width approximation with next-to-next-to-leading order accuracy in QCD.
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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].
M. Czakon, D. Heymes and A. Mitov, High-precision differential predictions for top-quark pairs at the LHC, Phys. Rev. Lett. 116 (2016) 082003 [arXiv:1511.00549] [INSPIRE].
M. Czakon, P. Fiedler, D. Heymes and A. Mitov, NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron, JHEP 05 (2016) 034 [arXiv:1601.05375] [INSPIRE].
M. Czakon, D. Heymes and A. Mitov, Dynamical scales for multi-TeV top-pair production at the LHC, JHEP 04 (2017) 071 [arXiv:1606.03350] [INSPIRE].
M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos and M. Zaro, Top-pair production at the LHC through NNLO QCD and NLO EW, JHEP 10 (2017) 186 [arXiv:1705.04105] [INSPIRE].
M. Czakon, D. Heymes, A. Mitov, D. Pagani, I. Tsinikos and M. Zaro, The top-quark charge asymmetry at the LHC and Tevatron through NNLO QCD and NLO EW, arXiv:1711.03945 [INSPIRE].
G. Bevilacqua, M. Czakon, A. van Hameren, C.G. Papadopoulos and M. Worek, Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order, JHEP 02 (2011) 083 [arXiv:1012.4230] [INSPIRE].
A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to WWbb production at hadron colliders, Phys. Rev. Lett. 106 (2011) 052001 [arXiv:1012.3975] [INSPIRE].
A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders, JHEP 10 (2012) 110 [arXiv:1207.5018] [INSPIRE].
A. Denner and M. Pellen, Off-shell production of top-antitop pairs in the lepton + jets channel at NLO QCD, JHEP 02 (2018) 013 [arXiv:1711.10359] [INSPIRE].
G. Bevilacqua, H.B. Hartanto, M. Kraus and M. Worek, Top Quark Pair Production in Association with a Jet with Next-to-Leading-Order QCD Off-Shell Effects at the Large Hadron Collider, Phys. Rev. Lett. 116 (2016) 052003 [arXiv:1509.09242] [INSPIRE].
G. Bevilacqua, H.B. Hartanto, M. Kraus and M. Worek, Off-shell Top Quarks with One Jet at the LHC: A comprehensive analysis at NLO QCD, JHEP 11 (2016) 098 [arXiv:1609.01659] [INSPIRE].
M. Brucherseifer, F. Caola and K. Melnikov, \( \mathcal{O}\left({\alpha}_s^2\right) \) corrections to fully-differential top quark decays, JHEP 04 (2013) 059 [arXiv:1301.7133] [INSPIRE].
J. Gao, C.S. Li and H.X. Zhu, Top Quark Decay at Next-to-Next-to Leading Order in QCD, Phys. Rev. Lett. 110 (2013) 042001 [arXiv:1210.2808] [INSPIRE].
J. Gao and A.S. Papanastasiou, Top-quark pair-production and decay at high precision, Phys. Rev. D 96 (2017) 051501 [arXiv:1705.08903] [INSPIRE].
P. Bärnreuther, M. Czakon and P. Fiedler, Virtual amplitudes and threshold behaviour of hadronic top-quark pair-production cross sections, JHEP 02 (2014) 078 [arXiv:1312.6279] [INSPIRE].
T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for \( q{\overline{q}}^{\prime}\to {V}_1{V}_2\to 4 \) leptons, JHEP 09 (2015) 128 [arXiv:1503.04812] [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].
A. von Manteuffel and C. Studerus, Massive planar and non-planar double box integrals for light N f contributions to \( gg\to t\overline{t} \), JHEP 10 (2013) 037 [arXiv:1306.3504] [INSPIRE].
R. Bonciani, A. Ferroglia, T. Gehrmann, A. von Manteuffel and C. Studerus, Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel, JHEP 12 (2013) 038 [arXiv:1309.4450] [INSPIRE].
S.M. Aybat, L.J. Dixon and G.F. Sterman, The Two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev. D 74 (2006) 074004 [hep-ph/0607309] [INSPIRE].
A. Mitov, G.F. Sterman and I. Sung, The Massive Soft Anomalous Dimension Matrix at Two Loops, Phys. Rev. D 79 (2009) 094015 [arXiv:0903.3241] [INSPIRE].
T. Becher and M. Neubert, On the Structure of Infrared Singularities of Gauge-Theory Amplitudes, JHEP 06 (2009) 081 [Erratum JHEP 11 (2013) 024] [arXiv:0903.1126] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev. D 79 (2009) 125004 [Erratum ibid. D 80 (2009) 109901] [arXiv:0904.1021] [INSPIRE].
M. Czakon, A. Mitov and G.F. Sterman, Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log, Phys. Rev. D 80 (2009) 074017 [arXiv:0907.1790] [INSPIRE].
A. Ferroglia, M. Neubert, B.D. Pecjak and L.L. Yang, Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories, JHEP 11 (2009) 062 [arXiv:0908.3676] [INSPIRE].
A. Mitov, G.F. Sterman and I. Sung, Computation of the Soft Anomalous Dimension Matrix in Coordinate Space, Phys. Rev. D 82 (2010) 034020 [arXiv:1005.4646] [INSPIRE].
