Muon Anomalous $g -2$ and Gauged $L_μ- L_τ$ Models

Abstract

In this paper we study $Z'$ contribution to $g -2$ of the muon anomalous magnetic dipole moment in gauged $U(1)_{L_μ- L_τ}$ models. Here $L_i$ are the lepton numbers. We find that there are three classes of models which can produce a large value of $g-2$ to account for possible discrepancy between the experimental data and the Standard Model prediction. The three classes are: a) Models with an exact $U(1)_{L_μ- L_τ}$. In these models, $Z'$ is massless. The new gauge interaction coupling $e a/\cosθ_W$ is constrained to be $ 0.8\times 10^{-3} < |a| < 2.24\times 10^{-3}$. b) Models with broken $U(1)_{L_μ- L_τ}$ and the breaking scale is not related to electroweak symmetry breaking scale. The $Z'$ gauge boson is massive. The allowed range of the coupling and the $Z'$ mass are constrained, but $Z'$ mass can be large; And c) The $U(1)_{L_μ-L_τ}$ is broken and the breaking scale is related to the electroweak scale. In this case the $Z'$ mass is constrained to be $\sim 1.2$ GeV. We find that there are interesting experimental signatures in $μ^+μ^-\to μ^+μ^-, τ^+τ^-$ in these models.