Widening the $U(1{)}_{L_{\mu }-L_{\tau }}$ $Z^{\prime }$ mass range for resolving the muon $g-2$ anomaly

Abstract

Exchanging a $Z^{\prime }$ gauge boson is a favored mechanism to solve the muon $(g-2{)}_{\mu }$ anomaly. Among such models the $Z^{\prime }$ from $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge group has been extensively studied. In this model the same interaction addressing $(g-2{)}_{\mu }$, leads to an enhanced muon neutrino trident (MNT) process ${\nu }_{\mu }N\to {\nu }_{\mu }\mu \bar{\mu }N$ constraining the $Z^{\prime }$ mass to be less than a few hundred MeV. Many other $Z^{\prime }$ models face the same problem. It has long been realized that the coupling of $Z^{\prime }$ in the model can admit $(\bar{\mu }{\gamma }^{\mu }\tau +{\bar{\nu }}_{\mu }{\gamma }^{\mu }L{\nu }_{\tau })Z_{\mu }^{\prime }$ interaction which does not contribute to the MNT process. It can solve $(g-2{)}_{\mu }$ anomaly for a much wider $Z^{\prime }$ mass range. However this new interaction induces $\tau \to \mu {\bar{\nu }}_{\mu }{\nu }_{\tau }$ which rules out it as a solution to $(g-2{)}_{\mu }$ anomaly. Here we propose a mechanism by introducing type-II seesaw $SU(2{)}_L$ triplet scalars to evade constraints from all known data to allow a wide $Z^{\prime }$ mass range to solve the $(g-2{)}_{\mu }$ anomaly. This mechanism opens a new window for $Z^{\prime }$ physics.

Comments: to be appear on PLB