Abstract
We present the analytic calculation of the two-loop QCD corrections to the decay width of a Higgs boson into a photon and a Z boson. The calculation is carried out using integration-by-parts identities for the reduction to master integrals of the scalar integrals, in terms of which we express the amplitude. The calculation of the master integrals is performed using differential equations applied to a set of functions suitably chosen to be of uniform weight. The final result is expressed in terms of logarithms and polylogarithmic functions Li2, Li3, Li4 and Li2,2.
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References
ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
LHC Higgs Cross section Working Group collaboration, J.R. Andersen et al., Handbook of LHC Higgs cross sections: 3. Higgs properties, arXiv:1307.1347 [INSPIRE].
CMS collaboration, Search for a Higgs boson decaying into a Z and a photon in pp collisions at \( \sqrt{s}=7 \) and 8 TeV, Phys. Lett. B 726 (2013) 587 [arXiv:1307.5515] [INSPIRE].
ATLAS collaboration, Search for Higgs boson decays to a photon and a Z boson in pp collisions at \( \sqrt{s}=7 \) and 8 TeV with the ATLAS detector, Phys. Lett. B 732 (2014) 8 [arXiv:1402.3051] [INSPIRE].
R.N. Cahn, M.S. Chanowitz and N. Fleishon, Higgs particle production by Z → Hγ, Phys. Lett. B 82 (1979) 113 [INSPIRE].
L. Bergstrom and G. Hulth, Induced Higgs couplings to neutral bosons in e + e − collisions, Nucl. Phys. B 259 (1985) 137 [Erratum ibid. B 276 (1986) 744] [INSPIRE].
I. Low, J. Lykken and G. Shaughnessy, Singlet scalars as Higgs imposters at the Large Hadron Collider, Phys. Rev. D 84 (2011) 035027 [arXiv:1105.4587] [INSPIRE].
I. Low, J. Lykken and G. Shaughnessy, Have we observed the Higgs (imposter)?, Phys. Rev. D 86 (2012) 093012 [arXiv:1207.1093] [INSPIRE].
A. Azatov, R. Contino, A. Di Iura and J. Galloway, New prospects for Higgs compositeness in h → Zγ, Phys. Rev. D 88 (2013) 075019 [arXiv:1308.2676] [INSPIRE].
M. Carena, I. Low and C.E.M. Wagner, Implications of a modified Higgs to diphoton decay width, JHEP 08 (2012) 060 [arXiv:1206.1082] [INSPIRE].
C.-W. Chiang and K. Yagyu, Higgs boson decays to γγ and Zγ in models with Higgs extensions, Phys. Rev. D 87 (2013) 033003 [arXiv:1207.1065] [INSPIRE].
C.-S. Chen, C.-Q. Geng, D. Huang and L.-H. Tsai, New scalar contributions to h → Zγ, Phys. Rev. D 87 (2013) 075019 [arXiv:1301.4694] [INSPIRE].
M. Spira, A. Djouadi and P.M. Zerwas, QCD corrections to the HZγ coupling, Phys. Lett. B 276 (1992) 350 [INSPIRE].
M.J.G. Veltman, Diagrammatica: the path to Feynman rules, Cambridge Lect. Notes Phys. 4 (1994) 1 [INSPIRE].
W.A. Bardeen, A.J. Buras, D.W. Duke and T. Muta, Deep inelastic scattering beyond the leading order in asymptotically free gauge theories, Phys. Rev. D 18 (1978) 3998 [INSPIRE].
P. Marquard, A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Quark mass relations to four-loop order in perturbative QCD, Phys. Rev. Lett. 114 (2015) 142002 [arXiv:1502.01030] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
C.G. Bollini and J.J. Giambiagi, Lowest order divergent graphs in ν-dimensional space, Phys. Lett. B 40 (1972) 566 [INSPIRE].
C.G. Bollini and J.J. Giambiagi, Dimensional renormalization: the number of dimensions as a regularizing parameter, Nuovo Cim. B 12 (1972) 20 [INSPIRE].
