The $U(1{)}_{L_{\mu }-L_{\tau }}$ model meets the new $(g-2{)}_{\mu }$ data and muon neutrino trident scattering

Abstract

The Muon $g-2$ collaboration at Fermilab has announced their final result of the anomalous magnetic moment of the muon. By adopting the lattice-QCD evaluation of the leading-order hadronic-vacuum-polarization, this result is now in agreement with the latest theoretical prediction to the $1\sigma$ level. This new result further constrains the allowed parameter space, but does not rule out all possible new physics contributions the muon $g-2$. We study the implications for one of the relevant models, the gauged $U(1{)}_{L_{\mu }-L_{\tau }}$. When using this model to resolve the previous $4\sigma$ tension, results from muon neutrino trident (MNT) scattering experiments would restrict the mass of the new gauge boson ($Z^{\prime }$) to be less than $300$ MeV. Since the theory and experimental data difference for muon $g-2$ is lowered down to $1\sigma$, the requirement for $m_{Z^{\prime }}\lesssim 300\mathrm{MeV}$ is much relaxed. Within the updated allowed range of $Z^{\prime }$ boson mass, we study the models implications for electron and tauon $g-2$ as well as future muon colliders. We find that muon collider can effectively probe the $U(1{)}_{L_{\mu }-L_{\tau }}$.

5 pages, 2 figures, v2 includes additional plot (new panel in figure 1) and more discussion. Matches version in PLB

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