Abstract
We extend useful properties of the H → γγ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form — regardless of the nature of the internal particle — still holds at this order. We also present an algorithmic way to renormalise two-loop amplitudes, by locally cancelling the ultraviolet singularities at integrand level, thus allowing a full four-dimensional numerical implementation of the method. Our results are compared with analytic expressions already available in the literature, finding a perfect numerical agreement. The success of this computation plays a crucial role for the development of a fully local four-dimensional framework to compute physical observables at Next-to-Next-to Leading order and beyond.
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References
A. van Hameren, OneLOop: For the evaluation of one-loop scalar functions, Comput. Phys. Commun. 182 (2011) 2427 [arXiv:1007.4716] [INSPIRE].
S. Carrazza, R.K. Ellis and G. Zanderighi, QCDLoop: a comprehensive framework for one-loop scalar integrals, Comput. Phys. Commun. 209 (2016) 134 [arXiv:1605.03181] [INSPIRE].
S. Borowka, G. Heinrich, S.P. Jones, M. Kerner, J. Schlenk and T. Zirke, SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Comput. Phys. Commun. 196 (2015) 470 [arXiv:1502.06595] [INSPIRE].
A.V. Smirnov, FIESTA4: Optimized Feynman integral calculations with GPU support, Comput. Phys. Commun. 204 (2016) 189 [arXiv:1511.03614] [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].
H.-Q. Zheng and D.-D. Wu, First order QCD corrections to the decay of the Higgs boson into two photons, Phys. Rev. D 42 (1990) 3760 [INSPIRE].
A. Djouadi, M. Spira, J.J. van der Bij and P.M. Zerwas, QCD corrections to gamma gamma decays of Higgs particles in the intermediate mass range, Phys. Lett. B 257 (1991) 187 [INSPIRE].
S. Dawson and R.P. Kauffman, QCD corrections to H → γγ, Phys. Rev. D 47 (1993) 1264 [INSPIRE].
J. Fleischer, O.V. Tarasov and V.O. Tarasov, Analytical result for the two loop QCD correction to the decay H → 2γ, Phys. Lett. B 584 (2004) 294 [hep-ph/0401090] [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].
U. Aglietti, R. Bonciani, G. Degrassi and A. Vicini, Two loop light fermion contribution to Higgs production and decays, Phys. Lett. B 595 (2004) 432 [hep-ph/0404071] [INSPIRE].
S. Actis, G. Passarino, C. Sturm and S. Uccirati, NNLO Computational Techniques: The Cases H → γγ and H → gg, Nucl. Phys. B 811 (2009) 182 [arXiv:0809.3667] [INSPIRE].
G. Passarino, C. Sturm and S. Uccirati, Complete Two-Loop Corrections to H → γγ, Phys. Lett. B 655 (2007) 298 [arXiv:0707.1401] [INSPIRE].
G. Degrassi and F. Maltoni, Two-loop electroweak corrections to the Higgs-boson decay H →γγ, Nucl. Phys. B 724 (2005) 183 [hep-ph/0504137] [INSPIRE].
F. Fugel, B.A. Kniehl and M. Steinhauser, Two loop electroweak correction of \( \mathcal{O}\left({G}_F{M}_t^2\right) \) to the Higgs-boson decay into photons, Nucl. Phys. B 702 (2004) 333 [hep-ph/0405232] [INSPIRE].
P. Maierhöfer and P. Marquard, Complete three-loop QCD corrections to the decay H → γγ, Phys. Lett. B 721 (2013) 131 [arXiv:1212.6233] [INSPIRE].
M. Steinhauser, Corrections of O(α 2s ) to the decay of an intermediate mass Higgs boson into two photons, in The Higgs puzzle — what can we learn from LEP-2, LHC, NLC and FMC? Proceedings, Ringberg Workshop, Tegernsee, Germany, December 8-13, 1996, pp. 177-185 (1996) [hep-ph/9612395] [INSPIRE].
C. Anastasiou et al., High precision determination of the gluon fusion Higgs boson cross-section at the LHC, JHEP 05 (2016) 058 [arXiv:1602.00695] [INSPIRE].
M. Bonetti, K. Melnikov and L. Tancredi, Higher order corrections to mixed QCD-EW contributions to Higgs boson production in gluon fusion, Phys. Rev. D 97 (2018) 056017 [Erratum ibid. D 97 (2018) 099906] [arXiv:1801.10403] [INSPIRE].
