$CP$ violation in $\eta^{(\prime)}\to\pi^+\pi^-\mu^+\mu^-$ decays

TL;DR

This paper investigates $CP$ violation in $ ext{eta}^{( ext{prime})}$ decays to $ ext{pi}^+ ext{pi}^- ext{mu}^+ ext{mu}^-$, deriving hadronic matrix elements and proposing an angular asymmetry as a probe for new physics beyond current constraints.

Contribution

It calculates hadronic matrix elements for $ ext{eta}^{( ext{prime})}$ decays and links an angular asymmetry to Wilson coefficients, providing a new method to test $CP$ violation.

Findings

Projected sensitivities are moderate due to phase space and chiral suppression.

The angular asymmetry offers a measurement without muon polarization.

Upcoming experiments could explore these $CP$ violating effects.

Abstract

It has been pointed out recently that a certain set of dimension-6 scalar $P$- and $CP$-violating light-quark-muon operators may be tested in $\eta$ and $\eta'$ decays to various final states involving $\mu^+\mu^-$ pairs, at a level not yet excluded by constraints from electric dipole moments. We here work out the hadronic matrix elements required for the predictions for the decays $\eta, \eta' \to\pi^+\pi^-\mu^+\mu^-$. We relate a new asymmetry in the angular distribution between the dipion and dimuon decay planes to the corresponding Wilson coefficients. Despite the advantage of not requiring the measurement of muon polarization, the projected sensitivities are shown to be moderate due to a combination of small phase space and chiral suppression. Such sensitivity studies are most timely in view of upcoming or planned high-statistics $\eta^{(\prime)}$ experiments such as the JLab eta factory or REDTOP.