Three-loop form factors for Higgs boson pair production in the large top mass limit
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Abstract
We consider the virtual corrections to Higgs boson pair production at next-to- next-to-leading order, in the large top quark mass limit. We compute five expansion terms for the box-type form factors and eight expansion terms for the triangle form factor, which serve as useful input for the construction of approximations. We present analytic results for the form factors in the soft-virtual approximation.
From a technical point of view the calculation is quite challenging since huge intermediate expressions are produced. We describe our methods and optimizations to overcome these difficulties, which might be useful for other calculations.
Keywords
NLO Computations QCD PhenomenologyNotes
Open Access
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References
- [1]J. Baglio, A. Djouadi, R. Gröber, M.M. Mühlleitner, J. Quevillon and M. Spira, The measurement of the Higgs self-coupling at the LHC: theoretical status, JHEP04 (2013) 151 [arXiv:1212.5581] [INSPIRE].
- [2]E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys.B 309 (1988) 282 [INSPIRE].
- [3]T. Plehn, M. Spira and P.M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys.B 479 (1996) 46 [Erratum ibid.B 531 (1998) 655] [hep-ph/9603205] [INSPIRE].
- [4]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].
- [5]S. Borowka et al., Full top quark mass dependence in Higgs boson pair production at NLO, JHEP10 (2016) 107 [arXiv:1608.04798] [INSPIRE].ADSCrossRefGoogle Scholar
- [6]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].
- [7]S. Dawson, S. Dittmaier and M. Spira, Neutral Higgs boson pair production at hadron colliders: QCD corrections, Phys. Rev.D 58 (1998) 115012 [hep-ph/9805244] [INSPIRE].
- [8]J. Grigo, K. Melnikov and M. Steinhauser, Virtual corrections to Higgs boson pair production in the large top quark mass limit, Nucl. Phys.B 888 (2014) 17 [arXiv:1408.2422] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [9]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].
- [10]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].
- [11]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].ADSCrossRefGoogle Scholar
- [12]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].ADSCrossRefGoogle Scholar
- [13]J. Davies et al., Double Higgs boson production at NLO: combining the exact numerical result and high-energy expansion, arXiv:1907.06408 [INSPIRE].
- [14]
- [15]F. Maltoni, E. Vryonidou and M. Zaro, Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO, JHEP11 (2014) 079 [arXiv:1408.6542] [INSPIRE].
- [16]R. Gr¨ober, A. Maier and T. Rauh, Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes, JHEP03 (2018) 020 [arXiv:1709.07799] [INSPIRE].
- [17]J. Davies, R. Gröber, A. Maier, T. Rauh and M. Steinhauser, Top quark mass dependence of the Higgs boson-gluon form factor at three loops, Phys. Rev.D 100 (2019) 034017 [arXiv:1906.00982] [INSPIRE].
- [18]R.V. Harlander, M. Prausa and J. Usovitsch, The light-fermion contribution to the exact Higgs-gluon form factor in QCD, arXiv:1907.06957 [INSPIRE].
- [19]D. de Florian and J. Mazzitelli, Two-loop virtual corrections to Higgs pair production, Phys. Lett.B 724 (2013) 306 [arXiv:1305.5206] [INSPIRE].
- [20]D. de Florian and J. Mazzitelli, Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD, Phys. Rev. Lett.111 (2013) 201801 [arXiv:1309.6594] [INSPIRE].ADSCrossRefGoogle Scholar
- [21]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].ADSMathSciNetCrossRefGoogle Scholar
- [22]J. Davies, F. Herren, G. Mishima and M. Steinhauser, Real-virtual corrections to Higgs boson pair production at NNLO: three closed top quark loops, JHEP05 (2019) 157 [arXiv:1904.11998] [INSPIRE].ADSCrossRefGoogle Scholar
- [23]M. Grazzini et al., Higgs boson pair production at NNLO with top quark mass effects, JHEP05 (2018) 059 [arXiv:1803.02463] [INSPIRE].ADSCrossRefGoogle Scholar
- [24]D.Y. Shao, C.S. Li, H.T. Li and J. Wang, Threshold resummation effects in Higgs boson pair production at the LHC, JHEP07 (2013) 169 [arXiv:1301.1245] [INSPIRE].ADSCrossRefGoogle Scholar
- [25]D. de Florian and J. Mazzitelli, Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC, JHEP09 (2015) 053 [arXiv:1505.07122] [INSPIRE].CrossRefGoogle Scholar
- [26]D. de Florian et al., Differential Higgs Boson Pair Production at Next-to-Next-to-Leading Order in QCD, JHEP09 (2016) 151 [arXiv:1606.09519] [INSPIRE].
