Renormalization of the multi-Higgs-doublet Standard Model and one-loop lepton mass corrections

TL;DR

This paper develops a renormalization scheme for the multi-Higgs-doublet Standard Model with right-handed neutrinos, addressing one-loop lepton mass corrections, VEV shifts, and gauge independence to ensure finite, physical results.

Contribution

It introduces a comprehensive renormalization approach that includes VEV shifts and tadpole contributions, ensuring finiteness and gauge independence in one-loop lepton mass calculations.

Findings

Finite, gauge-independent one-loop lepton masses achieved.

Renormalization of VEVs and tadpole contributions are essential.

Physical masses depend on renormalized parameters and VEVs.

Abstract

Motivated by models for neutrino masses and lepton mixing, we consider the renormalization of the lepton sector of a general multi-Higgs-doublet Standard Model with an arbitrary number of right-handed neutrino singlets. We propose to make the theory finite by $\overline{\mbox{MS}}$ renormalization of the parameters of the unbroken theory. However, using a general $R_\xi$ gauge, in the explicit one-loop computations of one-point and two-point functions it becomes clear that---in addition---a renormalization of the vacuum expectation values (VEVs) is necessary. Moreover, in order to ensure vanishing one-point functions of the physical scalar mass eigenfields, finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, are required. As a consequence of our renormalization scheme, physical masses are functions of the renormalized parameters and VEVs and thus derived quantities. Applying our scheme to one-loop corrections of lepton masses, we perform a thorough discussion of finiteness and $\xi$-independence. In the latter context, the tadpole contributions figure prominently.