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

A bstract 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 $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> 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 $$ \Delta {a}_{\mu}^{\textrm{VLL}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mi>VLL</mml:mi> </mml:msubsup> </mml:math> . In the interesting case of large masses and opposite-sign coupling, the lowest-order correlation implies a fixed value of $$ \Delta {a}_{\mu}^{\textrm{VLL}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:msubsup> <mml:mi>a</mml:mi> <mml:mi>μ</mml:mi> <mml:mi>VLL</mml:mi> </mml:msubsup> </mml:math> around 22 . 5 × 10 −10 , while the higher-order corrections significantly reduce this value to the interval (10 . . . 18) × 10 −10 .