Two-photon widths of the $\chi_{c0,2}$ states and helicity analysis for $\chi_{c2}\rightarrow\gamma\gamma$

Abstract

Based on a data sample of $106×10^6$ $\psi '$ events collected with the BESIII detector, the decays $\psi '\rightarrow\gamma\chi_{c0,2}, \chi_{c0,2}\rightarrow\gamma\gamma$ are studied to determine the two-photon widths of the $\chi_{c0,2}$ states. The two-photon decay branching fractions are determined to be $\mathscr{B}(\chi_{c0,2}\rightarrow\gamma\gamma)=(2.24±0.19±0.12±0.08)×10^{-4}$ and $\mathscr{B}(\chi_{c0,2}\rightarrow\gamma\gamma)=(3.21±0.18±0.17±0.13)×10^{-4}$. From these, the two-photon widths are determined to be $\Gamma_{\gamma\gamma}(\chi_{c0})=(2.33±0.20±0.13±0.17)$ $\text{keV}$, $\Gamma_{\gamma\gamma}(\chi_{c2})=(0.63±0.04±0.04±0.04)$ $\text{keV}$, and $\mathscr{R}=\Gamma_{\gamma\gamma}(\chi_{c2})/\Gamma_{\gamma\gamma}(\chi_{c0})=0.271±0.029±0.013±0.027$, where the uncertainties are statistical, systematic, and those from the PDG $\mathscr{B}(\psi '\rightarrow\gamma\chi_{c0,2}$ and $\Gamma(\chi_{c0,2})$ errors, respectively. The ratio of the two-photon widths for helicity $\lambda=0$ and helicity $\lambda=2$ components in the decay $\chi_{c2}\rightarrow\gamma\gamma$ is measured for the first time to be $f_{0/2}=\Gamma^{\lambda=0}_{\gamma\gamma}(\chi_{c2})/\Gamma^{\lambda=2}_{\gamma\gamma}(\chi_{c2})=0.00±0.02±0.02$.