Probing maximal flavor changing $Z^{\prime }$ in $U(1{)}_{L_{\mu }-L_{\tau }}$ at $\mu$TRISTAN

Abstract

We explore the potential to detect the $U(1{)}_{L_{\mu }-L_{\tau }}$ model featuring triplet scalars $\Delta$ at the $\mu$TRISTAN collider. The new gauge boson $Z^{\prime }$, arising from the spontaneous breaking of $U(1{)}_{L_{\mu }-L_{\tau }}$, can exhibit maximal flavor changing interactions under the exchange symmetry, while $\Delta$ mediates the flavor conserving interactions. The absence of muon $(g-2{)}_{\mu }$ can be explained by interference effects arising from opposite contributions of $Z^{\prime }$ and $\Delta$, with similar interference patterns also manifesting in the tau decay process $\tau \to \mu \nu \bar{\nu }$. These counteracting effects render the model phenomenologically interesting and warrant further investigation. For the mass $m_{Z^{\prime }}$ in the range of hundreds of GeV, we find that ${\mu }^{+}{\mu }^{+}$ and ${\mu }^{+}{e}^{-}$ collider at the $\mu$TRISTAN can probe many regions inaccessible to current experiments and offer greater projected sensitivity than opposite-sign muon colliders. This suggests that $\mu$TRISTAN can serve as complementary exploration to the $U(1{)}_{L_{\mu }-L_{\tau }}$ model, providing compelling motivation for the next generation of high-energy lepton colliders.

Comments: 14 pages, 4 figures. Any comments are welcome