Search for the $C\!P$-violating strong decays $\eta \to \pi^+\pi^-$ and $\eta^\prime(958) \to \pi^+\pi^-$

TL;DR

This study searches for $C ext{-}P$-violating decays of $ ext{eta}$ and $ ext{eta}^ extprime$ into $ ext{pi}^+ ext{pi}^-$ using LHCb data, setting new upper limits on their branching fractions.

Contribution

First search for these rare $C ext{-}P$-violating decays using large LHCb data, improving existing upper limits especially for $ ext{eta}^ extprime$ decays.

Findings

No evidence for the decays was observed.

Upper limits on branching fractions were set: $1.6 imes 10^{-5}$ for $ ext{eta}$ and $1.8 imes 10^{-5}$ for $ ext{eta}^ extprime$.

The limit for $ ext{eta}^ extprime$ is three times more restrictive than previous results.

Abstract

A search for the $C\!P$-violating strong decays $\eta \to \pi^+\pi^-$ and $\eta^\prime(958) \to \pi^+\pi^-$ has been performed using approximately $2.5 \times 10^{7}$ events of each of the decays $D^+ \to \pi^+\pi^+\pi^-$ and $D_s^+ \to \pi^+\pi^+\pi^-$, recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collision data recorded during LHC Run 1 and 0.3 fb$^{-1}$ recorded in Run 2. No evidence is seen for $D^+_{(s)} \to \pi^+ \eta^{(\prime)}$ with $\eta^{(\prime)} \to \pi^+\pi^-$, and upper limits at 90% confidence level are set on the branching fractions, $\mathcal{B}(\eta \to \pi^+\pi^-) < 1.6 \times 10^{-5}$ and $\mathcal{B}(\eta^\prime \to \pi^+\pi^-) < 1.8 \times 10^{-5}$. The limit for the $\eta$ decay is comparable with the existing one, while that for the $\eta^\prime$ is a factor of three smaller than the previous limit.