New Constraints on Gauged U(1)$_{L_\mu-L_\tau}$ Models via $Z-Z'$ Mixing

JHEP 12, 2024, 018 It is known that the model based on U(1)$_{L_\mu-L_\tau}$ gauge symmetry can explain not only the discrepancy between the measured value of muon $g-2$ and the theoretical prediction, but also the structure of the neutrino mass and mixings. We revisit the analysis of the mass matrix structure in the minimal U(1)$_{L_\mu-L_\tau}$ models based on the latest experimental result, where the minimal stands for the symmetry breaking caused only by a single scalar field. We find that the model called type ${\bf 2}_{+1}$, where an SU(2)$_L$ doublet scalar $\Phi_{+1}$ with the U(1)$_{L_\mu - L_\tau}$ charge $+1$ and the hypercharge $+1/2$, predicts the $\bf B_3$ texture and is marginally acceptable under the current neutrino oscillation data and cosmological observation. When the U(1)$_{L_\mu - L_\tau}$ gauge symmetry is broken by the vacuum expectation value of the standard model non-singlet representation such as $\Phi_{+1}$, there are additional contributions to the flavor-changing meson decay process and atomic parity violation via the $Z-Z'$ mixing. We newly evaluate the model-dependent constraints on the model and conclude that the type ${\bf 2}_{+1}$ model is robustly ruled out. The model is extended to have an additional vacuum expectation value of a standard model singlet scalar in order to avoid the stringent constraint from the flavor-changing meson decay. Finally, we find the allowed range of the ratio of these vacuum expectation values.