Abstract
We compute three-loop corrections to the process gg → HH originating from one-particle reducible diagrams. This requires the computation of two-loop corrections to the gluon-gluon-Higgs vertex with an off-shell gluon. We describe in detail our approach to obtain semi-analytic results for the vertex form factors and present results for the two form factors contributing to Higgs boson pair production.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys. B 309 (1988) 282 [INSPIRE].
T. Plehn, M. Spira and P.M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys. B 479 (1996) 46 [hep-ph/9603205] [INSPIRE].
S. Borowka et al., Higgs Boson Pair Production in Gluon Fusion at Next-to-Leading Order with Full Top-Quark Mass Dependence, Phys. Rev. Lett. 117 (2016) 012001 [Erratum ibid. 117 (2016) 079901] [arXiv:1604.06447] [INSPIRE].
S. Borowka et al., Full top quark mass dependence in Higgs boson pair production at NLO, JHEP 10 (2016) 107 [arXiv:1608.04798] [INSPIRE].
J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, M. Spira and J. Streicher, Gluon fusion into Higgs pairs at NLO QCD and the top mass scheme, Eur. Phys. J. C 79 (2019) 459 [arXiv:1811.05692] [INSPIRE].
L. Bellafronte, G. Degrassi, P.P. Giardino, R. Gröber and M. Vitti, Gluon fusion production at NLO: merging the transverse momentum and the high-energy expansions, JHEP 07 (2022) 069 [arXiv:2202.12157] [INSPIRE].
J. Davies, G. Mishima, K. Schönwald and M. Steinhauser, Analytic approximations of 2 → 2 processes with massive internal particles, JHEP 06 (2023) 063 [arXiv:2302.01356] [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].
G. Degrassi, P.P. Giardino and R. Gröber, On the two-loop virtual QCD corrections to Higgs boson pair production in the Standard Model, Eur. Phys. J. C 76 (2016) 411 [arXiv:1603.00385] [INSPIRE].
J. Davies, G. Mishima, M. Steinhauser and D. Wellmann, Double-Higgs boson production in the high-energy limit: planar master integrals, JHEP 03 (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, JHEP 01 (2019) 176 [arXiv:1811.05489] [INSPIRE].
R. Bonciani, G. Degrassi, P.P. Giardino and R. Gröber, Analytical Method for Next-to-Leading-Order QCD Corrections to Double-Higgs Production, Phys. Rev. Lett. 121 (2018) 162003 [arXiv:1806.11564] [INSPIRE].
R. Gröber, A. Maier and T. Rauh, Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes, JHEP 03 (2018) 020 [arXiv:1709.07799] [INSPIRE].
X. Xu and L.L. Yang, Towards a new approximation for pair-production and associated-production of the Higgs boson, JHEP 01 (2019) 211 [arXiv:1810.12002] [INSPIRE].
G. Wang, Y. Wang, X. Xu, Y. Xu and L.L. Yang, Efficient computation of two-loop amplitudes for Higgs boson pair production, Phys. Rev. D 104 (2021) L051901 [arXiv:2010.15649] [INSPIRE].
J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, J. Ronca and M. Spira, gg → HH: Combined uncertainties, Phys. Rev. D 103 (2021) 056002 [arXiv:2008.11626] [INSPIRE].
E. Bagnaschi, G. Degrassi and R. Gröber, Higgs boson pair production at NLO in the POWHEG approach and the top quark mass uncertainties, Eur. Phys. J. C 83 (2023) 1054 [arXiv:2309.10525] [INSPIRE].
J. Davies and M. Steinhauser, Three-loop form factors for Higgs boson pair production in the large top mass limit, JHEP 10 (2019) 166 [arXiv:1909.01361] [INSPIRE].
J. Davies, F. Herren, G. Mishima and M. Steinhauser, Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit, JHEP 01 (2022) 049 [arXiv:2110.03697] [INSPIRE].
J. Grigo, J. Hoff and M. Steinhauser, Higgs boson pair production: top quark mass effects at NLO and NNLO, Nucl. Phys. B 900 (2015) 412 [arXiv:1508.00909] [INSPIRE].
J. Davies, K. Schönwald and M. Steinhauser, Towards gg → HH at next-to-next-to-leading order: Light-fermionic three-loop corrections, Phys. Lett. B 845 (2023) 138146 [arXiv:2307.04796] [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].
M. Gerlach, F. Herren and M. Lang, tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions, Comput. Phys. Commun. 282 (2023) 108544 [arXiv:2201.05618] [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 the proceedings of the 6th International Workshop on New Computing Techniques in Physics Research: Software Engineering, Artificial Intelligence Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation, Heraklion, Greece, 12–16 April 1999, hep-ph/9905298 [INSPIRE].
B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [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].
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].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
A. von Manteuffel and L. Tancredi, A non-planar two-loop three-point function beyond multiple polylogarithms, JHEP 06 (2017) 127 [arXiv:1701.05905] [INSPIRE].
M. Fael, F. Lange, K. Schönwald and M. Steinhauser, A semi-analytic method to compute Feynman integrals applied to four-loop corrections to the \( \overline{MS} \)-pole quark mass relation, JHEP 09 (2021) 152 [arXiv:2106.05296] [INSPIRE].
