Abstract
We calculate the full set of next-to-leading order (NLO) corrections to h → b\( \overline{b} \) decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-Z mixing, electric charge renormalization, and especially the treatment of tadpoles in SMEFT. In particular, we highlight the role of decoupling relations in eliminating potentially large tadpole corrections to the decay rate in hybrid renormalization schemes which employ the \( \overline{\mathrm{MS}} \) scheme for some Standard Model parameters (such as the b-quark mass and electric charge) and the on-shell scheme for others.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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].
ATLAS, CMS collaboration, 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, Evidence for the spin-0 nature of the Higgs boson using ATLAS data, Phys. Lett.B 726 (2013) 120 [arXiv:1307.1432] [INSPIRE].
ATLAS collaboration, Study of the spin and parity of the Higgs boson in diboson decays with the ATLAS detector, Eur. Phys. J.C 75 (2015) 476 [Erratum ibid.C 76 (2016) 152] [arXiv:1506.05669] [INSPIRE].
ATLAS, CMS collaboration, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s} \) = 7 and 8 TeV, JHEP08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
CMS collaboration, Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state, Phys. Lett.B 775 (2017) 1 [arXiv:1707.00541] [INSPIRE].
CMS collaboration, Combined measurements of Higgs boson couplings in proton-proton collisions at \( \sqrt{s} \) = 13 TeV, Eur. Phys. J.C 79 (2019) 421 [arXiv:1809.10733] [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].
H. Baer et al., The International Linear Collider technical design report — Volume 2: physics, arXiv:1306.6352 [INSPIRE].
M.E. Peskin, Comparison of LHC and ILC capabilities for Higgs boson coupling measurements, arXiv:1207.2516 [INSPIRE].
T. Appelquist and J. Carazzone, Infrared singularities and massive fields, Phys. Rev.D 11 (1975) 2856 [INSPIRE].
C. Arzt, Reduced effective Lagrangians, Phys. Lett.B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys.347 (2016) 363 [arXiv:1507.07240] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485, …: higher dimension operators in the SM EFT, JHEP08 (2017) 016 [arXiv:1512.03433] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Operator bases, S-matrices and their partition functions, JHEP10 (2017) 199 [arXiv:1706.08520] [INSPIRE].
W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys.B 268 (1986) 621 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model Lagrangian, JHEP10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
G. Passarino, NLO inspired effective Lagrangians for Higgs physics, Nucl. Phys.B 868 (2013) 416 [arXiv:1209.5538] [INSPIRE].
M. Ghezzi, R. Gomez-Ambrosio, G. Passarino and S. Uccirati, NLO Higgs effective field theory and κ-framework, JHEP07 (2015) 175 [arXiv:1505.03706] [INSPIRE].
LHC Higgs Cross Section Working Group collaboration, Handbook of LHC Higgs Cross Sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922 [INSPIRE].
G. Passarino and M. Trott, The standard model effective field theory and next to leading order, arXiv:1610.08356 [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators I: formalism and λ dependence, JHEP10 (2013) 087 [arXiv:1308.2627] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators II: Yukawa dependence, JHEP01 (2014) 035 [arXiv:1310.4838] [INSPIRE].
R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the standard model dimension six operators III: gauge coupling dependence and phenomenology, JHEP04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
H. Mebane, N. Greiner, C. Zhang and S. Willenbrock, Constraints on electroweak effective operators at one loop, Phys. Rev.D 88 (2013) 015028 [arXiv:1306.3380] [INSPIRE].
C.-Y. Chen, S. Dawson and C. Zhang, Electroweak effective operators and Higgs physics, Phys. Rev.D 89 (2014) 015016 [arXiv:1311.3107] [INSPIRE].
S. Dawson and A. Ismail, Standard model EFT corrections to Z boson decays, Phys. Rev.D 98 (2018) 093003 [arXiv:1808.05948] [INSPIRE].
C. Hartmann, W. Shepherd and M. Trott, The Z decay width in the SMEFT: y tand λ corrections at one loop, JHEP03 (2017) 060 [arXiv:1611.09879] [INSPIRE].
