On-shell Renormalization with Vector-like Leptons, One-loop Muon-Higgs Coupling and Muon g-2

TL;DR

This paper develops an on-shell renormalization scheme for models with vector-like leptons, calculates the one-loop muon-Higgs coupling, and analyzes its impact on the muon g-2 anomaly, revealing significant higher-order corrections.

Contribution

It introduces a full on-shell renormalization scheme for vector-like lepton models and applies it to compute one-loop effects on muon-Higgs coupling and muon g-2.

Findings

Higher-order corrections reduce the muon g-2 contribution from about 22.5 to 10-18 times 10^{-10}

The scheme clarifies lepton mixing and counterterm determination in such models

Correlation between muon-Higgs coupling and muon g-2 is established at one-loop level.

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 $\overline{\text{MS}}$ 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 $\beta$-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 $\Delta a_\mu^{\text{VLL}}$. In the interesting case of large masses and opposite-sign coupling, the lowest-order correlation implies a fixed value of $\Delta a_\mu^{\text{VLL}}$ around $22.5\times 10^{-10}$, while the higher-order corrections significantly reduce this value to the interval $(10...18)\times 10^{-10}$.