J.F. Ashmore, A method of gauge invariant regularization, Lett. Nuovo Cim. 4 (1972) 289 [INSPIRE].
G.M. Cicuta and E. Montaldi, Analytic renormalization via continuous space dimension, Lett. Nuovo Cim. 4 (1972) 329 [INSPIRE].
R. Gastmans and R. Meuldermans, Dimensional regularization of the infrared problem, Nucl. Phys. B 63 (1973) 277 [INSPIRE].
A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
A.V. Smirnov and V.A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun. 184 (2013) 2820 [arXiv:1302.5885] [INSPIRE].
A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2014) 182 [arXiv:1408.2372] [INSPIRE].
C. Studerus, Reduze-Feynman integral reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — distributed Feynman integral reduction, arXiv:1201.4330 [INSPIRE].
F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [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].
A.V. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [INSPIRE].
A.V. Kotikov, Differential equations method: the calculation of vertex type Feynman diagrams, Phys. Lett. B 259 (1991) 314 [INSPIRE].
A.V. Kotikov, Differential equation method: the calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123 [INSPIRE].
E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188] [INSPIRE].
M. Caffo, H. Czyz, S. Laporta and E. Remiddi, The master differential equations for the two loop sunrise selfmass amplitudes, Nuovo Cim. A 111 (1998) 365 [hep-th/9805118] [INSPIRE].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
M. Argeri and P. Mastrolia, Feynman diagrams and differential equations, Int. J. Mod. Phys. A 22 (2007) 4375 [arXiv:0707.4037] [INSPIRE].
J.M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (2013) 251601 [arXiv:1304.1806] [INSPIRE].
J.M. Henn and V.A. Smirnov, Analytic results for two-loop master integrals for Bhabha scattering I, JHEP 11 (2013) 041 [arXiv:1307.4083] [INSPIRE].
J.M. Henn, A.V. Smirnov and V.A. Smirnov, Evaluating single-scale and/or non-planar diagrams by differential equations, JHEP 03 (2014) 088 [arXiv:1312.2588] [INSPIRE].
J.M. Henn, K. Melnikov and V.A. Smirnov, Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions, JHEP 05 (2014) 090 [arXiv:1402.7078] [INSPIRE].
F. Caola, J.M. Henn, K. Melnikov and V.A. Smirnov, Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons, JHEP 09 (2014) 043 [arXiv:1404.5590] [INSPIRE].
S. Caron-Huot and J.M. Henn, Iterative structure of finite loop integrals, JHEP 06 (2014) 114 [arXiv:1404.2922] [INSPIRE].
T. Gehrmann, A. von Manteuffel, L. Tancredi and E. Weihs, The two-loop master integrals for \( q\overline{q}\to VV \), JHEP 06 (2014) 032 [arXiv:1404.4853] [INSPIRE].
M. Argeri et al., Magnus and Dyson series for master integrals, JHEP 03 (2014) 082 [arXiv:1401.2979] [INSPIRE].
M. Höschele, J. Hoff and T. Ueda, Adequate bases of phase space master integrals for gg → h at NNLO and beyond, JHEP 09 (2014) 116 [arXiv:1407.4049] [INSPIRE].
F. Dulat and B. Mistlberger, Real-virtual-virtual contributions to the inclusive Higgs cross section at N3LO, arXiv:1411.3586 [INSPIRE].
G. Bell and T. Huber, Master integrals for the two-loop penguin contribution in non-leptonic B-decays, JHEP 12 (2014) 129 [arXiv:1410.2804] [INSPIRE].
T. Huber and S. Kränkl, Two-loop master integrals for non-leptonic heavy-to-heavy decays, JHEP 04 (2015) 140 [arXiv:1503.00735] [INSPIRE].
J.M. Henn, Lectures on differential equations for Feynman integrals, J. Phys. A 48 (2015) 153001 [arXiv:1412.2296] [INSPIRE].