E. Vryonidou and C. Zhang, Dimension-six electroweak top-loop effects in Higgs production and decay, JHEP08 (2018) 036 [arXiv:1804.09766] [INSPIRE].
J. Baglio, S. Dawson and I.M. Lewis, An NLO QCD effective field theory analysis of W +W −production at the LHC including fermionic operators, Phys. Rev.D 96 (2017) 073003 [arXiv:1708.03332] [INSPIRE].
J. Baglio, S. Dawson and I.M. Lewis, NLO effects in EFT fits to W +W −production at the LHC, Phys. Rev.D 99 (2019) 035029 [arXiv:1812.00214] [INSPIRE].
S. Dawson, P.P. Giardino and A. Ismail, Standard model EFT and the Drell-Yan process at high energy, Phys. Rev.D 99 (2019) 035044 [arXiv:1811.12260] [INSPIRE].
C. Degrande, B. Fuks, K. Mawatari, K. Mimasu and V. Sanz, Electroweak Higgs boson production in the standard model effective field theory beyond leading order in QCD, Eur. Phys. J.C 77 (2017) 262 [arXiv:1609.04833] [INSPIRE].
C. Zhang, Effective field theory approach to top-quark decay at next-to-leading order in QCD, Phys. Rev.D 90 (2014) 014008 [arXiv:1404.1264] [INSPIRE].
C. Zhang and F. Maltoni, Top-quark decay into Higgs boson and a light quark at next-to-leading order in QCD, Phys. Rev.D 88 (2013) 054005 [arXiv:1305.7386] [INSPIRE].
C. Zhang, Single top production at next-to-leading order in the standard model effective field theory, Phys. Rev. Lett.116 (2016) 162002 [arXiv:1601.06163] [INSPIRE].
C. Degrande et al., Single-top associated production with a Z or H boson at the LHC: the SMEFT interpretation, JHEP10 (2018) 005 [arXiv:1804.07773] [INSPIRE].
D. Buarque Franzosi and C. Zhang, Probing the top-quark chromomagnetic dipole moment at next-to-leading order in QCD, Phys. Rev.D 91 (2015) 114010 [arXiv:1503.08841] [INSPIRE].
O. Bessidskaia Bylund et al., Probing top quark neutral couplings in the standard model effective field theory at NLO in QCD, JHEP05 (2016) 052 [arXiv:1601.08193] [INSPIRE].
F. Maltoni, E. Vryonidou and C. Zhang, Higgs production in association with a top-antitop pair in the standard model effective field theory at NLO in QCD, JHEP10 (2016) 123 [arXiv:1607.05330] [INSPIRE].
N. Deutschmann, C. Duhr, F. Maltoni and E. Vryonidou, Gluon-fusion Higgs production in the standard model effective field theory, JHEP12 (2017) 063 [Erratum ibid.02 (2018) 159] [arXiv:1708.00460] [INSPIRE].
R. Grober, M. Muhlleitner, M. Spira and J. Streicher, NLO QCD corrections to Higgs pair production including dimension-6 operators, JHEP09 (2015) 092 [arXiv:1504.06577] [INSPIRE].
T. Neumann and Z.E. Sullivan, Off-shell single-top-quark production in the standard model effective field theory, JHEP06 (2019) 022 [arXiv:1903.11023] [INSPIRE].
D. de Florian, I. Fabre and J. Mazzitelli, Higgs boson pair production at NNLO in QCD including dimension 6 operators, JHEP10 (2017) 215 [arXiv:1704.05700] [INSPIRE].
A. Crivellin, S. Najjari and J. Rosiek, Lepton flavor violation in the standard model with general dimension-six operators, JHEP04 (2014) 167 [arXiv:1312.0634] [INSPIRE].
G.M. Pruna and A. Signer, The μ → eγ decay in a systematic effective field theory approach with dimension 6 operators, JHEP10 (2014) 014 [arXiv:1408.3565] [INSPIRE].
S. Dawson and P.P. Giardino, Higgs decays to ZZ and Zγ in the standard model effective field theory: An NLO analysis, Phys. Rev.D 97 (2018) 093003 [arXiv:1801.01136] [INSPIRE].
