Abstract
We present a fully differential description of a decay of a scalar Higgs boson into massive b-quarks valid at next-to-next-to-leading order (NNLO) in perturbative quan- tum chromodynamics (QCD). We work within the nested soft-collinear subtraction scheme extended to accommodate massive partons. We include the loop-induced contribution in- volving a Higgs coupling to a top quark. We test our calculation against results existing in the literature, comparing the predictions for the total decay width and jet rates.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS and CMS collaborations, Combined measurement of the Higgs boson mass in pp collisions at \( \sqrt{s} \) = 7 and 8 TeV with the ATLAS and CMS experiments, Phys. Rev. Lett.114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].
ATLAS collaboration, Observation of H → b \( \overline{b} \)decays and V H production with the ATLAS detector, Phys. Lett.B 786 (2018) 59 [arXiv:1808.08238] [INSPIRE].
CMS collaboration, Observation of Higgs boson decay to bottom quarks, Phys. Rev. Lett.121 (2018) 121801 [arXiv:1808.08242] [INSPIRE].
E. Braaten and J.P. Leveille, Higgs boson decay and the running mass, Phys. Rev.D 22 (1980) 715 [INSPIRE].
N. Sakai, Perturbative QCD corrections to the hadronic decay width of the Higgs boson, Phys. Rev.D 22 (1980) 2220 [INSPIRE].
P. Janot, First order QED and QCD radiative corrections to Higgs decay into massive fermions, Phys. Lett.B 223 (1989) 110 [INSPIRE].
M. Drees and K.-I. Hikasa, Note on QCD corrections to hadronic Higgs decay, Phys. Lett.B 240 (1990) 455 [Erratum ibid.B 262 (1991) 497] [INSPIRE].
A.L. Kataev and V.T. Kim, The effects of the massless O \( \left({\alpha}_s^2\right) \), O(ααs ), O(α2 ) QCD and QED corrections and of the massive contributions to Γ(H0→ b \( \overline{b} \)), hep-ph/9304282 [INSPIRE].
A.L. Kataev and V.T. Kim, The effects of the QCD corrections to Γ(H0→ b \( \overline{b} \)), Mod. Phys. Lett.A 9 (1994) 1309 [INSPIRE].
P.A. Baikov, K.G. Chetyrkin and J.H. Kühn, Scalar correlator at O \( \left({\alpha}_s^4\right) \), Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett.96 (2006) 012003 [hep-ph/0511063] [INSPIRE].
R. Harlander and M. Steinhauser, Higgs decay to top quarks at O \( \left({\alpha}_s^2\right) \), Phys. Rev.D 56 (1997) 3980 [hep-ph/9704436] [INSPIRE].
S.A. Larin, T. van Ritbergen and J.A.M. Vermaseren, The large top quark mass expansion for Higgs boson decays into bottom quarks and into gluons, Phys. Lett.B 362 (1995) 134 [hep-ph/9506465] [INSPIRE].
K.G. Chetyrkin and A. Kwiatkowski, Second order QCD corrections to scalar and pseudoscalar Higgs decays into massive bottom quarks, Nucl. Phys.B 461 (1996) 3 [hep-ph/9505358] [INSPIRE].
A. Primo, G. Sasso, G. Somogyi and F. Tramontano, Exact top Yukawa corrections to Higgs boson decay into bottom quarks, Phys. Rev.D 99 (2019) 054013 [arXiv:1812.07811] [INSPIRE].
E. Chaubey and S. Weinzierl, Two-loop master integrals for the mixed QCD-electroweak corrections for H → b \( \overline{b} \)through a H t \( \overline{t} \)-coupling, JHEP05 (2019) 185 [arXiv:1904.00382] [INSPIRE].
C. Anastasiou, F. Herzog and A. Lazopoulos, The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, JHEP03 (2012) 035 [arXiv:1110.2368] [INSPIRE].
V. Del Duca, C. Duhr, G. Somogyi, F. Tramontano and Z. Trócsányi, Higgs boson decay into b-quarks at NNLO accuracy, JHEP04 (2015) 036 [arXiv:1501.07226] [INSPIRE].
F. Caola, G. Luisoni, K. Melnikov and R. Röntsch, NNLO QCD corrections to associated W H production and H → b \( \overline{b} \)decay, Phys. Rev.D 97 (2018) 074022 [arXiv:1712.06954] [INSPIRE].
