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The $U(1)_{L_μ-L_τ}$ model meets the new $(g-2)_μ$ data and muon neutrino trident scattering

Ming-Wei Li, Xiao-Gang He, Andrew Cheek, Xinhui Chu

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 $1σ$ 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 $U(1)_{L_μ- L_τ}$. When using this model to resolve the previous $4σ$ 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 $1σ$, 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 $U(1)_{L_μ- L_τ}$.

The $U(1)_{L_μ-L_τ}$ model meets the new $(g-2)_μ$ data and muon neutrino trident scattering

Abstract

The Muon 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 level. This new result further constrains the allowed parameter space, but does not rule out all possible new physics contributions the muon . We study the implications for one of the relevant models, the gauged . When using this model to resolve the previous tension, results from muon neutrino trident (MNT) scattering experiments would restrict the mass of the new gauge boson () to be less than MeV. Since the theory and experimental data difference for muon is lowered down to , the requirement for is much relaxed. Within the updated allowed range of boson mass, we study the models implications for electron and tauon as well as future muon colliders. We find that muon collider can effectively probe the .

Paper Structure

This paper contains 1 section, 6 equations, 2 figures.

Table of Contents

  1. Acknowledgments

Figures (2)

  • Figure 1: Left panel: $\Delta a_\mu^{Z^\prime} /\tilde{g}^2$ as a function of $m^2_\mu/m^2_{Z'}$. Right panel: $\tilde{g}\,\,{\rm vs.}\,\,m_{Z^\prime}$ plane with shaded exclusion regions from Muon $g-2$ 2025 measurement (green) Muong-2:2025xyk, BaBar (blue) BaBar:2016sci, CMS (orange) CMS:2018yxg, NA64 (red) NA64:2024klw and CCFR (purple) CCFR:1991lpl. We also show the Muon $g-2$ 2021 best fit region between the two dashed green lines.
  • Figure 2: Left panel: The $\mu \bar{\mu} \to \tau \bar{\tau}$ process ratio $r=\sigma_{\mu-\tau}/\sigma^{\rm SM}_{\mu-\tau}$ as a function of $m_{Z'}$, from 10 GeV to 400 GeV. We set $\tilde{g}^2 /m^2_{Z'} = 4.14\times 10^{-6}/\,{\rm GeV}^2$ and show $\sqrt{s}=1\,{\rm TeV}$ (blue solid line) and $3\,{\rm TeV}$ (red dot-dashed line). Right panel: The $\mu \bar{\mu} \to \tau \bar{\tau}$ cross section as a function of $\sqrt{s}$ assuming the SM only (dashed orange line) and the $U(1)_{L_\mu - L_\tau}$ model (solid blue line) between 10 GeV and 500 GeV. We also take $\tilde{g}^2 /m^2_{Z'} = 4.14\times 10^{-6}/\,{\rm GeV}^2$ and $m_{Z'} = 150$ GeV.