Radiative transition decay width of ${\psi }_2(3823)\to \gamma {\chi }_{c1}$ from lattice QCD

Abstract

We present an exploratory $N_f=2$ lattice QCD study of ${\psi }_2(3823)\to \gamma {\chi }_{c1}$ at a pion mass $m_{\pi }\approx 350$~MeV. The related two-point and three-piont functions are calculated using the distillation method. The electromagnetic multipole form factor $\hat{V}(0)=2.083(11)$ for $J/\psi \to \gamma {\eta }_c$ is consistent with previous lattice results, the form factors ${\hat{E}}_1(0)$, ${\hat{M}}_2(0)$ and ${\hat{E}}_3(0)$ for $\Gamma ({\chi }_{c2}\to \gamma J/\psi )$ have the same hierarchy as that derived from experiments and the predicted decay width $\Gamma ({\chi }_{c2}\to \gamma J/\psi )=368(5)\text{keV}$ is in excellent agreement with the PDG value $374(10)\text{keV}$ and previous lattice QCD results in the quenched approximation. The same strategy is applied to the study of the process ${\psi }_2(3823)\to \gamma {\chi }_{c1}$ and the partial decay width is predicted to be $337(27)\text{keV}$. According to the BESIII constraints on the ${\psi }_2(3823)$ decay channels and some phenomenological results, we estimate the total width $\Gamma ({\psi }_2(3823))=520(100)\text{keV}$.