Abstract
We present numerical results for the two-loop virtual amplitude entering the NNLO corrections to Higgs boson production in association with a top quark pair at the LHC, focusing, as a proof of concept of our method, on the part of the quark-initiated channel containing loops of massless or massive quarks. Results for the UV renormalised and IR subtracted two-loop amplitude for each colour structure are given at selected phase-space points and visualised in terms of surfaces as a function of two-dimensional slices of the full phase space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
References
ATLAS collaboration, Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector, Phys. Lett. B 784 (2018) 173 [arXiv:1806.00425] [INSPIRE].
CMS collaboration, Observation of \( \textrm{t}\overline{\textrm{t}}H \) production, Phys. Rev. Lett. 120 (2018) 231801 [arXiv:1804.02610] [INSPIRE].
CMS collaboration, Evidence for associated production of a Higgs boson with a top quark pair in final states with electrons, muons, and hadronically decaying τ leptons at \( \sqrt{s} \) = 13 TeV, JHEP 08 (2018) 066 [arXiv:1803.05485] [INSPIRE].
CMS collaboration, Search for CP violation in ttH and tH production in multilepton channels in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, JHEP 07 (2023) 092 [arXiv:2208.02686] [INSPIRE].
ATLAS collaboration, Probing the CP nature of the top-Higgs Yukawa coupling in \( t\overline{t}H \) and tH events with H → \( b\overline{b} \) decays using the ATLAS detector at the LHC, Phys. Lett. B 849 (2024) 138469 [arXiv:2303.05974] [INSPIRE].
Z. Kunszt, Associated Production of Heavy Higgs Boson with Top Quarks, Nucl. Phys. B 247 (1984) 339 [INSPIRE].
J.N. Ng and P. Zakarauskas, A QCD Parton Calculation of Conjoined Production of Higgs Bosons and Heavy Flavors in \( p\overline{p} \) Collision, Phys. Rev. D 29 (1984) 876 [INSPIRE].
W. Beenakker et al., Higgs radiation off top quarks at the Tevatron and the LHC, Phys. Rev. Lett. 87 (2001) 201805 [hep-ph/0107081] [INSPIRE].
L. Reina and S. Dawson, Next-to-leading order results for \( t\overline{t} \) h production at the Tevatron, Phys. Rev. Lett. 87 (2001) 201804 [hep-ph/0107101] [INSPIRE].
W. Beenakker et al., NLO QCD corrections to \( t\overline{t} \) H production in hadron collisions, Nucl. Phys. B 653 (2003) 151 [hep-ph/0211352] [INSPIRE].
S. Dawson, L.H. Orr, L. Reina and D. Wackeroth, Associated top quark Higgs boson production at the LHC, Phys. Rev. D 67 (2003) 071503 [hep-ph/0211438] [INSPIRE].
S. Dawson et al., Associated Higgs production with top quarks at the large hadron collider: NLO QCD corrections, Phys. Rev. D 68 (2003) 034022 [hep-ph/0305087] [INSPIRE].
R. Frederix et al., Scalar and pseudoscalar Higgs production in association with a top-antitop pair, Phys. Lett. B 701 (2011) 427 [arXiv:1104.5613] [INSPIRE].
M.V. Garzelli, A. Kardos, C.G. Papadopoulos and Z. Trocsanyi, Standard Model Higgs boson production in association with a top anti-top pair at NLO with parton showering, EPL 96 (2011) 11001 [arXiv:1108.0387] [INSPIRE].
H.B. Hartanto, B. Jager, L. Reina and D. Wackeroth, Higgs boson production in association with top quarks in the POWHEG BOX, Phys. Rev. D 91 (2015) 094003 [arXiv:1501.04498] [INSPIRE].
S. Frixione et al., Weak corrections to Higgs hadroproduction in association with a top-quark pair, JHEP 09 (2014) 065 [arXiv:1407.0823] [INSPIRE].