C. Hartmann and M. Trott, Higgs decay to two photons at one loop in the standard model effective field theory, Phys. Rev. Lett.115 (2015) 191801 [arXiv:1507.03568] [INSPIRE].
A. Dedes et al., The decay h → γγ in the standard-model effective field theory, JHEP08 (2018) 103 [arXiv:1805.00302] [INSPIRE].
C. Hartmann and M. Trott, On one-loop corrections in the standard model effective field theory; the Γ(h → γ γ) case, JHEP07 (2015) 151 [arXiv:1505.02646] [INSPIRE].
S. Dawson and P.P. Giardino, Electroweak corrections to Higgs boson decays to γγ and W +W −in standard model EFT, Phys. Rev.D 98 (2018) 095005 [arXiv:1807.11504] [INSPIRE].
A. Dedes, K. Suxho and L. Trifyllis, The decay h → Zγ in the standard-model effective field theory, JHEP06 (2019) 115 [arXiv:1903.12046] [INSPIRE].
R. Gauld, B.D. Pecjak and D.J. Scott, One-loop corrections to h → b \( \overline{b} \)and h → τ \( \overline{\tau} \)decays in the standard model dimension-6 EFT: four-fermion operators and the large-m tlimit, JHEP05 (2016) 080 [arXiv:1512.02508] [INSPIRE].
R. Gauld, B.D. Pecjak and D.J. Scott, QCD radiative corrections for h → b \( \overline{b} \)in the standard model dimension-6 EFT, Phys. Rev.D 94 (2016) 074045 [arXiv:1607.06354] [INSPIRE].
J. Fleischer and F. Jegerlehner, Radiative corrections to Higgs decays in the extended Weinberg-Salam model, Phys. Rev.D 23 (1981) 2001 [INSPIRE].
B.A. Kniehl, Radiative corrections for H → f \( \overline{f} \) (γ) in the standard model, Nucl. Phys.B 376 (1992) 3 [INSPIRE].
A. Alloul et al., FeynRules 2.0 — A complete toolbox for tree-level phenomenology, Comput. Phys. Commun.185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun.140 (2001) 418 [hep-ph/0012260] [INSPIRE].
T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun.118 (1999) 153 [hep-ph/9807565] [INSPIRE].
H.H. Patel, Package-X: A Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun.197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys.41 (1993) 307 [arXiv:0709.1075] [INSPIRE].
S. Actis, A. Ferroglia, M. Passera and G. Passarino, Two-loop renormalization in the standard model. Part I: prolegomena, Nucl. Phys.B 777 (2007) 1 [hep-ph/0612122] [INSPIRE].
A. Denner, L. Jenniches, J.-N. Lang and C. Sturm, Gauge-independent \( \overline{MS} \)renormalization in the 2HDM, JHEP09 (2016) 115 [arXiv:1607.07352] [INSPIRE].
A.V. Bednyakov, B.A. Kniehl, A.F. Pikelner and O.L. Veretin, On the b-quark running mass in QCD and the SM, Nucl. Phys.B 916 (2017) 463 [arXiv:1612.00660] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, Phys. Rev.D 98 (2018) 030001 [INSPIRE].
A. Dedes et al., Feynman rules for the standard model effective field theory in R ξ-gauges, JHEP06 (2017) 143 [arXiv:1704.03888] [INSPIRE].
A. Helset, M. Paraskevas and M. Trott, Gauge fixing the standard model effective field theory, Phys. Rev. Lett.120 (2018) 251801 [arXiv:1803.08001] [INSPIRE].
M. Misiak et al., Effective field theories in R ξgauges, JHEP02 (2019) 051 [arXiv:1812.11513] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, CRC press (1993).
G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys.B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].
I. Brivio, Y. Jiang and M. Trott, The SMEFTsim package, theory and tools, JHEP12 (2017) 070 [arXiv:1709.06492] [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: 1904.06358
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Cullen, J.M., Pecjak, B.D. & Scott, D.J. NLO corrections to h → b\( \overline{b} \) decay in SMEFT. J. High Energ. Phys. 2019, 173 (2019). https://doi.org/10.1007/JHEP08(2019)173
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2019)173