$C\text{\hspace{0.17em}⁣}P$ violation in $\eta$ muonic decays

In this study, we investigate the imprints of $C\text{\hspace{0.17em}⁣}P$ violation in certain $\eta$ muonic decays that could arise within the Standard Model effective field theory. In particular, we study the sensitivities that could be reached at REDTOP, a proposed $\eta$ facility. After estimating the bounds that the neutron EDM places, we find still viable to discover signals of $C\text{\hspace{0.17em}⁣}P$ violation via the muons’ polarization in $\eta \to {\mu }^{+}{\mu }^{-}$ decays at REDTOP, with a single effective operator as its plausible source.