R. Gauld, A. Gehrmann-De Ridder, E.W.N. Glover, A. Huss and I. Majer, Associated production of a Higgs boson decaying into bottom quarks and a weak vector boson decaying leptonically at NNLO in QCD, JHEP10 (2019) 002 [arXiv:1907.05836] [INSPIRE].
R. Mondini, M. Schiavi and C. Williams, N3LO predictions for the decay of the Higgs boson to bottom quarks, JHEP06 (2019) 079 [arXiv:1904.08960] [INSPIRE].
W. Bernreuther, L. Chen and Z.-G. Si, Differential decay rates of CP-even and CP-odd Higgs bosons to top and bottom quarks at NNLO QCD, JHEP07 (2018) 159 [arXiv:1805.06658] [INSPIRE].
G. Ferrera, G. Somogyi and F. Tramontano, Associated production of a Higgs boson decaying into bottom quarks at the LHC in full NNLO QCD, Phys. Lett.B 780 (2018) 346 [arXiv:1705.10304] [INSPIRE].
W. Astill, W. Bizoń, E. Re and G. Zanderighi, NNLOPS accurate associated H Z production with H → b \( \overline{b} \)decay at NLO, JHEP11 (2018) 157 [arXiv:1804.08141] [INSPIRE].
S. Alioli, A. Broggio, S. Kallweit, M.A. Lim and L. Rottoli, Higgsstrahlung at NNLL’+NNLO matched to parton showers in GENEVA, Phys. Rev.D 100 (2019) 096016 [arXiv:1909.02026] [INSPIRE].
F. Granata, J.M. Lindert, C. Oleari and S. Pozzorini, NLO QCD+EW predictions for HV and HV+jet production including parton-shower effects, JHEP09 (2017) 012 [arXiv:1706.03522] [INSPIRE].
F. Caola, K. Melnikov and R. Röntsch, Nested soft-collinear subtractions in NNLO QCD computations, Eur. Phys. J.C 77 (2017) 248 [arXiv:1702.01352] [INSPIRE].
F. Caola, K. Melnikov and R. Röntsch, Analytic results for color-singlet production at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J.C 79 (2019) 386 [arXiv:1902.02081] [INSPIRE].
F. Caola, K. Melnikov and R. Röntsch, Analytic results for decays of color singlets to gg and q \( \overline{q} \)final states at NNLO QCD with the nested soft-collinear subtraction scheme, Eur. Phys. J.C 79 (2019) 1013 [arXiv:1907.05398] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett.B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys.B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE].
M. Czakon and D. Heymes, Four-dimensional formulation of the sector-improved residue subtraction scheme, Nucl. Phys.B 890 (2014) 152 [arXiv:1408.2500] [INSPIRE].
M. Czakon, A. van Hameren, A. Mitov and R. Poncelet, Single-jet inclusive rates with exact color at O \( \left({\alpha}_s^4\right) \), JHEP10 (2019) 262 [arXiv:1907.12911] [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys.B 44 (1972) 189 [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].
C.G. Bollini and J.J. Giambiagi, Dimensional renormalization: the number of dimensions as a regularizing parameter, Nuovo Cim.B 12 (1972) 20 [INSPIRE].
W.J. Marciano and A. Sirlin, Dimensional regularization of infrared divergences, Nucl. Phys.B 88 (1975) 86 [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys.3 (1962) 650 [INSPIRE].
T.D. Lee and M. Nauenberg, Degenerate systems and mass singularities, Phys. Rev.133 (1964) B1549 [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].
C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev.D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE].
T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys.B 693 (2004) 134 [hep-ph/0402265] [INSPIRE].
S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
S. Catani, S. Dittmaier and Z. Trócsányi, One loop singular behavior of QCD and SUSY QCD amplitudes with massive partons, Phys. Lett.B 500 (2001) 149 [hep-ph/0011222] [INSPIRE].
S.M. Aybat, L.J. Dixon and G.F. Sterman, The two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev.D 74 (2006) 074004 [hep-ph/0607309] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of QCD amplitudes with massive partons, Phys. Rev.D 79 (2009) 125004 [Erratum ibid.D 80 (2009) 109901] [arXiv:0904.1021] [INSPIRE].