F. Driencourt-Mangin, G. Rodrigo and G.F.R. Sborlini, Universal dual amplitudes and asymptotic expansions for gg → H and H → γγ in four dimensions, Eur. Phys. J. C 78 (2018) 231 [arXiv:1702.07581] [INSPIRE].
S. Catani, T. Gleisberg, F. Krauss, G. Rodrigo and J.-C. Winter, From loops to trees by-passing Feynman’s theorem, JHEP 09 (2008) 065 [arXiv:0804.3170] [INSPIRE].
I. Bierenbaum, S. Catani, P. Draggiotis and G. Rodrigo, A Tree-Loop Duality Relation at Two Loops and Beyond, JHEP 10 (2010) 073 [arXiv:1007.0194] [INSPIRE].
I. Bierenbaum, S. Buchta, P. Draggiotis, I. Malamos and G. Rodrigo, Tree-Loop Duality Relation beyond simple poles, JHEP 03 (2013) 025 [arXiv:1211.5048] [INSPIRE].
F. Wilczek, Decays of Heavy Vector Mesons Into Higgs Particles, Phys. Rev. Lett. 39 (1977) 1304 [INSPIRE].
H.M. Georgi, S.L. Glashow, M.E. Machacek and D.V. Nanopoulos, Higgs Bosons from Two Gluon Annihilation in Proton Proton Collisions, Phys. Rev. Lett. 40 (1978) 692 [INSPIRE].
T.G. Rizzo, Gluon Final States in Higgs Boson Decay, Phys. Rev. D 22 (1980) 178 [INSPIRE].
J.R. Ellis, M.K. Gaillard and D.V. Nanopoulos, A Phenomenological Profile of the Higgs Boson, Nucl. Phys. B 106 (1976) 292 [INSPIRE].
B.L. Ioffe and V.A. Khoze, What Can Be Expected from Experiments on Colliding e + e − Beams with e Approximately Equal to 100-GeV?, Sov. J. Part. Nucl. 9 (1978) 50 [INSPIRE].
M.A. Shifman, A.I. Vainshtein, M.B. Voloshin and V.I. Zakharov, Low-Energy Theorems for Higgs Boson Couplings to Photons, Sov. J. Nucl. Phys. 30 (1979) 711 [INSPIRE].
S. Becker, C. Reuschle and S. Weinzierl, Numerical NLO QCD calculations, JHEP 12 (2010) 013 [arXiv:1010.4187] [INSPIRE].
G.F.R. Sborlini, F. Driencourt-Mangin, R. Hernandez-Pinto and G. Rodrigo, Four-dimensional unsubtraction from the loop-tree duality, JHEP 08 (2016) 160 [arXiv:1604.06699] [INSPIRE].
G.F.R. Sborlini, F. Driencourt-Mangin and G. Rodrigo, Four-dimensional unsubtraction with massive particles, JHEP 10 (2016) 162 [arXiv:1608.01584] [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].
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].
R.P. Feynman, Quantum theory of gravitation, Acta Phys. Polon. 24 (1963) 697 [INSPIRE].
C. Gnendiger et al., To d, or not to d: recent developments and comparisons of regularization schemes, Eur. Phys. J. C 77 (2017) 471 [arXiv:1705.01827] [INSPIRE].
S. Buchta, G. Chachamis, P. Draggiotis, I. Malamos and G. Rodrigo, On the singular behaviour of scattering amplitudes in quantum field theory, JHEP 11 (2014) 014 [arXiv:1405.7850] [INSPIRE].
S. Buchta, G. Chachamis, P. Draggiotis and G. Rodrigo, Numerical implementation of the loop-tree duality method, Eur. Phys. J. C 77 (2017) 274 [arXiv:1510.00187] [INSPIRE].
R.J. Hernandez-Pinto, G.F.R. Sborlini and G. Rodrigo, Towards gauge theories in four dimensions, JHEP 02 (2016) 044 [arXiv:1506.04617] [INSPIRE].
P. Bolzoni, G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, JHEP 01 (2011) 059 [arXiv:1011.1909] [INSPIRE].
S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys. B 704 (2005) 349 [hep-ph/0406160] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
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Driencourt-Mangin, F., Rodrigo, G., Sborlini, G.F.R. et al. Universal four-dimensional representation of H → γγ at two loops through the Loop-Tree Duality. J. High Energ. Phys. 2019, 143 (2019). https://doi.org/10.1007/JHEP02(2019)143
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DOI: https://doi.org/10.1007/JHEP02(2019)143