- [27]D. De Florian and J. Mazzitelli, Soft gluon resummation for Higgs boson pair production including finite Mt effects, JHEP08 (2018) 156 [arXiv:1807.03704] [INSPIRE].ADSCrossRefGoogle Scholar
- [28]P. Banerjee, S. Borowka, P.K. Dhani, T. Gehrmann and V. Ravindran, Two-loop massless QCD corrections to the g + g → H + H four-point amplitude, JHEP11 (2018) 130 [arXiv:1809.05388] [INSPIRE].ADSCrossRefGoogle Scholar
- [29]M. Spira, Effective Multi-Higgs Couplings to Gluons, JHEP10 (2016) 026 [arXiv:1607.05548] [INSPIRE].ADSCrossRefGoogle Scholar
- [30]M. Gerlach, F. Herren and M. Steinhauser, Wilson coefficients for Higgs boson production and decoupling relations to \( \mathcal{O}\left({\alpha}_s^4\right) \), JHEP11 (2018) 141 [arXiv:1809.06787] [INSPIRE].
- [31]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].ADSCrossRefGoogle Scholar
- [32]A. Pak, M. Rogal and M. Steinhauser, Virtual three-loop corrections to Higgs boson production in gluon fusion for finite top quark mass, Phys. Lett.B 679 (2009) 473 [arXiv:0907.2998] [INSPIRE].ADSCrossRefGoogle Scholar
- [33]P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys.105 (1993) 279 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [34]R. Harlander, T. Seidensticker and M. Steinhauser, Complete corrections of O(αα s) to the decay of the Z boson into bottom quarks, Phys. Lett.B 426 (1998) 125 [hep-ph/9712228] [INSPIRE].
- [35]T. Seidensticker, Automatic application of successive asymptotic expansions of Feynman diagrams, hep-ph/9905298 [INSPIRE].
- [36]
- [37]B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].
- [38]V.A. Smirnov, Analytic tools for Feynman integrals, Springer Tracts Mod. Phys.250 (2012) 1 [INSPIRE].MathSciNetCrossRefGoogle Scholar
- [39]T.G. Birthwright, E.W.N. Glover and P. Marquard, Master integrals for massless two-loop vertex diagrams with three offshell legs, JHEP09 (2004) 042 [hep-ph/0407343] [INSPIRE].
- [40]R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP02 (2008) 002 [arXiv:0712.1851] [INSPIRE].ADSCrossRefGoogle Scholar
- [41]F. Chavez and C. Duhr, Three-mass triangle integrals and single-valued polylogarithms, JHEP11 (2012) 114 [arXiv:1209.2722] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
- [42]K.G. Chetyrkin, A closed analytical formula for two loop massive tadpoles with arbitrary tensor numerators, hep-ph/0212040 [INSPIRE].
- [43]M. Steinhauser, MATAD: A program package for the computation of MAssive TADpoles, Comput. Phys. Commun.134 (2001) 335 [hep-ph/0009029] [INSPIRE].
- [44]A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun.189 (2015) 182 [arXiv:1408.2372] [INSPIRE].ADSCrossRefGoogle Scholar
- [45]J. Fleischer and O.V. Tarasov, Calculation of Feynman diagrams from their small momentum expansion, Z. Phys.C 64 (1994) 413 [hep-ph/9403230] [INSPIRE].
- [46]K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to O(α 3 ) and their connection to low-energy theorems, Nucl. Phys.B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].
- [47]S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
- [48]D. de Florian and J. Mazzitelli, A next-to-next-to-leading order calculation of soft-virtual cross sections, JHEP12 (2012) 088 [arXiv:1209.0673] [INSPIRE].CrossRefGoogle Scholar
- [49]
- [50]R. Harlander and P. Kant, Higgs production and decay: Analytic results at next-to-leading order QCD, JHEP12 (2005) 015 [hep-ph/0509189] [INSPIRE].
- [51]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].
- [52]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].