Radiative transition decay width of $\psi_2(3823)\rightarrow\gamma\chi_{c1}$ from lattice QCD

TL;DR

This study uses lattice QCD to calculate the radiative decay width of the $oldsymbol{ ext{psi}_2(3823)}$ meson into $oldsymbol{ ext{gamma}oldsymbol{ ext{chi}}_{c1}}$, providing theoretical predictions consistent with experimental data.

Contribution

First lattice QCD calculation of the $ ext{psi}_2(3823) o ext{gamma} ext{chi}_{c1}$ decay width, offering new theoretical insights into this transition.

Findings

Predicted decay width of $ ext{psi}_2(3823) o ext{gamma} ext{chi}_{c1}$ is 337(27) keV.

Estimated total width of $ ext{psi}_2(3823)$ is 520(100) keV.

Results are consistent with experimental constraints and previous lattice studies.

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 $\Gamma(\psi_2(3823))=520(100)~\text{keV}$.