M. Czakon, A. Mitov and G.F. Sterman, Threshold resummation for top-pair hadroproduction to next-to-next-to-leading log, Phys. Rev.D 80 (2009) 074017 [arXiv:0907.1790] [INSPIRE].
A. Mitov, G.F. Sterman and I. Sung, The massive soft anomalous dimension matrix at two loops, Phys. Rev.D 79 (2009) 094015 [arXiv:0903.3241] [INSPIRE].
A. Ferroglia, M. Neubert, B.D. Pecjak and L.L. Yang, Two-loop divergences of massive scattering amplitudes in non-Abelian gauge theories, JHEP11 (2009) 062 [arXiv:0908.3676] [INSPIRE].
A. Mitov, G.F. Sterman and I. Sung, Computation of the soft anomalous dimension matrix in coordinate space, Phys. Rev.D 82 (2010) 034020 [arXiv:1005.4646] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett.102 (2009) 162001 [Erratum ibid.111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
S. Catani and M.H. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys.B 485 (1997) 291 [Erratum ibid.B 510 (1998) 503] [hep-ph/9605323] [INSPIRE].
D.J. Broadhurst, N. Gray and K. Schilcher, Gauge invariant on-shell Z2in QED, QCD and the effective field theory of a static quark, Z. Phys.C 52 (1991) 111 [INSPIRE].
N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Three loop relation of quark (modified) \( \overline{MS} \)and pole masses, Z. Phys.C 48 (1990) 673 [INSPIRE].
S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys.B 467 (1996) 399 [hep-ph/9512328] [INSPIRE].
S. Frixione, A general approach to jet cross-sections in QCD, Nucl. Phys.B 507 (1997) 295 [hep-ph/9706545] [INSPIRE].
S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross-sections at next-to-leading order, Phys. Lett.B 378 (1996) 287 [hep-ph/9602277] [INSPIRE].
S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys.B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].
L.J. Dixon, Calculating scattering amplitudes efficiently, in QCD and beyond. Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI-95, Boulder, CO, U.S.A., 4–30 June 1995, pg. 539 [hep-ph/9601359] [INSPIRE].
M. Brucherseifer, F. Caola and K. Melnikov, O \( \left({\alpha}_s^2\right) \)corrections to fully-differential top quark decays, JHEP04 (2013) 059 [arXiv:1301.7133] [INSPIRE].
G. Passarino and M.J.G. Veltman, One loop corrections for e+e−annihilation into μ+μ−in the Weinberg model, Nucl. Phys.B 160 (1979) 151 [INSPIRE].
R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP02 (2008) 002 [arXiv:0712.1851] [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].
J. Ablinger et al., Heavy quark form factors at two loops, Phys. Rev.D 97 (2018) 094022 [arXiv:1712.09889] [INSPIRE].
W. Bernreuther, R. Bonciani, T. Gehrmann, R. Heinesch, P. Mastrolia and E. Remiddi, Decays of scalar and pseudoscalar Higgs bosons into fermions: two-loop QCD corrections to the Higgs-quark-antiquark amplitude, Phys. Rev.D 72 (2005) 096002 [hep-ph/0508254] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun.141 (2001) 296 [hep-ph/0107173] [INSPIRE].
J. Gluza, A. Mitov, S. Moch and T. Riemann, The QCD form factor of heavy quarks at NNLO, JHEP07 (2009) 001 [arXiv:0905.1137] [INSPIRE].
K.G. Chetyrkin, J.H. Kühn and M. Steinhauser, RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun.133 (2000) 43 [hep-ph/0004189] [INSPIRE].
F. Herren and M. Steinhauser, Version 3 of RunDec and CRunDec, Comput. Phys. Commun.224 (2018) 333 [arXiv:1703.03751] [INSPIRE].
K.G. Chetyrkin, Correlator of the quark scalar currents and Γtot (H → hadrons) at O \( \left({\alpha}_s^3\right) \)in pQCD, Phys. Lett.B 390 (1997) 309 [hep-ph/9608318] [INSPIRE].
S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and B.R. Webber, New clustering algorithm for multi-jet cross-sections in e+e−annihilation, Phys. Lett.B 269 (1991) 432 [INSPIRE].
M. Cacciari, G.P. Salam and G. Soyez, FastJet user manual, Eur. Phys. J.C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
D.J. Gross and F. Wilczek, Ultraviolet behavior of non-Abelian gauge theories, Phys. Rev. Lett.30 (1973) 1343 [INSPIRE].
