Abstract
We compute next-to-leading order virtual two-loop corrections to the process gg → Z Z in the low- and high-energy limits, considering the contributions with virtual top quarks. Analytic results for all 20 form factors are presented including expansion terms up to \( 1/{m}_t^{12} \) and \( {m}_t^{32} \). We use a Padé approximation procedure to extend the radius of convergence of the high-energy expansion and apply this approach to the finite virtual next-to-leading order corrections.
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ATLAS collaboration, Measurement of Z Z production in the ℓℓνν final state with the ATLAS detector in pp collisions at \( \sqrt{s} \) = 13 TeV, JHEP10 (2019) 127 [arXiv:1905.07163] [INSPIRE].
CMS collaboration, Measurements of the pp → Z Z production cross section and the Z → 4ℓ branching fraction and constraints on anomalous triple gauge couplings at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J.C 78 (2018) 165 [Erratum ibid.C 78 (2018) 515] [arXiv:1709.08601] [INSPIRE].
ATLAS collaboration, Constraints on off-shell Higgs boson production and the Higgs boson total width in Z Z → 4 ℓ and Z Z → 2 ℓ 2ν final states with the ATLAS detector, Phys. Lett.B 786 (2018) 223 [arXiv:1808.01191] [INSPIRE].
CMS collaboration, Measurements of the Higgs boson width and anomalous H V V couplings from on-shell and off-shell production in the four-lepton final state, Phys. Rev.D 99 (2019) 112003 [arXiv:1901.00174] [INSPIRE].
N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson signal, JHEP08 (2012) 116 [arXiv:1206.4803] [INSPIRE].
F. Caola and K. Melnikov, Constraining the Higgs boson width with Z Z production at the LHC, Phys. Rev.D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].
J.M. Campbell, R.K. Ellis and C. Williams, Bounding the Higgs width at the LHC using full analytic results for gg → e−e+μ−μ+ , JHEP04 (2014) 060 [arXiv:1311.3589] [INSPIRE].
F. Cascioli et al., Z Z production at hadron colliders in NNLO QCD, Phys. Lett.B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].
G. Heinrich, S. Jahn, S.P. Jones, M. Kerner and J. Pires, NNLO predictions for Z -boson pair production at the LHC, JHEP03 (2018) 142 [arXiv:1710.06294] [INSPIRE].
T. Gehrmann, A. von Manteuffel, L. Tancredi and E. Weihs, The two-loop master integrals for \( q\overline{q} \)→ V V , JHEP06 (2014) 032 [arXiv:1404.4853] [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 quark-antiquark collisions, JHEP11 (2014) 041 [arXiv:1408.6409] [INSPIRE].
T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for \( q{\overline{q}}^{\prime } \)→ V1V2→ 4 leptons, JHEP09 (2015) 128 [arXiv:1503.04812] [INSPIRE].
M. Grazzini, S. Kallweit and D. Rathlev, Z Z production at the LHC: fiducial cross sections and distributions in NNLO QCD, Phys. Lett.B 750 (2015) 407 [arXiv:1507.06257] [INSPIRE].
S. Kallweit and M. Wiesemann, Z Z production at the LHC: NNLO predictions for 2ℓ 2ν and 4ℓ signatures, Phys. Lett.B 786 (2018) 382 [arXiv:1806.05941] [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].
A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for gg → V1V2→ 4 leptons, JHEP06 (2015) 197 [arXiv:1503.08835] [INSPIRE].
F. Caola, K. Melnikov, R. Röntsch and L. Tancredi, QCD corrections to Z Z production in gluon fusion at the LHC, Phys. Rev.D 92 (2015) 094028 [arXiv:1509.06734] [INSPIRE].
M. Grazzini, S. Kallweit, M. Wiesemann and J.Y. Yook, Z Z production at the LHC: NLO QCD corrections to the loop-induced gluon fusion channel, JHEP03 (2019) 070 [arXiv:1811.09593] [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 → Z Z , JHEP08 (2016) 011 [arXiv:1605.01380] [INSPIRE].
