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

TL;DR

This paper explores the potential for detecting new physics through $CP$ violation in specific $ ext{eta}$ and $ ext{eta'}$ decays at REDTOP, concluding that current experiments are less sensitive than nEDM measurements.

Contribution

It applies SMEFT to model $CP$ violation in $ ext{eta}$ decays and compares the sensitivity of REDTOP with nEDM experiments, highlighting the $ ext{eta} o ext{mu}^+ ext{mu}^-$ channel as most promising.

Findings

REDTOP's sensitivity to $CP$ violation is limited compared to nEDM experiments.

The $ ext{eta} o ext{mu}^+ ext{mu}^-$ decay remains the best channel for observing $CP$ violation.

Projected statistics at REDTOP are insufficient to surpass existing constraints.

Abstract

In this work we investigate the prospect of observing new-physics signatures via $C\!P$ 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 $C\!P$-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 $C\!P$-violation at this experimental facility.