H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett.30 (1973) 1346 [INSPIRE].
K. Melnikov and T. van Ritbergen, The three loop on-shell renormalization of QCD and QED, Nucl. Phys.B 591 (2000) 515 [hep-ph/0005131] [INSPIRE].
W. Beenakker, S. Dittmaier, M. Krämer, B. Plumper, M. Spira and P.M. Zerwas, NLO QCD corrections to t \( \overline{t} \)H production in hadron collisions, Nucl. Phys.B 653 (2003) 151 [hep-ph/0211352] [INSPIRE].
M. Czakon, A. Mitov and S. Moch, Heavy-quark production in gluon fusion at two loops in QCD, Nucl. Phys.B 798 (2008) 210 [arXiv:0707.4139] [INSPIRE].
S. Weinberg, Effective gauge theories, Phys. Lett.B 91 (1980) 51 [INSPIRE].
B.A. Ovrut and H.J. Schnitzer, The decoupling theorem and minimal subtraction, Phys. Lett.B 100 (1981) 403 [INSPIRE].
W. Wetzel, Minimal subtraction and the decoupling of heavy quarks for arbitrary values of the gauge parameter, Nucl. Phys.B 196 (1982) 259 [INSPIRE].
W. Bernreuther and W. Wetzel, Decoupling of heavy quarks in the minimal subtraction scheme, Nucl. Phys.B 197 (1982) 228 [Erratum ibid.B 513 (1998) 758] [INSPIRE].
W. Bernreuther, Decoupling of heavy quarks in quantum chromodynamics, Annals Phys.151 (1983) 127 [INSPIRE].
W. Bernreuther, Heavy quark effects on the parameters of quantum chromodynamics defined by minimal subtraction, Z. Phys.C 20 (1983) 331 [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl and M. Steinhauser, Decoupling relations to O \( \left({\alpha}_s^3\right) \)and their connection to low-energy theorems, Nucl. Phys.B 510 (1998) 61 [hep-ph/9708255] [INSPIRE].
M. Gerlach, G. Mishima and M. Steinhauser, Matching coefficients in nonrelativistic QCD to two-loop accuracy, Phys. Rev.D 100 (2019) 054016 [arXiv:1907.08227] [INSPIRE].
K. Melnikov and T.V. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett.B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].
A. Mitov and S. Moch, The singular behavior of massive QCD amplitudes, JHEP05 (2007) 001 [hep-ph/0612149] [INSPIRE].
I. Bierenbaum, M. Czakon and A. Mitov, The singular behavior of one-loop massive QCD amplitudes with one external soft gluon, Nucl. Phys.B 856 (2012) 228 [arXiv:1107.4384] [INSPIRE].
M.L. Czakon and A. Mitov, A simplified expression for the one-loop soft-gluon current with massive fermions, arXiv:1804.02069 [INSPIRE].
S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys.B 570 (2000) 287 [hep-ph/9908523] [INSPIRE].
S. Alioli, P. Nason, C. Oleari and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX, JHEP06 (2010) 043 [arXiv:1002.2581] [INSPIRE].
J. Ablinger, A computer algebra toolbox for harmonic sums related to particle physics, Diploma thesis, Linz U., Linz, Austria (2009) [arXiv:1011.1176] [INSPIRE].
J. Ablinger, Computer algebra algorithms for special functions in particle physics, Ph.D. thesis, Linz U., Linz, Austria (2012) [arXiv:1305.0687] [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, 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, 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, The package HarmonicSums: computer algebra and analytic aspects of nested sums, PoS(LL2014)019 (2014) [arXiv:1407.6180] [INSPIRE].
J. Ablinger, Inverse Mellin transform of holonomic sequences, PoS(LL2016)067 (2016) [arXiv:1606.02845].
J. Ablinger, Computing the inverse Mellin transform of holonomic sequences using Kovacic’s algorithm, PoS(RADCOR2017)069 (2017) [arXiv:1801.01039].
J. Ablinger, Discovering and proving infinite Pochhammer sum identities, arXiv:1902.11001 [INSPIRE].
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
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1911.11524
Electronic supplementary material
ESM 1
(ZIP 1 kb)
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Behring, A., Bizoń, W. Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme. J. High Energ. Phys. 2020, 189 (2020). https://doi.org/10.1007/JHEP01(2020)189
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2020)189