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

Abstract

Abstract 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 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 ∆ a μ 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 ∆ a μ 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.

Keywords

• Higher Order Electroweak Calculations
• Renormalization and Regularization
• Vector-Like Fermions
• Renormalization Group