Abstract
We compute the top quark contribution to the two-loop amplitude for on-shell Z boson pair production in gluon fusion, gg → ZZ. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision.
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T. Binoth, M. Ciccolini, N. Kauer and M. Krämer, Gluon-induced W-boson pair production at the LHC, JHEP 12 (2006) 046 [hep-ph/0611170] [INSPIRE].
E. W. N. Glover and J. J. van der Bij, Z boson pair production via gluon fusion, Nucl. Phys. B 321 (1989) 561 [INSPIRE].
E. W. N. Glover and J. J. van der Bij, Vector boson pair production via gluon fusion, Phys. Lett. B 219 (1989) 488 [INSPIRE].
F. Caola, J. M. Henn, K. Melnikov, A. V. Smirnov and V. A. Smirnov, Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion, JHEP 06 (2015) 129 [arXiv:1503.08759] [INSPIRE].
A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for gg → V1V2 → 4 leptons, JHEP 06 (2015) 197 [arXiv:1503.08835] [INSPIRE].
K. Melnikov and M. Dowling, Production of two Z-bosons in gluon fusion in the heavy top quark approximation, Phys. Lett. B 744 (2015) 43 [arXiv:1503.01274] [INSPIRE].
J. M. Campbell, R. K. Ellis, M. Czakon and S. Kirchner, Two loop correction to interference in gg → ZZ, JHEP 08 (2016) 011 [arXiv:1605.01380] [INSPIRE].
R. Gröber, A. Maier and T. Rauh, Top quark mass effects in gg → ZZ at two loops and off-shell Higgs boson interference, Phys. Rev. D 100 (2019) 114013 [arXiv:1908.04061] [INSPIRE].
J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, gg → ZZ: analytic two-loop results for the low- and high-energy regions, JHEP 04 (2020) 024 [arXiv:2002.05558] [INSPIRE].
B. Agarwal, S. P. Jones and A. von Manteuffel, Two-loop helicity amplitudes for gg → ZZ with full top-quark mass effects, arXiv:2011.15113 [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. Bogner and S. Weinzierl, Resolution of singularities for multi-loop integrals, Comput. Phys. Commun. 178 (2008) 596 [arXiv:0709.4092] [INSPIRE].
C. Brønnum-Hansen and C.-Y. Wang, Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion, JHEP 01 (2021) 170 [arXiv:2009.03742] [INSPIRE].
X. Liu, Y.-Q. Ma and C.-Y. Wang, A Systematic and Efficient Method to Compute Multi-loop Master Integrals, Phys. Lett. B 779 (2018) 353 [arXiv:1711.09572] [INSPIRE].
X. Liu, Y.-Q. Ma, W. Tao and P. Zhang, Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow, Chin. Phys. C 45 (2021) 013115 [arXiv:2009.07987] [INSPIRE].
B. A. Kniehl and J. H. Kühn, QCD Corrections to the Z Decay Rate, Nucl. Phys. B 329 (1990) 547 [INSPIRE].
G. J. Gounaris, J. Layssac and F. M. Renard, New and standard physics contributions to anomalous Z and gamma selfcouplings, Phys. Rev. D 62 (2000) 073013 [hep-ph/0003143] [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P. M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
R. Harlander and P. Kant, Higgs production and decay: Analytic results at next-to-leading order QCD, JHEP 12 (2005) 015 [hep-ph/0509189] [INSPIRE].
C. Anastasiou, S. Beerli, S. Bucherer, A. Daleo and Z. Kunszt, Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop, JHEP 01 (2007) 082 [hep-ph/0611236] [INSPIRE].
D. J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].
H. D. Politzer, Reliable Perturbative Results for Strong Interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].
K. Melnikov and T. van Ritbergen, The Three loop on-shell renormalization of QCD and QED, Nucl. Phys. B 591 (2000) 515 [hep-ph/0005131] [INSPIRE].
W. Beenakker, S. Dittmaier, M. Krämer, B. Plumper, M. Spira and P.M. Zerwas, NLO QCD corrections to \( t\overline{t}H \) production in hadron collisions, Nucl. Phys. B 653 (2003) 151 [hep-ph/0211352] [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].
S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
J. A. M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
J. Kuipers, T. Ueda and J. A. M. Vermaseren, Code Optimization in FORM, Comput. Phys. Commun. 189 (2015) 1 [arXiv:1310.7007] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
S. A. Larin, The Renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral Reduction with Kira 2.0 and Finite Field Methods, arXiv:2008.06494 [INSPIRE].
G. ’t Hooft and M. J. G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
S. Borowka et al., pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, Comput. Phys. Commun. 222 (2018) 313 [arXiv:1703.09692] [INSPIRE].
S. Borowka, G. Heinrich, S. Jahn, S. P. Jones, M. Kerner and J. Schlenk, A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec, Comput. Phys. Commun. 240 (2019) 120 [arXiv:1811.11720] [INSPIRE].
L. Chen, A prescription for projectors to compute helicity amplitudes in D dimensions, arXiv:1904.00705 [INSPIRE].
T. Ahmed, A. H. Ajjath, L. Chen, P. K. Dhani, P. Mukherjee and V. Ravindran, Polarised Amplitudes and Soft-Virtual Cross Sections for \( b\overline{b} \) → ZH at NNLO in QCD, JHEP 01 (2020) 030 [arXiv:1910.06347] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
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Brønnum-Hansen, C., Wang, CY. Top quark contribution to two-loop helicity amplitudes for Z boson pair production in gluon fusion. J. High Energ. Phys. 2021, 244 (2021). https://doi.org/10.1007/JHEP05(2021)244
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DOI: https://doi.org/10.1007/JHEP05(2021)244