J.M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [arXiv:1304.1806] [INSPIRE].
R.N. Lee, Reducing differential equations for multiloop master integrals, JHEP 04 (2015) 108 [arXiv:1411.0911] [INSPIRE].
R.N. Lee and A.A. Pomeransky, Normalized Fuchsian form on Riemann sphere and differential equations for multiloop integrals, arXiv:1707.07856 [INSPIRE].
R.N. Lee, A.V. Smirnov and V.A. Smirnov, Solving differential equations for Feynman integrals by expansions near singular points, arXiv:1709.07525 [INSPIRE].
O. Gituliar and V. Magerya, Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form, Comput. Phys. Commun. 219 (2017) 329 [arXiv:1701.04269] [INSPIRE].
M. Prausa, epsilon: A tool to find a canonical basis of master integrals, Comput. Phys. Commun. 219 (2017) 361 [arXiv:1701.00725] [INSPIRE].
C. Meyer, Transforming differential equations of multi-loop Feynman integrals into canonical form, JHEP 04 (2017) 006 [arXiv:1611.01087] [INSPIRE].
C. Meyer, Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA, Comput. Phys. Commun. 222 (2018) 295 [arXiv:1705.06252] [INSPIRE].
J.M. Henn, Lectures on differential equations for Feynman integrals, J. Phys. A 48 (2015) 153001 [arXiv:1412.2296] [INSPIRE].
L. Adams, E. Chaubey and S. Weinzierl, Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms, Phys. Rev. Lett. 118 (2017) 141602 [arXiv:1702.04279] [INSPIRE].
M. Caffo, H. Czyz, S. Laporta and E. Remiddi, The Master differential equations for the two loop sunrise selfmass amplitudes, Nuovo Cim. A 111 (1998) 365 [hep-th/9805118] [INSPIRE].
S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys. B 704 (2005) 349 [hep-ph/0406160] [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998) 497 [arXiv:1105.2076] [INSPIRE].
E.K. Leinartas, Factorization of rational functions of several variables into partial fractions, Soviet Math. 22 (1978) 35.
A. Raichev, Leinartas’s partial fraction decomposition, arXiv:1206.4740.
M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [hep-ph/0511200] [INSPIRE].
H.R.P. Ferguson and D.H. Bailey, Numerical results on relations between fundamental constants using a new algorithm, Math. Comput. 53 (1989) 649.
S. Moch and P. Uwer, XSummer: Transcendental functions and symbolic summation in form, Comput. Phys. Commun. 174 (2006) 759 [math-ph/0508008] [INSPIRE].
P.N. Brown, G.D. Byrne and A.C. Hindmarsh, VODE: A Variable-Coefficient ODE Solver, SIAM J. Sci. Stat. Comput. 10 (1989) 1038.
D.H. Bailey, Y. Hida and X.S. Li, Quad-double/Double-double Computation Package, (2017) http://crd.lbl.gov/∼dhbailey/mpdist/.
W. Bernreuther and A. Brandenburg, Tracing CP-violation in the production of top quark pairs by multiple TeV proton proton collisions, Phys. Rev. D 49 (1994) 4481 [hep-ph/9312210] [INSPIRE].
P. Bärnreuther, M. Czakon and A. Mitov, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to \( q\overline{q}\to t\overline{t}+X \), Phys. Rev. Lett. 109 (2012) 132001 [arXiv:1204.5201] [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].
M. Czakon and A. Mitov, NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction, JHEP 01 (2013) 080 [arXiv:1210.6832] [INSPIRE].
M. Czakon, A. Mitov and S. Moch, Heavy-quark production in massless quark scattering at two loops in QCD, Phys. Lett. B 651 (2007) 147 [arXiv:0705.1975] [INSPIRE].
M. Czakon, A. Mitov and S. Moch, Heavy-quark production in gluon fusion at two loops in QCD, Nucl. Phys. B 798 (2008) 210 [arXiv:0707.4139] [INSPIRE].
D.J. Broadhurst, N. Gray and K. Schilcher, Gauge invariant on-shell Z 2 in QED, QCD and the effective field theory of a static quark, Z. Phys. C 52 (1991) 111 [INSPIRE].
W. Bernreuther and W. Wetzel, Decoupling of Heavy Quarks in the Minimal Subtraction Scheme, Nucl. Phys. B 197 (1982) 228 [Erratum ibid. B 513 (1998) 758] [INSPIRE].
G.P. Korchemsky and A.V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order, Nucl. Phys. B 283 (1987) 342 [INSPIRE].
N. Kidonakis, Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production, Phys. Rev. Lett. 102 (2009) 232003 [arXiv:0903.2561] [INSPIRE].
M. Czakon and P. Fiedler, The soft function for color octet production at threshold, Nucl. Phys. B 879 (2014) 236 [arXiv:1311.2541] [INSPIRE].
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Chen, L., Czakon, M. & Poncelet, R. Polarized double-virtual amplitudes for heavy-quark pair production. J. High Energ. Phys. 2018, 85 (2018). https://doi.org/10.1007/JHEP03(2018)085
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DOI: https://doi.org/10.1007/JHEP03(2018)085