Muon Anomalous $g-2$ and Gauged $L_{\mu }-L_{\tau }$ Models

Abstract

In this paper we study $Z^{\prime }$ contribution to $g-2$ of the muon anomalous magnetic dipole moment in gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ 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 $U(1{)}_{L_{\mu }-L_{\tau }}$. In these models, $Z^{\prime }$ is massless. The new gauge interaction coupling $ea/\cos {\theta }_W$ is constrained to be $0.8\times 10^{-3}<|a|<2.24\times 10^{-3}$. b) Models with broken $U(1{)}_{L_{\mu }-L_{\tau }}$ and the breaking scale is not related to electroweak symmetry breaking scale. The $Z^{\prime }$ gauge boson is massive. The allowed range of the coupling and the $Z^{\prime }$ mass are constrained, but $Z^{\prime }$ mass can be large; And c) The $U(1{)}_{L_{\mu }-L_{\tau }}$ is broken and the breaking scale is related to the electroweak scale. In this case the $Z^{\prime }$ mass is constrained to be $\sim 1.2$ GeV. We find that there are interesting experimental signatures in ${\mu }^{+}{\mu }^{-}\to {\mu }^{+}{\mu }^{-},{\tau }^{+}{\tau }^{-}$ in these models.

13 pages, 9 figures

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