Systematic analysis of the D-wave charmonium states with the QCD sum rules

TL;DR

This paper uses QCD sum rules to analyze various D-wave charmonium states, predicting their masses and supporting their identification with experimentally observed particles, while also proposing the existence of an unobserved state.

Contribution

It provides systematic mass predictions for D-wave charmonium states using QCD sum rules, aligning them with experimental data and suggesting future detection of unobserved states.

Findings

Predicted masses support identification with known charmonium states.

Estimated unobserved $ ext{eta}_{c2}$ state at 3.83 GeV.

Encourages future experimental searches for missing states.

Abstract

We systematically study the 1D charmonium spin-triplet (with the $J^{PC}=1^{--}, 2^{--}, 3^{--}$) and spin-singlet (with the $J^{PC}=2^{-+}$) via the QCD sum rules in comparison with the recent experimental results. The predicted mass $M_{\psi_1}=3.77\pm{0.09}\,\rm {GeV}$ supports identifying the $\psi_1$ as the $\psi(3770)$, the value $M_{\psi_2}=3.82\pm{0.09}\,\rm {GeV}$ is consistent with the reported observation of the $\psi_2(3823)$, the prediction $M_{\psi_3}=3.84\pm{0.08}\,\rm {GeV}$ supports identifying the $\psi_3$ as the $\psi_3(3842)$. Additionally, we estimate the unobserved $\eta_{c2}$ state lies at $3.83\pm{0.09}\,\rm {GeV}$, and suggest detection prospects in the future. More experimental data will help us to unravel the mass spectrum of the charmonium states near the open-charm thresholds.