Abstract
A recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories — called Gauge-Invariant Vacuum expectation value Scheme (GIVS) — is applied to a singlet Higgs extension of the Standard Model and to the Two-Higgs Doublet Model. In contrast to previously used tadpole schemes, the GIVS unifies the gauge-invariance property with perturbative stability. For the Standard Model this was demonstrated for the conversion between on-shell and \( \overline{\mathrm{MS}} \) renormalized masses, where the GIVS leads to very moderate, gauge-independent electroweak corrections. In models with extended scalar sectors, issues with tadpole renormalization exist if Higgs mixing angles are renormalized with \( \overline{\mathrm{MS}} \) conditions, which is the major subject of this article. In detail, we first formulate non-linear representations of the extended scalar sectors, which is an interesting subject in its own right. Then we formulate the GIVS which employs these non-linear representations in the calculation of the tadpole renormalization constants, while actual higher-order calculations in the GIVS proceed in linear representations as usual. Finally, for the considered models we discuss the next-to-leading-order (electroweak and QCD) corrections to the decay processes h/H → WW/ZZ → 4 fermions of the CP-even neutral Higgs bosons h and H using \( \overline{\mathrm{MS}} \)-renormalized Higgs mixing angles with the GIVS and previously used tadpole treatments.
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Dittmaier, S., Rzehak, H. Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations. Part II. Extended Higgs sectors. J. High Energ. Phys. 2022, 245 (2022). https://doi.org/10.1007/JHEP08(2022)245
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DOI: https://doi.org/10.1007/JHEP08(2022)245