Y. Zhang et al., QCD NLO and EW NLO corrections to \( t\overline{t}H \) production with top quark decays at hadron collider, Phys. Lett. B 738 (2014) 1 [arXiv:1407.1110] [INSPIRE].
S. Frixione et al., Electroweak and QCD corrections to top-pair hadroproduction in association with heavy bosons, JHEP 06 (2015) 184 [arXiv:1504.03446] [INSPIRE].
A. Denner and R. Feger, NLO QCD corrections to off-shell top-antitop production with leptonic decays in association with a Higgs boson at the LHC, JHEP 11 (2015) 209 [arXiv:1506.07448] [INSPIRE].
D. Stremmer and M. Worek, Production and decay of the Higgs boson in association with top quarks, JHEP 02 (2022) 196 [arXiv:2111.01427] [INSPIRE].
A. Denner, J.-N. Lang and M. Pellen, Full NLO QCD corrections to off-shell tt¯bb¯ production, Phys. Rev. D 104 (2021) 056018 [arXiv:2008.00918] [INSPIRE].
G. Bevilacqua et al., tt¯bb¯ at the LHC: On the size of off-shell effects and prompt b-jet identification, Phys. Rev. D 107 (2023) 014028 [arXiv:2202.11186] [INSPIRE].
A. Denner, J.-N. Lang, M. Pellen and S. Uccirati, Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC, JHEP 02 (2017) 053 [arXiv:1612.07138] [INSPIRE].
D. Pagani, T. Vitos and M. Zaro, Improving NLO QCD event generators with high-energy EW corrections, arXiv:2309.00452 [INSPIRE].
A. Kulesza, L. Motyka, T. Stebel and V. Theeuwes, Soft gluon resummation for associated \( t\overline{t}H \) production at the LHC, JHEP 03 (2016) 065 [arXiv:1509.02780] [INSPIRE].
A. Broggio et al., Associated production of a top pair and a Higgs boson beyond NLO, JHEP 03 (2016) 124 [arXiv:1510.01914] [INSPIRE].
A. Broggio, A. Ferroglia, B.D. Pecjak and L.L. Yang, NNLL resummation for the associated production of a top pair and a Higgs boson at the LHC, JHEP 02 (2017) 126 [arXiv:1611.00049] [INSPIRE].
A. Kulesza, L. Motyka, T. Stebel and V. Theeuwes, Associated \( t\overline{t}H \) production at the LHC: Theoretical predictions at NLO+NNLL accuracy, Phys. Rev. D 97 (2018) 114007 [arXiv:1704.03363] [INSPIRE].
M. van Beekveld and W. Beenakker, The role of the threshold variable in soft-gluon resummation of the \( t\overline{t}h \) production process, JHEP 05 (2021) 196 [arXiv:2012.09170] [INSPIRE].
W.-L. Ju and L.L. Yang, Resummation of soft and Coulomb corrections for \( t\overline{t}h \) production at the LHC, JHEP 06 (2019) 050 [arXiv:1904.08744] [INSPIRE].
A. Kulesza et al., Associated production of a top quark pair with a heavy electroweak gauge boson at NLO+NNLL accuracy, Eur. Phys. J. C 79 (2019) 249 [arXiv:1812.08622] [INSPIRE].
A. Broggio et al., Top-quark pair hadroproduction in association with a heavy boson at NLO+NNLL including EW corrections, JHEP 08 (2019) 039 [arXiv:1907.04343] [INSPIRE].
P. Azzi et al., Report from Working Group 1: Standard Model Physics at the HL-LHC and HE-LHC, CERN Yellow Rep. Monogr. 7 (2019) 1 [arXiv:1902.04070] [INSPIRE].
S. Catani, I. Fabre, M. Grazzini and S. Kallweit, \( t\overline{t}H \) production at NNLO: the flavour off-diagonal channels, Eur. Phys. J. C 81 (2021) 491 [arXiv:2102.03256] [INSPIRE].
