Abstract
We compute the contribution of third generation quarks (t, b) to the two-loop amplitude for on-shell W boson pair production in gluon fusion gg → WW. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
M. Grazzini, S. Kallweit, S. Pozzorini, D. Rathlev and M. Wiesemann, W + W − production at the LHC: fiducial cross sections and distributions in NNLO QCD, JHEP 08 (2016) 140 [arXiv:1605.02716] [INSPIRE].
N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson signal, JHEP 08 (2012) 116 [arXiv:1206.4803] [INSPIRE].
F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ 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: complementary results from H → W W , Phys. Rev. D 89 (2014) 053011 [arXiv:1312.1628] [INSPIRE].
A. Azatov, C. Grojean, A. Paul and E. Salvioni, Taming the off-shell Higgs boson, Zh. Eksp. Teor. Fiz. 147 (2015) 410 [J. Exp. Theor. Phys. 120 (2015) 354] [arXiv:1406.6338] [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].
C. Kao and D.A. Dicus, Production of W + W − from gluon fusion, Phys. Rev. D 43 (1991) 1555 [INSPIRE].
M. Dührssen, K. Jakobs, J.J. van der Bij and P. Marquard, The process gg → WW as a background to the Higgs signal at the LHC, JHEP 05 (2005) 064 [hep-ph/0504006] [INSPIRE].
F. Caola, K. Melnikov, R. Röntsch and L. Tancredi, QCD corrections to ZZ production in gluon fusion at the LHC, Phys. Rev. D 92 (2015) 094028 [arXiv:1509.06734] [INSPIRE].
F. Caola, K. Melnikov, R. Röntsch and L. Tancredi, QCD corrections to W + W − production through gluon fusion, Phys. Lett. B 754 (2016) 275 [arXiv:1511.08617] [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.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].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
P. Maierhöfer, J. Usovitsch and P. Uwer, Kira — A Feynman integral reduction program, Comput. Phys. Commun. 230 (2018) 99 [arXiv:1705.05610] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [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].
E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188] [INSPIRE].
M.L. Czakon and M. Niggetiedt, Exact quark-mass dependence of the Higgs-gluon form factor at three loops in QCD, JHEP 05 (2020) 149 [arXiv:2001.03008] [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].
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].
U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Analytic results for virtual QCD corrections to Higgs production and decay, JHEP 01 (2007) 021 [hep-ph/0611266] [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].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, On γ5 in higher-order QCD calculations and the NNLO evolution of the polarized valence distribution, Phys. Lett. B 748 (2015) 432 [arXiv:1506.04517] [INSPIRE].
S.A. Larin and J.A.M. Vermaseren, The \( {\alpha}_s^3 \) corrections to the Bjorken sum rule for polarized electroproduction and to the Gross-Llewellyn Smith sum rule, Phys. Lett. B 259 (1991) 345 [INSPIRE].
L. Chen, M. Czakon and R. Poncelet, Polarized double-virtual amplitudes for heavy-quark pair production, JHEP 03 (2018) 085 [arXiv:1712.08075] [INSPIRE].
A. Behring and W. Bizoń, Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme, JHEP 01 (2020) 189 [arXiv:1911.11524] [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.
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].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, FeynCalc 9.3: new features and improvements, Comput. Phys. Commun. 256 (2020) 107478 [arXiv:2001.04407] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2020 (2020) 083C01 [INSPIRE].
A.V. Smirnov and V.A. Smirnov, How to choose master integrals, Nucl. Phys. B 960 (2020) 115213 [arXiv:2002.08042] [INSPIRE].
J. Usovitsch, Factorization of denominators in integration-by-parts reductions, arXiv:2002.08173 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, New approach to evaluation of multiloop Feynman integrals: the Gegenbauer polynomial x space technique, Nucl. Phys. B 174 (1980) 345 [INSPIRE].
R. Scharf and J.B. Tausk, Scalar two loop integrals for gauge boson selfenergy diagrams with a massless fermion loop, Nucl. Phys. B 412 (1994) 523 [INSPIRE].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
T. Gehrmann, T. Huber and D. Maître, Two-loop quark and gluon form-factors in dimensional regularisation, Phys. Lett. B 622 (2005) 295 [hep-ph/0507061] [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].
A.V. Smirnov, FIESTA4: optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189 [arXiv:1511.03614] [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].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2009.03742
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Brønnum-Hansen, C., Wang, CY. Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion. J. High Energ. Phys. 2021, 170 (2021). https://doi.org/10.1007/JHEP01(2021)170
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2021)170