Complementarity of $\mu$TRISTAN and Belle II in searches for charged-lepton flavour violation

TL;DR

This paper explores how the proposed $bbTRISTAN$ collider can complement Belle II in searching for charged-lepton flavor violation, especially in detecting new resonances and setting bounds beyond direct reach.

Contribution

It demonstrates the potential of $bbTRISTAN$ to directly produce and study new mediating resonances for CLFV and compares its sensitivity to Belle II for specific models.

Findings

$bbTRISTAN$ can produce competitive bounds for heavy resonances.

It can uniquely probe models only accessible by $bbTRISTAN$.

Sensitivity analysis for different $k_{1,2,3}$ models shows complementary reach.

Abstract

We analyse the potential of the proposed $\mu^+ \mu^+$ and $\mu^+ e^-$ collider $\mu$TRISTAN to complement the searches for charged-lepton flavour-violation (CLFV) that can be carried out by Belle II. $\mu$TRISTAN offers the possibility of directly producing and studying new resonances that could mediate CLFV for a certain range of masses. In addition, we find that it can produce competitive bounds to those from Belle II for cases where the new resonance lies beyond direct reach. We illustrate these points with three $Z_3$ "lepton triality" models, where we also find an example that can only be probed by $\mu$TRISTAN. These three models feature doubly-charged scalars, denoted $k_{1,2,3}$ respectively, that induce both CLFV and flavour-conserving processes. Tree-level $k_1$ exchange induces the CLFV scattering process $\mu^+ e^- \to e^+ \tau^-$, while $k_2$ interactions induce $\mu^+ \mu^+ \to \tau^+ e^+$, $\mu^+ e^- \to \tau^+ \mu^-$ and make a non-SM contribution to the flavour-conserving scattering $\mu^+ \mu^+ \to \mu^+ \mu^+$. The $k_3$ model has a non-SM contribution to the flavour-conserving process $\mu^+ e^- \to \mu^+ e^-$. Other scattering processes involving $k_1$, $k_2$ or $k_3$ are not relevant for $\mu$TRISTAN and outside the scope of our analysis. We quantify the sensitivity of $\mu$TRISTAN for each of these processes. For the $k_1$ and $k_2$ cases we compare the $\mu$TRISTAN reach to the expected sensitivity of Belle II to the crossing symmetry related CLFV $\tau$ decays.