Standard Model anomalies and vacuum stability for lepton portals with extra $U(1)$ symmetry

TL;DR

This paper explores a lepton portal model with an extra $U(1)'$ symmetry that addresses the muon $(g-2)_$ and $W$ boson mass anomalies, analyzing its vacuum stability and high-energy behavior through renormalization group methods.

Contribution

It introduces a $U(1)'$ lepton portal model explaining anomalies and studies its vacuum stability and perturbativity up to high scales.

Findings

Landau pole around 10-100 TeV in the alignment limit.

Misalignment scenario extends perturbativity up to $10^9$ GeV.

Model can accommodate SM anomalies while maintaining vacuum stability.

Abstract

Recently, the experimental values of the muon $(g-2)_\mu$ and of the $W$ boson mass $m_{_W}$ have both indicated significant deviations from the SM predictions, motivating the exploration of extensions with extra particles and symmetries. We revisit a lepton portal model with $U(1)'$ gauge symmetry where an extra Higgs doublet, a scalar singlet and one $SU(2)_L$ singlet vector-like fermion are introduced. In this model, $(g-2)_\mu$ can be explained by extra one-loop contributions from the vector-like lepton and the $Z'$ boson, whereas $m_{_W}$ can be increased by a tree-level mixing between the $Z$ and $Z'$. Setting the $Z'$ and lepton couplings at low energies to account for the SM anomalies, we perform a Renormalization Group analysis to investigate on the high-energy behaviour of the model, in particular on the issue of vacuum stability. We find that in the alignment limit for the two Higgs doublets, the Landau pole and the scale where perturbativity is lost are of order $10-100\,{\rm TeV}$, not far from the scales experimentally reached so far, and sensibly lower than the stability scale. We show how the Landau pole can be increased up to $\sim10^9\,{\rm GeV}$ in a misaligned scenario where the experimental anomalies are still accommodated and a positive shift of the Higgs quartic coupling to improve stability can be achieved.