Helicity amplitude and branching fraction measurement of $\ddot{I}{‡}_{cJ}\to \hat{I}›\bar{\hat{I}}›$

Abstract

Utilizing $2712.4\pm 14.3$ million $\ddot{I}ˆ(3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{cJ}\to {\hat{I}}^3\hat{I}›\bar{\hat{I}}›$ decay ($J=0,1,2$). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for $\ddot{I}{‡}_{c2}\to \hat{I}›\bar{\hat{I}}›$ decay is determined for the first time to be $R_{\ddot{I}{‡}_{c2}}=0.575\pm 0.048\pm 0.018$, with a relative phase angle $\hat{I}”\hat{I}{¦}_{\ddot{I}{‡}_{c2}}=0.37\pm 0.15\pm 0.05$~rad. The parameters of the angular distribution of $\ddot{I}{‡}_{c2}$ are determined to be $\hat{I}{\pm }_{\ddot{I}{‡}_{c2}}=-0.211\pm 0.100\pm 0.050$ and ${\hat{I}}_{\ddot{I}{‡}_{c2}}^2=-0.039\pm 0.089\pm 0.033$, based on the distribution $dN/d\cos \hat{I}¸=1+\hat{I}{\pm }_{\ddot{I}{‡}_{c2}}{\cos }^2\hat{I}¸+{\hat{I}}_{\ddot{I}{‡}_{c2}}^2{\cos }^4\hat{I}¸$. The width of $\ddot{I}{‡}_{c0}$ is determined to be $12.31\pm 0.26\pm 0.12$~MeV. Additionally, the branching fractions for $\ddot{I}{‡}_{cJ}\to \hat{I}›\bar{\hat{I}}›$ are measured to be $(3.662\pm 0.048\pm 0.111)\times 10^{-4}$, $(1.182\pm 0.026\pm 0.042)\times 10^{-4}$, and $(1.704\pm 0.035\pm 0.057)\times 10^{-4}$ for $\ddot{I}{‡}_{c0}$, $\ddot{I}{‡}_{c1}$ and $\ddot{I}{‡}_{c2}$, respectively, where the first uncertainty is statistical and the second systematic.

This is the first submission of the manuscript. 13 pages, 15 figures