Abstract
We study the gauge dependence of the neutrino mass renormalization in a two Higgs doublet model, that is extended with one singlet seesaw neutrino. This model gives only one light neutrino a mass at tree level, while the second light mass is generated at loop level via the interaction with the second Higgs doublet. At one loop level, one neutrino stays massless. We use multiplicative renormalization constants to define counterterms. The renormalized mass parameters are defined as the complex poles of the propagators, using the complex mass scheme for mass renormalization. With this setup, we analytically get the expressions for the neutrino mass counterterms and isolate the gauge dependent part. We show, how relating this gauge dependent part with the tadpole renormalization leads to gauge independent counterterm definitions, hence gauge independent bare masses for neutrinos.
Highlights
Neutrino oscillations are known for more than 30 years [1]
We analytically checked in the complex mass scheme (CMS) or the OS scheme that the gauge dependent term of the mass counterterms for the neutrinos of the GN model comes only from the tadpole contributions, Eq (60), as suggested in [18]
Using multiplicative renormalization constants and the relations between them, shown in Eqs. (44) and (45), we present how the gauge dependence of neutrino mass counterterms can be seen as a contribution coming from δv, the renormalization constant of the vacuum expectation value (VEV) in the usual tadpole renormalization (e.g., [36])
Summary
Neutrino oscillations are known for more than 30 years [1]. They prove that neutrinos are not massless. This radiative mass generation makes it possible to account for both experimentally measured mass differences at one loop level having only one sterile neutrino in the seesaw mechanism. We look at the gauge parameter dependence of the neutrino mass renormalization in this GN model with a CP symmetric 2HDM potential It is proven in general [10], that the position of the complex pole of the propagator is independent of the gauge. In the GN model, we analytically check that the gauge dependent terms for the fermion two point function vanish if the tadpole diagrams are attached to the propagator as discussed in [18]. VI by discussing the cancellation of the gauge dependence of neutrino propagators in the GN model
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