Lepton flavor physics at $\mu^+ \mu^+$ colliders

TL;DR

This paper explores the potential of future muon colliders, especially $oldsymbol{ extmu^+ extmu^+}$ colliders, to detect lepton flavor violations, showing they could outperform rare decay searches and provide insights into neutrino mass models.

Contribution

It demonstrates the enhanced sensitivity of $oldsymbol{ extmu^+ extmu^+}$ colliders to lepton flavor violations within the type-II seesaw model, linking collider signals to neutrino mass parameters.

Findings

$oldsymbol{ extmu^+ extmu^+ o extmu^+ au^+}$ events can exceed 100 at 2 TeV with 1 ab$^{-1}$ luminosity.

Future colliders have better sensitivity than rare decay searches depending on flavor hierarchy.

Neutrino mass scale and CP phases significantly influence the expected event rates.

Abstract

We discuss sensitivities to lepton flavor violating (and conserving) interactions at future muon colliders, especially at $\mu^+\mu^+$ colliders. Compared with the searches for rare decays of $\mu$ and $\tau$, we find that the TeV-scale future colliders have better sensitivities depending on the pattern of hierarchy in the flavor mixings. As an example, we study the case with the type-II seesaw model, where the flavor mixing parameters have direct relation to the neutrino mass matrix. At a $\mu^+ \mu^+$ collider, the number of events of the $\mu^+ \mu^+ \to \mu^+ \tau^+$ process can be larger than $\mathcal{O}(100)$ with the center of mass energy $\sqrt s = 2$ TeV, and with an integrated luminosity ${\cal L} = 1$ ab$^{-1}$, while satisfying bounds from rare decays of $\mu$ and $\tau$. We discuss impacts of the overall mass scale of neutrinos as well as CP violating phases to the number of expected events.