S. Catani, M. Grazzini and A. Torre, Transverse-momentum resummation for heavy-quark hadroproduction, Nucl. Phys. B 890 (2014) 518 [arXiv:1408.4564] [INSPIRE].
S. Catani et al., Higgs Boson Production in Association with a Top-Antitop Quark Pair in Next-to-Next-to-Leading Order QCD, Phys. Rev. Lett. 130 (2023) 111902 [arXiv:2210.07846] [INSPIRE].
J. Chen et al., Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair, JHEP 04 (2022) 025 [arXiv:2202.02913] [INSPIRE].
C. Brancaccio, M. Czakon, T. Generet and M. Krämer, Higgs-boson production in top-quark fragmentation, JHEP 08 (2021) 145 [arXiv:2106.06516] [INSPIRE].
F. Febres Cordero et al., Two-Loop Master Integrals for Leading-Color pp → \( t\overline{t}H \) Amplitudes with a Light-Quark Loop, arXiv:2312.08131 [INSPIRE].
F. Buccioni, P.A. Kreer, X. Liu and L. Tancredi, One loop QCD corrections to gg → \( t\overline{t}H \) at \( \mathcal{O} \)(ϵ2), JHEP 03 (2024) 093 [arXiv:2312.10015] [INSPIRE].
G. Wang, T. Xia, L.L. Yang and X. Ye, Two-loop QCD amplitudes for \( t\overline{t}H \) production from boosted limit, arXiv:2402.00431 [INSPIRE].
K. Hepp, Proof of the Bogolyubov-Parasiuk theorem on renormalization, Commun. Math. Phys. 2 (1966) 301 [INSPIRE].
M. Roth and A. Denner, High-energy approximation of one loop Feynman integrals, Nucl. Phys. B 479 (1996) 495 [hep-ph/9605420] [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].
G. Heinrich, Sector Decomposition, Int. J. Mod. Phys. A 23 (2008) 1457 [arXiv:0803.4177] [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].
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. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [hep-ph/9802376] [INSPIRE].
R. Bonciani et al., 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].
M.K. Mandal, P. Mastrolia, J. Ronca and W.J. Bobadilla Torres, Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD, JHEP 09 (2022) 129 [arXiv:2204.03466] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev. D 79 (2009) 125004 [Erratum ibid. 80 (2009) 109901] [arXiv:0904.1021] [INSPIRE].
V. Magerya, Amplitude library (Alibrary): gluing all the tools needed for computing multi-loop amplitudes in QCD and beyond, https://github.com/magv/alibrary.
P. Nogueira, Automatic Feynman Graph Generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
V. Maheria, Semi- and Fully-Inclusive Phase-Space Integrals at Four Loops, Ph.D. thesis, Hamburg University, Germany (2022) [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
G. Heinrich et al., Numerical scattering amplitudes with pySecDec, Comput. Phys. Commun. 295 (2024) 108956 [arXiv:2305.19768] [INSPIRE].
G. Heinrich et al., Expansion by regions with pySecDec, Comput. Phys. Commun. 273 (2022) 108267 [arXiv:2108.10807] [INSPIRE].
S. Borowka et al., A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec, Comput. Phys. Commun. 240 (2019) 120 [arXiv:1811.11720] [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. Alekhin, J. Blümlein, S. Moch and R. Placakyte, Parton distribution functions, αs, and heavy-quark masses for LHC Run II, Phys. Rev. D 96 (2017) 014011 [arXiv:1701.05838] [INSPIRE].
A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].
R.V. Harlander, S.Y. Klein and M. Lipp, FeynGame, Comput. Phys. Commun. 256 (2020) 107465 [arXiv:2003.00896] [INSPIRE].
R. Harlander, S.Y. Klein and M.C. Schaaf, FeynGame-2.1 – Feynman diagrams made easy, PoS EPS-HEP2023 (2024) 657 [arXiv:2401.12778] [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].
