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{mathrm{MS}} renormalization of the parameters of the unbroken theory. However, using a general Rξ 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 ξ-independence. In the latter context, the tadpole contributions figure prominently.
Highlights
In this paper we propose a renormalization scheme for the multi-Higgs-doublet Standard Model
Extensions of the scalar sector play an important role in lepton mass and mixing models
In this paper we have considered an important class of such models, the multi-Higgs-doublet Standard Model (mHDSM), which has an arbitrary number nH of Higgs doublets and an arbitrary number nR of right-handed neutrino singlets with Majorana mass terms
Summary
In this paper we propose a renormalization scheme for the multi-Higgs-doublet Standard Model (mHDSM). Having obtained δ∆k, δΓk, δvk and the counterterm of the scalar one-point function, all ingredients required for the counterterms of the fermion self-energies are at hand and can be determined We demonstrate that these make the neutrino selfenergy Σν and the charged-lepton self-energy Σl finite.. In an n-point function with n ≥ 2 one can either take into account these VEV shifts or, equivalently, include all tadpole diagrams instead, as shown for the SM in [22, 23] We show this explicitly in the mHDSM at the one-loop level for the neutrino and charged-lepton self-energies. In appendix D we convert the loop functions that we use in section 6 to other functions commonly used in the literature
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