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

Abstract

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 $2_{+1}$, 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 ${\mathbf{B}}_3$ 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 $Z-Z^{\prime }$ mixing. We newly evaluate the model-dependent constraints on the model and conclude that the type $2_{+1}$ 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.

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Cited by in corpus (1)

• The Muon Magnetic Moment and Physics Beyond the Standard Model