New-physics searches in $C\text{\hspace{0.17em}⁣}P$-violating $\eta$ muonic decays

In this work we investigate the possibility to observe $C\text{\hspace{0.17em}⁣}P$-violation in $\eta$ decays containing muons at the proposed REDTOP experiment. Employing the SMEFT to parametrize the new-physics $C\text{\hspace{0.17em}⁣}P$-violating effects, we find that a single operator exists for which is possible to observe $C\text{\hspace{0.17em}⁣}P$-violation at REDTOP in $\eta \to {\mu }^{+}{\mu }^{-}$ decays, while evading bounds from the neutron electric dipole moment and $D^{-}\to \mu \bar{\nu }$