Improved measurements of two-photon widths of the $\ddot{I}{‡}_{cJ}$ states and helicity analysis for $\ddot{I}{‡}_{c2}\to {\hat{I}}^3{\hat{I}}^3$

Abstract

Based on $448.1\times 10^6$ $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, the decays $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{cJ},\ddot{I}{‡}_{cJ}\to {\hat{I}}^3{\hat{I}}^3(J=0,1,2)$ are studied. The decay branching fractions of $\ddot{I}{‡}_{c0,c2}\to {\hat{I}}^3{\hat{I}}^3$ are measured to be $\mathcal{B}(\ddot{I}{‡}_{c0}\to {\hat{I}}^3{\hat{I}}^3)=(1.93\pm 0.08\pm 0.05\pm 0.05)\times 10^{-4}$ and $\mathcal{B}(\ddot{I}{‡}_{c2}\to {\hat{I}}^3{\hat{I}}^3)=(3.10\pm 0.09\pm 0.07\pm 0.11)\times 10^{-4}$, which correspond to two-photon decay widths of $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c0})=2.03\pm 0.08\pm 0.06\pm 0.13\mathrm{keV}$ and $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c2})=0.60\pm 0.02\pm 0.01\pm 0.04\mathrm{keV}$ with a ratio of $\mathcal{R}=\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c2})/\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c0})=0.295\pm 0.014\pm 0.007\pm 0.027$, where the uncertainties are statistical, systematic and associated with the uncertainties of $\mathcal{B}(\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c0,c2})$ and the total widths $\hat{I}“(\ddot{I}{‡}_{c0,c2})$, respectively. For the forbidden decay of $\ddot{I}{‡}_{c1}\to {\hat{I}}^3{\hat{I}}^3$, no signal is observed, and an upper limit on the two-photon width is obtained to be $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c1})<5.3\mathrm{eV}$ at the 90\% confidence level. The ratio of the two-photon widths between helicity-zero and helicity-two components in the decay $\ddot{I}{‡}_{c2}\to {\hat{I}}^3{\hat{I}}^3$ is also measured to be $f_{0/2}=\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}^{\hat{I}»=0}(\ddot{I}{‡}_{c2})/\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}^{\hat{I}»=2}(\ddot{I}{‡}_{c2})=(0.0\pm 0.6\pm 1.2)\times 10^{-2}$, where the uncertainties are statistical and systematic, respectively.

11 pages, 4 figures, 4 tables