Muonic Force and Neutrino Non-Standard Interactions at Muon Colliders

The discovery of neutrino oscillations implies that neutrinos are massive and mixed, necessitating an extension of the Standard Model, which may require the introduction of non-standard neutrino interactions (NSI). We investigate the potential of a high-energy muon collider to probe such NSIs with muons, specifically focusing on muonic forces. By analyzing the monophoton signal from the process $\mu^+ \mu^- \rightarrow \nu \overline{\nu } \gamma$, we explore four-fermion contact interactions involving two muons and two neutrinos. Moreover, we examine minimal models that generate scalar and vector-mediated NSIs and study their phenomenology. Projected sensitivities for the strength of NSIs, $\epsilon_{\alpha \beta}^{\mu \mu}$, are presented at a 95$\%$ confidence level for a center-of-mass energy of 3 TeV and integrated luminosities of $\mathcal{L} = 1$ and $10~\mathrm{ab}^{-1}$, showcasing the complementarity between a muon collider and other experimental probes.