P. Maierhöfer, J. Usovitsch and P. Uwer, Kira — A Feynman integral reduction program, Comput. Phys. Commun. 230 (2018) 99 [arXiv:1705.05610] [INSPIRE].
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods, Comput. Phys. Commun. 266 (2021) 108024 [arXiv:2008.06494] [INSPIRE].
J. Klappert and F. Lange, Reconstructing rational functions with FireFly, Comput. Phys. Commun. 247 (2020) 106951 [arXiv:1904.00009] [INSPIRE].
J. Klappert, S.Y. Klein and F. Lange, Interpolation of dense and sparse rational functions and other improvements in FireFly, Comput. Phys. Commun. 264 (2021) 107968 [arXiv:2004.01463] [INSPIRE].
A. von Manteuffel, E. Panzer and R.M. Schabinger, A quasi-finite basis for multi-loop Feynman integrals, JHEP 02 (2015) 120 [arXiv:1411.7392] [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].
V. Magerya, Rational Tracer: a Tool for Faster Rational Function Reconstruction, arXiv:2211.03572 [INSPIRE].
A. von Manteuffel and R.M. Schabinger, A novel approach to integration by parts reduction, Phys. Lett. B 744 (2015) 101 [arXiv:1406.4513] [INSPIRE].
T. Peraro, Scattering amplitudes over finite fields and multivariate functional reconstruction, JHEP 12 (2016) 030 [arXiv:1608.01902] [INSPIRE].
T. Goda and P. L’Ecuyer, Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights, SIAM J. Sci. Comput. 44 (2022) A2765 [arXiv:2201.09413].
C. Duhr, A. Klemm, C. Nega and L. Tancredi, The ice cone family and iterated integrals for Calabi-Yau varieties, JHEP 02 (2023) 228 [arXiv:2212.09550] [INSPIRE].
D.H. Bailey, X.S. Li and Y. Hida, QD: A Double-Double/Quad-Double Package, (2023), https://doi.org/10.11578/dc.20210416.14, https://www.davidhbailey.com/dhbsoftware/.
J. Richard Shewchuk, Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, Discrete Comput. Geom. 18 (1997) 305.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops, JHEP 01 (2020) 150 [arXiv:1907.13234] [INSPIRE].
M. Hidding, DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions, Comput. Phys. Commun. 269 (2021) 108125 [arXiv:2006.05510] [INSPIRE].
X. Liu and Y.-Q. Ma, AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow, Comput. Phys. Commun. 283 (2023) 108565 [arXiv:2201.11669] [INSPIRE].
GoSam collaboration, Automated One-Loop Calculations with GoSam, Eur. Phys. J. C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].
GoSam collaboration, GOSAM -2.0: a tool for automated one-loop calculations within the Standard Model and beyond, Eur. Phys. J. C 74 (2014) 3001 [arXiv:1404.7096] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
S. Catani, M.H. Seymour and Z. Trocsanyi, Regularization scheme independence and unitarity in QCD cross-sections, Phys. Rev. D 55 (1997) 6819 [hep-ph/9610553] [INSPIRE].
W. Bernreuther and W. Wetzel, Decoupling of Heavy Quarks in the Minimal Subtraction Scheme, Nucl. Phys. B 197 (1982) 228 [INSPIRE].
Acknowledgments
This research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant 396021762 - TRR 257. SJ is supported by a Royal Society University Research Fellowship (Grant URF/R1/201268) and by the U.K. Science and Technology Facilities Council under contract ST/T001011/1.
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: 2402.03301
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
Agarwal, B., Heinrich, G., Jones, S.P. et al. Two-loop amplitudes for \( t\overline{t}H \) production: the quark-initiated Nf-part. J. High Energ. Phys. 2024, 13 (2024). https://doi.org/10.1007/JHEP05(2024)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)013