Abstract
We calculate a set of one-loop corrections to h → \( b\overline{b} \) and h → \( \tau \overline{\tau} \) decays in the dimension-6 Standard Model effective field theory (SMEFT). In particular, working in the limit of vanishing gauge couplings, we calculate directly in the broken phase of the theory all large logarithmic corrections and in addition the finite corrections in the large-m t limit. Moreover, we give exact results for one-loop contributions from four-fermion operators. We obtain these corrections within an extension of the widely used on-shell renormalisation scheme appropriate for SMEFT calculations, and show explicitly how UV divergent bare amplitudes from a total of 21 different SMEFT operators are rendered finite within this scheme. As a by-product of the calculation, we also compute to one-loop order the logarithmically enhanced and finite large-m t corrections to muon decay in the limit of vanishing gauge couplings, which is necessary to implement the G F input parameter scheme within the SMEFT.
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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].
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].
S. Bolognesi et al., On the spin and parity of a single-produced resonance at the LHC, Phys. Rev. D 86 (2012) 095031 [arXiv:1208.4018] [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, Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at \( \sqrt{s} \) = 7 and 8 TeV in the ATLAS experiment, Eur. Phys. J. C 76 (2016) 6 [arXiv:1507.04548] [INSPIRE].
CMS collaboration, Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV, Eur. Phys. J. C 75 (2015) 212 [arXiv:1412.8662] [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, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
J. Ellis and T. You, Sensitivities of Prospective Future e + e − Colliders to Decoupled New Physics, JHEP 03 (2016) 089 [arXiv:1510.04561] [INSPIRE].
E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence, JHEP 10 (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, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].
J. Elias-Miró, J.R. Espinosa, E. Masso and A. Pomarol, Renormalization of dimension-six operators relevant for the Higgs decays h → γγ, γZ, JHEP 08 (2013) 033 [arXiv:1302.5661] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through D = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [INSPIRE].
J. Elias-Miró, C. Grojean, R.S. Gupta and D. Marzocca, Scaling and tuning of EW and Higgs observables, JHEP 05 (2014) 019 [arXiv:1312.2928] [INSPIRE].
R. Alonso, H.-M. Chang, E.E. Jenkins, A.V. Manohar and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734 (2014) 302 [arXiv:1405.0486] [INSPIRE].
G. Passarino, NLO Inspired Effective Lagrangians for Higgs Physics, Nucl. Phys. B 868 (2013) 416 [arXiv:1209.5538] [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].
C. Grojean, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization Group Scaling of Higgs Operators and Γ(h → γγ), JHEP 04 (2013) 016 [arXiv:1301.2588] [INSPIRE].
C. Englert and M. Spannowsky, Effective Theories and Measurements at Colliders, Phys. Lett. B 740 (2015) 8 [arXiv:1408.5147] [INSPIRE].
C. Zhang, Effective approach to top-quark decay and FCNC processes at NLO accuracy, J. Phys. Conf. Ser. 556 (2014) 012030 [arXiv:1410.2825] [INSPIRE].
G.M. Pruna and A. Signer, The μ → eγ decay in a systematic effective field theory approach with dimension 6 operators, JHEP 10 (2014) 014 [arXiv:1408.3565] [INSPIRE].
B. Henning, X. Lu and H. Murayama, How to use the Standard Model effective field theory, JHEP 01 (2016) 023 [arXiv:1412.1837] [INSPIRE].
M. Ghezzi, R. Gomez-Ambrosio, G. Passarino and S. Uccirati, NLO Higgs effective field theory and κ-framework, JHEP 07 (2015) 175 [arXiv:1505.03706] [INSPIRE].
A. David and G. Passarino, Through precision straits to next standard model heights, Rev. Phys. 1 (2016) 13 [arXiv:1510.00414] [INSPIRE].
R. Grober, M. Muhlleitner, M. Spira and J. Streicher, NLO QCD Corrections to Higgs Pair Production including Dimension-6 Operators, JHEP 09 (2015) 092 [arXiv:1504.06577] [INSPIRE].
C. Hartmann and M. Trott, On one-loop corrections in the standard model effective field theory; the Γ(h → γ γ) case, JHEP 07 (2015) 151 [arXiv:1505.02646] [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. 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].
R. Gauld, B.D. Pecjak and D. Scott, Radiative corrections to h → \( b\overline{b} \) and h → \( \tau \overline{\tau} \) decays in the Standard Model Dimension-6 EFT: gauge coupling dependence, in progress.
B.A. Kniehl, Radiative corrections for H → f \( \overline{f} \)¯(γ) in the standard model, Nucl. Phys. B 376 (1992) 3 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-Six Terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
R. Harnik, J. Kopp and J. Zupan, Flavor Violating Higgs Decays, JHEP 03 (2013) 026 [arXiv:1209.1397] [INSPIRE].
CMS collaboration, Search for Lepton-Flavour-Violating Decays of the Higgs Boson, Phys. Lett. B 749 (2015) 337 [arXiv:1502.07400] [INSPIRE].
R.S. Chivukula and H. Georgi, Composite Technicolor Standard Model, Phys. Lett. B 188 (1987) 99 [INSPIRE].
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].
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
B.A. Kniehl and A. Pilaftsis, Mixing renormalization in Majorana neutrino theories, Nucl. Phys. B 474 (1996) 286 [hep-ph/9601390] [INSPIRE].
A. Sirlin, Radiative Corrections in the SU(2) L × U(1) Theory: A Simple Renormalization Framework, Phys. Rev. D 22 (1980) 971 [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].
A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, 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].
M. Butenschoen, F. Fugel and B.A. Kniehl, \( \mathcal{O}\left({G}_F^2{m}_t^4\right) \) two-loop electroweak correction to Higgs-boson decay to bottom quarks, Nucl. Phys. B 772 (2007) 25 [hep-ph/0702215] [INSPIRE].
CMS and ATLAS collaborations, 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, CMS-PAS-HIG-15-002 (2015).
S. Dawson et al., Working Group Report: Higgs Boson, arXiv:1310.8361 [INSPIRE].
H. Baer et al., The International Linear Collider Technical Design Report — Volume 2: Physics, arXiv:1306.6352 [INSPIRE].
K. Fujii et al., Physics Case for the International Linear Collider, arXiv:1506.05992 [INSPIRE].
TLEP Design Study Working Group collaboration, M. Bicer et al., First Look at the Physics Case of TLEP, JHEP 01 (2014) 164 [arXiv:1308.6176] [INSPIRE].
J. Fan, M. Reece and L.-T. Wang, Possible Futures of Electroweak Precision: ILC, FCC-ee and CEPC, JHEP 09 (2015) 196 [arXiv:1411.1054] [INSPIRE].
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Gauld, R., Pecjak, B.D. & Scott, D.J. One-loop corrections to h → \( b\overline{b} \) and h → \( \tau \overline{\tau} \) decays in the Standard Model dimension-6 EFT: four-fermion operators and the large-m t limit. J. High Energ. Phys. 2016, 80 (2016). https://doi.org/10.1007/JHEP05(2016)080
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DOI: https://doi.org/10.1007/JHEP05(2016)080