R. Gröber, A. Maier and T. Rauh, Top quark mass effects in gg → Z Z at two loops and off-shell Higgs boson interference, Phys. Rev.D 100 (2019) 114013 [arXiv:1908.04061] [INSPIRE].
R. Harlander and P. Kant, Higgs production and decay: analytic results at next-to-leading order QCD, JHEP12 (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, JHEP01 (2007) 082 [hep-ph/0611236] [INSPIRE].
U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Analytic results for virtual QCD corrections to Higgs production and decay, JHEP01 (2007) 021 [hep-ph/0611266] [INSPIRE].
L.J. Dixon, A brief introduction to modern amplitude methods, in Proceedings, 2012 European School of High-Energy Physics (ESHEP 2012), La Pommeraye, Anjou, France, 6–19 June 2012, CERN-2014-008.31, (2014), pg. 31 [arXiv:1310.5353] [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, JHEP06 (2015) 129 [arXiv:1503.08759] [INSPIRE].
D. Wellmann, Top quark mass effects in Higgs and Z boson pair production and Higgs boson decays, Ph.D. thesis, KIT, Karlsruhe, Germany (2020)
S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
TTP20-006 gg → Z Z : analytic two-loop results for the low- and high-energy region supplementary material, https://www.ttp.kit.edu/preprints/2020/ttp20-006/.
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys.105 (1993) 279 [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun.140 (2001) 418 [hep-ph/0012260] [INSPIRE].
T. Hahn, S. Paßehr and C. Schappacher, FormCalc 9 and extensions, PoS(LL2016)068 (2016) [arXiv:1604.04611] [INSPIRE].
H.H. Patel, Package-X 2.0: a Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun.218 (2017) 66 [arXiv:1612.00009] [INSPIRE].
J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double-Higgs boson production in the high-energy limit: planar master integrals, JHEP03 (2018) 048 [arXiv:1801.09696] [INSPIRE].
J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double Higgs boson production at NLO in the high-energy limit: complete analytic results, JHEP01 (2019) 176 [arXiv:1811.05489] [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser.523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with modular arithmetic, arXiv:1901.07808 [INSPIRE].
D. Maître, Extension of HPL to complex arguments, Comput. Phys. Commun.183 (2012) 846 [hep-ph/0703052] [INSPIRE].
J. Grigo, J. Hoff, K. Melnikov and M. Steinhauser, On the Higgs boson pair production at the LHC, Nucl. Phys.B 875 (2013) 1 [arXiv:1305.7340] [INSPIRE].
R. Harlander, T. Seidensticker and M. Steinhauser, Complete corrections of O(ααs ) to the decay of the Z boson into bottom quarks, Phys. Lett.B 426 (1998) 125 [hep-ph/9712228] [INSPIRE].
T. Seidensticker, Automatic application of successive asymptotic expansions of Feynman diagrams, in 6thInternational Workshop on New Computing Techniques in Physics Research: Software Engineering, Artificial Intelligence Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, 12–16 April 1999 [hep-ph/9905298] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].
J. Davies et al., Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion, JHEP11 (2019) 024 [arXiv:1907.06408] [INSPIRE].
G. Heinrich, S.P. Jones, M. Kerner, G. Luisoni and E. Vryonidou, NLO predictions for Higgs boson pair production with full top quark mass dependence matched to parton showers, JHEP08 (2017) 088 [arXiv:1703.09252] [INSPIRE].
B. Agarwal and A. Von Manteuffel, On the two-loop amplitude for gg → Z Z production with full top-mass dependence, PoS(RADCOR2019)008 (2019) [arXiv:1912.08794] [INSPIRE].
M. Galassi et al., GNU scientific library reference manual, third edition, Network Theory Ltd, (2009) [ISBN:0954612078].
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Davies, J., Mishima, G., Steinhauser, M. et al. gg → Z Z: analytic two-loop results for the low- and high-energy regions. J. High Energ. Phys. 2020, 24 (2020). https://doi.org/10.1007/JHEP04(2020)024
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DOI: https://doi.org/10.1007/JHEP04(2020)024