New-physics signatures via $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ and ${\eta }^{\prime }\to \eta {\mu }^{+}{\mu }^{-}$ decays

Abstract

In this work we investigate the prospect of observing new-physics signatures via $CP$ violation in ${\eta }^{(\prime )}\to {\pi }^0{\mu }^{+}{\mu }^{-}$ and ${\eta }^{\prime }\to \eta {\mu }^{+}{\mu }^{-}$ decays at the REDTOP experiment. We make use of the SMEFT to parametrise the new-physics $CP$-violating effects and find that the projected REDTOP statistics are not competitive with respect to nEDM experiments. This reasserts the $\eta \to {\mu }^{+}{\mu }^{-}$ process as the most promising channel to find $CP$-violation at this experimental facility.

Comments: 12 pages, 1 figure, 1 table; v2 includes a comment about the neutron EDM constraint and possible accidental Wilson coefficient cancellations