On-shell Mass Renormalisation and RG-improved Effective Potential in Vector-like Lepton Models

We discuss the on-shell mass renormalisation in a class of six vector-like lepton (VLL) extensions of the Standard Model with seesaw-like contributions to the SM lepton masses. The schemes absorb large radiative corrections to the SM lepton masses arising from mixing between the SM and VLLs with up to $5\times5$ mixing matrices and allows for efficient computation of observables and the low-scale $\overline{\text{MS}}$ values of model parameters. We determine and solve the redundancy-free 2-loop renormalisation-group (RG) equations, compute the RG-improved effective potential and study the vacuum instability scales of each of the VLL models. We find rich phase behaviour and parameter regions that show instability scales as low as $10^5$ GeV as well as regions where the one-loop corrections to the input parameters can lead to a stable vacuum.