R.N. Lee, Reducing differential equations for multiloop master integrals, JHEP 04 (2015) 108 [arXiv:1411.0911] [INSPIRE].
C. Kurz, Two-loop QCD corrections for the production and decays of Higgs bosons, Diploma Thesis, University of Freiburg, Freiburg Germany December 2005.
K.T. Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977) 831 [INSPIRE].
A.B. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998) 497 [arXiv:1105.2076] [INSPIRE].
D.J. Broadhurst, Massive three-loop Feynman diagrams reducible to SC * primitives of algebras of the sixth root of unity, Eur. Phys. J. C 8 (1999) 311 [hep-th/9803091] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
A.V. Smirnov and M.N. Tentyukov, Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA), Comput. Phys. Commun. 180 (2009) 735 [arXiv:0807.4129] [INSPIRE].
A.V. Smirnov, V.A. Smirnov and M. Tentyukov, FIESTA 2: parallelizeable multiloop numerical calculations, Comput. Phys. Commun. 182 (2011) 790 [arXiv:0912.0158] [INSPIRE].
A.V. Smirnov, FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions, Comput. Phys. Commun. 185 (2014) 2090 [arXiv:1312.3186] [INSPIRE].
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].
A.B. Goncharov, M. Spradlin, C. Vergu and A. Volovich, Classical polylogarithms for amplitudes and Wilson loops, Phys. Rev. Lett. 105 (2010) 151605 [arXiv:1006.5703] [INSPIRE].
F.C.S. Brown, Multiple zeta values and periods of moduli spaces \( {\mathfrak{M}}_{0,n} \), Annales Sci. Ecole Norm. Sup. 42 (2009) 371 [math/0606419] [INSPIRE].
C. Duhr, H. Gangl and J.R. Rhodes, From polygons and symbols to polylogarithmic functions, JHEP 10 (2012) 075 [arXiv:1110.0458] [INSPIRE].
C. Duhr, Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes, JHEP 08 (2012) 043 [arXiv:1203.0454] [INSPIRE].
T. Gehrmann, S. Guns and D. Kara, The rare decay H → Zγ in perturbative QCD, in preparation.
L.-B. Chen, C.-F. Qiao and R.-L. Zhu, Reconstructing the 125 GeV SM Higgs boson through \( \ell \overline{\ell}\gamma \), Phys. Lett. B 726 (2013) 306 [arXiv:1211.6058] [INSPIRE].
D.A. Dicus and W.W. Repko, Calculation of the decay H → eēγ, Phys. Rev. D 87 (2013) 077301 [arXiv:1302.2159] [INSPIRE].
Y. Sun, H.-R. Chang and D.-N. Gao, Higgs decays to gamma ℓ + ℓ − in the standard model, JHEP 05 (2013) 061 [arXiv:1303.2230] [INSPIRE].
G. Passarino, Higgs boson production and decay: Dalitz sector, Phys. Lett. B 727 (2013) 424 [arXiv:1308.0422] [INSPIRE].
D.A. Dicus, C. Kao and W.W. Repko, Comparison of \( H\to \ell \overline{\ell}\gamma \) and \( H\to \gamma Z,Z\to \ell \overline{\ell} \) including the ATLAS cuts, Phys. Rev. D 89 (2014) 033013 [arXiv:1310.4380] [INSPIRE].
J. Kuipers, T. Ueda, J.A.M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].
J. Kublbeck, M. Böhm and A. Denner, Feyn Arts: computer algebraic generation of Feynman graphs and amplitudes, Comput. Phys. Commun. 60 (1990) 165 [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
J.A.M. Vermaseren, Axodraw, Comput. Phys. Commun. 83 (1994) 45 [INSPIRE].
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Bonciani, R., Del Duca, V., Frellesvig, H. et al. Next-to-leading order QCD corrections to the decay width H → Zγ. J. High Energ. Phys. 2015, 108 (2015). https://doi.org/10.1007/JHEP08(2015)108
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DOI: https://doi.org/10.1007/JHEP08(2015)108