Abstract
The renormalization of vacuum expectation value parameters, such as v in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if \( \overline{\mathrm{MS}} \) renormalization conditions are used for mass parameters. The latter is free from gauge dependences, but is prone to very large corrections in \( \overline{\mathrm{MS}} \) schemes, jeopardizing perturbative stability in predictions. In this paper we propose a new scheme for tadpole renormalization, dubbed Gauge-Invariant Vacuum expectation value Scheme (GIVS), which is a hybrid scheme of the two mentioned types, with the benefits of being gauge independent and perturbatively stable. The GIVS is based on the gauge-invariance property of Higgs fields, and the corresponding parameters like v, in non-linear representations of Higgs multiplets. We demonstrate the perturbative stability of the GIVS in the SM by discussing the conversion between on-shell and \( \overline{\mathrm{MS}} \) renormalized masses.
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References
D.A. Ross and J.C. Taylor, Renormalization of a unified theory of weak and electromagnetic interactions, Nucl. Phys. B 51 (1973) 125 [Erratum ibid. 58 (1973) 643] [INSPIRE].
A. Sirlin, Radiative Corrections in the SU(2)L × U(1) Theory: A Simple Renormalization Framework, Phys. Rev. D 22 (1980) 971 [INSPIRE].
K.I. Aoki, Z. Hioki, M. Konuma, R. Kawabe and T. Muta, Electroweak Theory. Framework of On-Shell Renormalization and Study of Higher Order Effects, Prog. Theor. Phys. Suppl. 73 (1982) 1 [INSPIRE].
M. Böhm, H. Spiesberger and W. Hollik, On the One Loop Renormalization of the Electroweak Standard Model and Its Application to Leptonic Processes, Fortsch. Phys. 34 (1986) 687 [INSPIRE].
F. Jegerlehner, Renormalizing the standard model, in Testing the Standard Model — TASI-90: Theoretical Advanced Study Inst. in Elementary Particle Physics, Boulder, Colorado, June 3–29, 1990, vol. C900603, pp. 476–590, (1990).
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].
A. Denner, G. Weiglein and S. Dittmaier, Application of the background field method to the electroweak standard model, Nucl. Phys. B 440 (1995) 95 [hep-ph/9410338] [INSPIRE].
A. Denner and S. Dittmaier, Electroweak Radiative Corrections for Collider Physics, Phys. Rept. 864 (2020) 1 [arXiv:1912.06823] [INSPIRE].
M. Krause, R. Lorenz, M. Mühlleitner, R. Santos and H. Ziesche, Gauge-independent Renormalization of the 2-Higgs-Doublet Model, JHEP 09 (2016) 143 [arXiv:1605.04853] [INSPIRE].
A. Denner, L. Jenniches, J.-N. Lang and C. Sturm, Gauge-independent \( \overline{MS} \) renormalization in the 2HDM, JHEP 09 (2016) 115 [arXiv:1607.07352] [INSPIRE].
A. Denner, S. Dittmaier and J.-N. Lang, Renormalization of mixing angles, JHEP 11 (2018) 104 [arXiv:1808.03466] [INSPIRE].
J. Fleischer and F. Jegerlehner, Radiative Corrections to Higgs Decays in the Extended Weinberg-Salam Model, Phys. Rev. D 23 (1981) 2001 [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].
F. Jegerlehner, M.Y. Kalmykov and B.A. Kniehl, On the difference between the pole and the \( \overline{MS} \) masses of the top quark at the electroweak scale, Phys. Lett. B 722 (2013) 123 [arXiv:1212.4319] [INSPIRE].
B.A. Kniehl, A.F. Pikelner and O.L. Veretin, Two-loop electroweak threshold corrections in the Standard Model, Nucl. Phys. B 896 (2015) 19 [arXiv:1503.02138] [INSPIRE].
A.L. Kataev and V.S. Molokoedov, Notes on interplay of the QCD and EW perturbative corrections to the pole-running top-quark mass ratio, arXiv:2201.12073 [INSPIRE].
L. Altenkamp, S. Dittmaier and H. Rzehak, Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions, JHEP 09 (2017) 134 [arXiv:1704.02645] [INSPIRE].
L. Altenkamp, S. Dittmaier and H. Rzehak, Precision calculations for h → WW/ZZ → 4 fermions in the Two-Higgs-Doublet Model with Prophecy4f, JHEP 03 (2018) 110 [arXiv:1710.07598] [INSPIRE].
B.W. Lee and J. Zinn-Justin, Spontaneously Broken Gauge Symmetries Part 3: Equivalence, Phys. Rev. D 5 (1972) 3155 [INSPIRE].
C. Grosse-Knetter and R. Kögerler, Unitary gauge, Stuckelberg formalism and gauge invariant models for effective lagrangians, Phys. Rev. D 48 (1993) 2865 [hep-ph/9212268] [INSPIRE].
S. Dittmaier and C. Grosse-Knetter, Deriving nondecoupling effects of heavy fields from the path integral: A heavy Higgs field in an SU(2) gauge theory, Phys. Rev. D 52 (1995) 7276 [hep-ph/9501285] [INSPIRE].
S. Dittmaier and C. Grosse-Knetter, Integrating out the standard Higgs field in the path integral, Nucl. Phys. B 459 (1996) 497 [hep-ph/9505266] [INSPIRE].
H. Kluberg-Stern and J.B. Zuber, Ward Identities and Some Clues to the Renormalization of Gauge Invariant Operators, Phys. Rev. D 12 (1975) 467 [INSPIRE].
N.K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].
P. Gambino and P.A. Grassi, The Nielsen identities of the SM and the definition of mass, Phys. Rev. D 62 (2000) 076002 [hep-ph/9907254] [INSPIRE].
S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press, Cambridge, U.K. (2013).
M. Böhm, A. Denner and H. Joos, Gauge theories of the strong and electroweak interaction, Teubner, Germany (2001).
M.D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, Cambridge, U.K. (2014).
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Dittmaier, S., Rzehak, H. Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations. Part I. Standard Model. J. High Energ. Phys. 2022, 125 (2022). https://doi.org/10.1007/JHEP05(2022)125
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DOI: https://doi.org/10.1007/JHEP05(2022)125