| Summary: | We analyse the potential of the proposed μ+μ+ and μ+e− collider μTRISTAN to complement the searches for charged-lepton flavour-violation (CLFV) that can be carried out by Belle II. μTRISTAN 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 Z3 “lepton triality” models, where we also find an example that can only be probed by μTRISTAN. These three models feature doubly-charged scalars, denoted k1,2,3 respectively, that induce both CLFV and flavour-conserving processes. Tree-level k1 exchange induces the CLFV scattering process μ+e−→e+τ−, while k2 interactions induce μ+μ+→τ+e+, μ+e−→τ+μ− and make a non-SM contribution to the flavour-conserving scattering μ+μ+→μ+μ+. The k3 model has a non-SM contribution to the flavour-conserving process μ+e−→μ+e−. Other scattering processes involving k1, k2 or k3 are not relevant for μTRISTAN and outside the scope of our analysis. We quantify the sensitivity of μTRISTAN for each of these processes. For the k1 and k2 cases we compare the μTRISTAN reach to the expected sensitivity of Belle II to the crossing symmetry related CLFV τ decays.
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