Abstract
Precision flavour observables play an important role in the interpretation of results at the LHC in terms of models of new physics. We present the result for the one-loop Z penguin in generic extensions of the standard model which exhibit exact perturbative unitarity. We use Slavnov-Taylor identities to study the implications of unitarity on the renormalisation of the Z penguin, and derive a manifestly finite result that depends on a reduced set of physical couplings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.H. Llewellyn Smith, High-energy behavior and gauge symmetry, Phys. Lett.B 46 (1973) 233 [INSPIRE].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Uniqueness of spontaneously broken gauge theories, Phys. Rev. Lett.30 (1973) 1268 [Erratum ibid.31 (1973) 572] [INSPIRE].
J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of gauge invariance from high-energy unitarity bounds on the s matrix, Phys. Rev.D 10 (1974) 1145 [Erratum ibid.D 11 (1975) 972] [INSPIRE].
B.W. Lee, C. Quigg and H.B. Thacker, Weak interactions at very high-energies: the role of the Higgs boson mass, Phys. Rev.D 16 (1977) 1519 [INSPIRE].
M.S. Chanowitz, M.A. Furman and I. Hinchliffe, Weak interactions of ultraheavy fermions, Phys. Lett.B 78 (1978) 285 [INSPIRE].
M.S. Chanowitz, M.A. Furman and I. Hinchliffe, Weak interactions of ultraheavy fermions. 2, Nucl. Phys.B 153 (1979) 402 [INSPIRE].
H.A. Weldon, The effects of multiple Higgs bosons on tree unitarity, Phys. Rev.D 30 (1984) 1547 [INSPIRE].
P. Langacker and H.A. Weldon, A mass sum rule for Higgs bosons in arbitrary models, Phys. Rev. Lett.52 (1984) 1377 [INSPIRE].
J.F. Gunion, H.E. Haber and J. Wudka, Sum rules for Higgs bosons, Phys. Rev.D 43 (1991) 904 [INSPIRE].
K.S. Babu, J. Julio and Y. Zhang, Perturbative unitarity constraints on general W ′ models and collider implications, Nucl. Phys.B 858 (2012) 468 [arXiv:1111.5021] [INSPIRE].
B. Grinstein, C.W. Murphy, D. Pirtskhalava and P. Uttayarat, Theoretical constraints on additional Higgs bosons in light of the 126 GeV Higgs, JHEP05 (2014) 083 [arXiv:1401.0070] [INSPIRE].
H.-C. Cheng and I. Low, TeV symmetry and the little hierarchy problem, JHEP09 (2003) 051 [hep-ph/0308199] [INSPIRE].
C. Bobeth, M. Misiak and J. Urban, Matching conditions for b → sγ and b → sgluon in extensions of the Standard Model, Nucl. Phys.B 567 (2000) 153 [hep-ph/9904413] [INSPIRE].
A.J. Buras and J. Girrbach, Completing NLO QCD corrections for tree level non-leptonic ΔF = 1 decays beyond the Standard Model, JHEP02 (2012) 143 [arXiv:1201.2563] [INSPIRE].
A.J. Buras and J. Girrbach, Complete NLO QCD corrections for tree level ΔF = 2 FCNC processes, JHEP03 (2012) 052 [arXiv:1201.1302] [INSPIRE].
M.S. Chanowitz and M.K. Gaillard, The TeV physics of strongly interacting W ’s and Z’s, Nucl. Phys.B 261 (1985) 379 [INSPIRE].
G.J. Gounaris, R. Kogerler and H. Neufeld, Relationship between longitudinally polarized vector bosons and their unphysical scalar partners, Phys. Rev.D 34 (1986) 3257 [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun.140 (2001) 418 [hep-ph/0012260] [INSPIRE].
C. Becchi, A. Rouet and R. Stora, Renormalization of gauge theories, Annals Phys.98 (1976) 287 [INSPIRE].
I.V. Tyutin, Gauge invariance in field theory and statistical physics in operator formalism, arXiv:0812.0580 [INSPIRE].
K. Fujikawa, B.W. Lee and A.I. Sanda, Generalized renormalizable gauge formulation of spontaneously broken gauge theories, Phys. Rev.D 6 (1972) 2923 [INSPIRE].
H.-J. He, Y.-P. Kuang and C.-P. Yuan, Equivalence theorem and probing the electroweak symmetry breaking sector, Phys. Rev.D 51 (1995) 6463 [hep-ph/9410400] [INSPIRE].
Y.-P. Yao and C.P. Yuan, Modification of the equivalence theorem due to loop corrections, Phys. Rev.D 38 (1988) 2237 [INSPIRE].
P. Gambino, P.A. Grassi and F. Madricardo, Fermion mixing renormalization and gauge invariance, Phys. Lett.B 454 (1999) 98 [hep-ph/9811470] [INSPIRE].
G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys.68 (1996) 1125 [hep-ph/9512380] [INSPIRE].
T. Inami and C.S. Lim, Effects of superheavy quarks and leptons in low-energy weak processes K L → μ \( \overline{\mu} \), K + → π+ν\( \overline{v} \)and K 0 ↔ \( \overline{K} \) 0, Prog. Theor. Phys.65 (1981) 297 [Erratum ibid.65 (1981) 1772] [INSPIRE].
J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs hunter’s guide, Front. Phys.80 (2000) 1 [INSPIRE].
G. Buchalla, A.J. Buras, M.K. Harlander, M.E. Lautenbacher and C. Salazar, Renormalization group analysis of charged Higgs effects in ϵ′/ϵ for a heavy top quark, Nucl. Phys.B 355 (1991) 305 [INSPIRE].
F. del Aguila, M. Pérez-Victoria and J. Santiago, Observable contributions of new exotic quarks to quark mixing, JHEP09 (2000) 011 [hep-ph/0007316] [INSPIRE].
G.C. Branco, L. Lavoura and J.P. Silva, CP violation, Int. Ser. Monogr. Phys.103 (1999) 1 [INSPIRE].
M.R. Ahmady, M. Nagashima and A. Sugamoto, Inclusive dileptonic rare B decays with an extra generation of vector-like quarks, Phys. Rev.D 64 (2001) 054011 [hep-ph/0105049] [INSPIRE].
J.A. Aguilar-Saavedra, A minimal set of top anomalous couplings, Nucl. Phys.B 812 (2009) 181 [arXiv:0811.3842] [INSPIRE].
J. Brod, A. Greljo, E. Stamou and P. Uttayarat, Probing anomalous t \( \overline{t} \)Z interactions with rare meson decays, JHEP02 (2015) 141 [arXiv:1408.0792] [INSPIRE].
J. Rosiek, Complete set of Feynman rules for the MSSM: erratum, hep-ph/9511250 [INSPIRE].
A.J. Buras, P. Gambino, M. Gorbahn, S. Jager and L. Silvestrini, ϵ′/ϵ and rare K and B decays in the MSSM, Nucl. Phys.B 592 (2001) 55 [hep-ph/0007313] [INSPIRE].
C.C. Nishi, Simple derivation of general Fierz-like identities, Am. J. Phys.73 (2005) 1160 [hep-ph/0412245] [INSPIRE].
M. Gorbahn, S. Jager, U. Nierste and S. Trine, The supersymmetric Higgs sector and B- \( \overline{B} \)mixing for large tan β, Phys. Rev.D 84 (2011) 034030 [arXiv:0901.2065] [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: 1903.05116
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
Brod, J., Gorbahn, M. The Z penguin in generic extensions of the Standard Model. J. High Energ. Phys. 2019, 27 (2019). https://doi.org/10.1007/JHEP09(2019)027
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2019)027