M. Fael, F. Lange, K. Schönwald and M. Steinhauser, Massive Vector Form Factors to Three Loops, Phys. Rev. Lett. 128 (2022) 172003 [arXiv:2202.05276] [INSPIRE].
M. Fael, F. Lange, K. Schönwald and M. Steinhauser, Singlet and nonsinglet three-loop massive form factors, Phys. Rev. D 106 (2022) 034029 [arXiv:2207.00027] [INSPIRE].
M. Fael, F. Lange, K. Schönwald and M. Steinhauser, Massive three-loop form factors: Anomaly contribution, Phys. Rev. D 107 (2023) 094017 [arXiv:2302.00693] [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].
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].
R.V. Harlander and K.J. Ozeren, Top mass effects in Higgs production at next-to-next-to-leading order QCD: Virtual corrections, Phys. Lett. B 679 (2009) 467 [arXiv:0907.2997] [INSPIRE].
J. Ablinger, J. Blümlein, P. Marquard, N. Rana and C. Schneider, Automated Solution of First Order Factorizable Systems of Differential Equations in One Variable, Nucl. Phys. B 939 (2019) 253 [arXiv:1810.12261] [INSPIRE].
J. Blümlein and S. Kurth, Harmonic sums and Mellin transforms up to two loop order, Phys. Rev. D 60 (1999) 014018 [hep-ph/9810241] [INSPIRE].
J.A.M. Vermaseren, Harmonic sums, Mellin transforms and integrals, Int. J. Mod. Phys. A 14 (1999) 2037 [hep-ph/9806280] [INSPIRE].
J. Blümlein, Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5, Comput. Phys. Commun. 180 (2009) 2218 [arXiv:0901.3106] [INSPIRE].
J. Ablinger, A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics, MSc Thesis, Johannes Kepler Universität Linz, Linz, Austria (2009) [arXiv:1011.1176] [INSPIRE].
J. Ablinger, J. Blümlein and C. Schneider, Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials, J. Math. Phys. 52 (2011) 102301 [arXiv:1105.6063] [INSPIRE].
J. Ablinger, Computer Algebra Algorithms for Special Functions in Particle Physics, Ph.D. Thesis, Johannes Kepler Universität Linz, Linz, Austria (2012) [arXiv:1305.0687] [INSPIRE].
J. Ablinger, J. Blümlein and C. Schneider, Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers, J. Phys. Conf. Ser. 523 (2014) 012060 [arXiv:1310.5645] [INSPIRE].
J. Ablinger, J. Blümlein and C. Schneider, Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms, J. Math. Phys. 54 (2013) 082301 [arXiv:1302.0378] [INSPIRE].
J. Ablinger, J. Blümlein, C.G. Raab and C. Schneider, Iterated Binomial Sums and their Associated Iterated Integrals, J. Math. Phys. 55 (2014) 112301 [arXiv:1407.1822] [INSPIRE].
J. Ablinger, The package HarmonicSums: Computer Algebra and Analytic aspects of Nested Sums, PoS LL2014 (2014) 019 [arXiv:1407.6180] [INSPIRE].
J. Ablinger, Discovering and Proving Infinite Binomial Sums Identities, Exp. Math. 26 (2016) 62 [arXiv:1507.01703] [INSPIRE].
J. Ablinger, Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic’s Algorithm, PoS RADCOR2017 (2018) 001 [arXiv:1801.01039] [INSPIRE].
C. Schneider, Symbolic summation assists combinatorics, Sémin. Lothar. Comb. 56 (2007) 1.
C. Schneider, Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation, arXiv:2102.01471.
B. Jantzen, A.V. Smirnov and V.A. Smirnov, Expansion by regions: revealing potential and Glauber regions automatically, Eur. Phys. J. C 72 (2012) 2139 [arXiv:1206.0546] [INSPIRE].
C. Schneider, Simplifying Multiple Sums in Difference Fields, in Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider and J. Bluemlein eds., Texts and Monographs in Symbolic Computation, Springer (2013), pp. 325–360 [https://doi.org/10.1007/978-3-7091-1616-6_14] [arXiv:1304.4134] [INSPIRE].
J. Ablinger, J. Blümlein, P. Marquard, N. Rana and C. Schneider, Three loop QCD corrections to heavy quark form factors, in the proceedings of the 19th International Workshop on Advanced Computing and Analysis Techniques in Physics Research: Empowering the revolution: Bringing Machine Learning to High Performance Computing (ACAT 2019), Saas-Fee, Switzerland, 11–15 March 2019, J. Phys. Conf. Ser. 1525 (2020) 012018 [arXiv:1905.03728] [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].
J. Davies, K. Schoenwald, M. Steinhauser and M. Vitti. TTP24-016 Three-loop corrections to Higgs boson pair production: reducible contribution, https://www.ttp.kit.edu/preprints/2024/ttp24-016/.
Acknowledgments
This research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant 396021762 — TRR 257 “Particle Physics Phenomenology after the Higgs Discovery” and has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement 101019620 (ERC Advanced Grant TOPUP). The work of JD is supported by the STFC Consolidated Grant ST/X000699/1.
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: 2405.20372
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
Davies, J., Schönwald, K., Steinhauser, M. et al. Three-loop corrections to Higgs boson pair production: reducible contribution. J. High Energ. Phys. 2024, 96 (2024). https://doi.org/10.1007/JHEP08(2024)096
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2024)096