# Study of electromagnetic Dalitz decays $\chi_{cJ} \rightarrow \mu^{+}\mu^{-}J/\psi$

## TL;DR

This study measures the branching fractions of certain electromagnetic Dalitz decays of $oldsymbol{ ext{chi}_cJ}$ particles into $oldsymbol{ ext{mu}^+ ext{mu}^- J/ ext{psi}}$ using a large dataset, observing $ ext{chi}_{c1,2}$ decays and setting limits on $ ext{chi}_{c0}$.

## Contribution

First measurement of $ ext{chi}_cJ$ electromagnetic Dalitz decays into $ ext{mu}^+ ext{mu}^- J/ ext{psi}$ with observed $ ext{chi}_{c1,2}$ decays and new upper limits for $ ext{chi}_{c0}$.

## Key findings

- Observed $ ext{chi}_{c1,2}$ decays with measured branching fractions.
- No significant $ ext{chi}_{c0}$ decay observed, upper limit set.
- Studied di-muon invariant mass dependent transition form factor.

## Abstract

Using $4.48 \times 10^{8}$ $\psi(3686)$ events collected with the BESIII detector, we search for the decays $\chi_{cJ} \rightarrow \mu^{+}\mu^{-}J/\psi$ through the radiative decays $\psi(3686) \rightarrow \gamma\chi_{cJ}$, where $J=0,1,2$. The decays $\chi_{c1,2} \rightarrow \mu^{+}\mu^{-}J/\psi$ are observed, and the corresponding branching fractions are measured to be $\mathcal{B}(\chi_{c1} \rightarrow \mu^{+}\mu^{-}J/\psi) = (2.51 \pm 0.18 \pm 0.20)\times10^{-4}$ and $\mathcal{B}(\chi_{c2} \rightarrow \mu^{+}\mu^{-}J/\psi) = (2.33 \pm 0.18 \pm 0.29)\times10^{-4}$, where the first uncertainty is statistical and the second one systematic. No significant $\chi_{c0} \rightarrow \mu^{+}\mu^{-}J/\psi$ decay is observed, and the upper limit on the branching fraction is determined to be $2.0\times10^{-5}$ at 90% confidence level. Also, we present a study of di-muon invariant mass dependent transition form factor for the decays $\chi_{c1,2} \rightarrow \mu^{+}\mu^{-}J/\psi$.