Model independent determination of the spin of the $\hat{I}{\text{c◯}}^{-}$ and its polarization alignment in $\ddot{I}ˆ(3686)\to \hat{I}{\text{c◯}}^{-}\bar{\hat{I}}{\text{c◯}}^{+}$

Abstract

We present an analysis of the process $\ddot{I}ˆ(3686)\to \hat{I}{\text{c◯}}^{-}\bar{\hat{I}}{\text{c◯}}^{+}$ ($\hat{I}{\text{c◯}}^{-}\to K^{-}\hat{I}›$, $\bar{\hat{I}}{\text{c◯}}^{+}\to K^{+}\bar{\hat{I}}›$, $\hat{I}›\to p\ddot{I}{€}^{-}$, $\bar{\hat{I}}›\to \bar{p}\ddot{I}{€}^{+}$) based on a data set of $448\times 10^6$ $\ddot{I}ˆ(3686)$ decays collected with the BESIII detector at the BEPCII electron-positron collider. The helicity amplitudes for the process $\ddot{I}ˆ(3686)\to \hat{I}{\text{c◯}}^{-}\bar{\hat{I}}{\text{c◯}}^{+}$ and the decay parameters of the subsequent decay $\hat{I}{\text{c◯}}^{-}\to K^{-}\hat{I}›$ $(\bar{\hat{I}}{\text{c◯}}^{+}\to K^{+}\bar{\hat{I}}›)$ are measured for the first time by a fit to the angular distribution of the complete decay chain. The branching fraction of $\ddot{I}ˆ(3686)\to \hat{I}{\text{c◯}}^{-}\bar{\hat{I}}{\text{c◯}}^{+}$ is measured to be $(5.82\pm 0.12\pm 0.24)\times 10^{-5}$, with an improved precision compared to previous measurements.