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

TL;DR

This paper examines how the recent Fermilab muon g-2 results impact the $U(1)_{L_-}$ model, showing that the constraints on the new gauge boson mass are relaxed and exploring implications for other leptons and future colliders.

Contribution

The study updates the constraints on the $U(1)_{L_-}$ model based on new muon g-2 data, analyzing its effects on electron and tau g-2, and prospects for muon collider detection.

Findings

Muon g-2 data now compatible with theory within 1σ.

Allowed $Z'$ mass range is relaxed to above 300 MeV.

Muon collider can effectively probe the $U(1)_{L_-}$ model.

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 ($Z'$) 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 $m_{Z'}\lesssim 300\,{\rm MeV}$ is much relaxed. Within the updated allowed range of $Z'$ 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 $U(1)_{L_\mu - L_\tau}$.