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 5×5 mixing matrices and allows for efficient computation of observables and the low-scale MS̄ 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 10⁵ GeV as well as regions where the one-loop corrections to the input parameters can lead to a stable vacuum.