On-shell renormalization with vector-like leptons, one-loop muon–Higgs coupling and muon g − 2

Models with vector-like leptons can strongly modify the lepton mass generation mechanism and lead to correlated effects in lepton–Higgs couplings and lepton dipole moments. Here we begin an analysis of higher-order corrections in such models by setting up a renormalization scheme with full on-shell conditions on the lepton self energies, masses and fields. A minimal set of fundamental parameters is renormalized in the $\overline{\mathrm{MS}}$ \( \overline{\textrm{MS}} \) scheme. We provide a detailed discussion of lepton mixing and redundancies at higher orders, show how the relevant counterterms can be obtained from the renormalization conditions, and determine the β-functions corresponding to the scheme. As a first application we calculate the one-loop effective muon–Higgs coupling and analyse its correlation with the muon anomalous magnetic moment $\text{∆}{a}_{\mu }^{\mathrm{VLL}}$ \( \Delta {a}_{\mu}^{\textrm{VLL}} \) . In the interesting case of large masses and opposite-sign coupling, the lowest-order correlation implies a fixed value of $\text{∆}{a}_{\mu }^{\mathrm{VLL}}$ \( \Delta {a}_{\mu}^{\textrm{VLL}} \) around 22.5 × 10⁻¹⁰, while the higher-order corrections significantly reduce this value to the interval (10 . . . 18) × 10⁻¹⁰.