Two-photon widths of the $\ddot{I}{‡}_{c0,2}$ states and helicity analysis for $χ_{c2}\arγγ$}

Abstract

Based on a data sample of 106 M $\ddot{I}{ˆ}^{\prime }$ events collected with the BESIII detector, the decays $ψ^{\prime}\arγχ_{c0, 2}$,$χ_{c0, 2}\arγγ$ are studied to determine the two-photon widths of the $\ddot{I}{‡}_{c0,2}$ states. The two-photon decay branching fractions are determined to be ${\cal B}(χ_{c0}\arγγ) = (2.24\pm 0.19\pm 0.12\pm 0.08)\times 10^{-4}$ and ${\cal B}(χ_{c2}\arγγ) = (3.21\pm 0.18\pm 0.17\pm 0.13)\times 10^{-4}$. From these, the two-photon widths are determined to be $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c0})=(2.33\pm 0.20\pm 0.13\pm 0.17)$ keV, $\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c2})=(0.63\pm 0.04\pm 0.04\pm 0.04)$ keV, and $\mathcal{R}$ $=\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c2})/\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}(\ddot{I}{‡}_{c0})=0.271\pm 0.029\pm 0.013\pm 0.027$, where the uncertainties are statistical, systematic, and those from the PDG ${\cal B}(ψ^{\prime}\arγχ_{c0,2})$ and $\hat{I}“(\ddot{I}{‡}_{c0,2})$ errors, respectively. The ratio of the two-photon widths for helicity $\hat{I}»=0$ and helicity $\hat{I}»=2$ components in the decay $χ_{c2}\arγγ$ is measured for the first time to be $f_{0/2}=\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}^{\hat{I}»=0}(\ddot{I}{‡}_{c2})/\hat{I}{“}_{{\hat{I}}^3{\hat{I}}^3}^{\hat{I}»=2}(\ddot{I}{‡}_{c2})=0.00\pm 0.02\pm 0.02$.

10 pages, 4 figures