Gauge dependence of tadpole and mass renormalization for a seesaw extended 2HDM

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.