Charmonium-like states with the exotic quantum number $J^{PC} = 3^{-+}$

TL;DR

This study uses QCD sum rules to predict the mass and decay channels of a hypothetical exotic charmonium-like tetraquark state with quantum numbers $J^{PC} = 3^{-+}$, providing insights into its possible experimental signatures.

Contribution

The paper introduces a method to construct tetraquark currents with covariant derivatives and systematically analyzes their decay modes, predicting a specific exotic state with a mass around 4.49 GeV.

Findings

Predicted mass of the $J^{PC} = 3^{-+}$ tetraquark state is approximately 4.49 GeV.

State decays into $P$-wave $ ho J/eta$ and $ ho ar D_2^*$ channels.

State does not decay into certain other channels like $ ho ar ext{chic}_2$ or $J/eta f_2(1270)$.

Abstract

We apply the method of QCD sum rules to study the $q c \bar q \bar c$ tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$, and extract the mass of the lowest-lying state to be ${4.49^{+0.45}_{-0.41}}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematic analysis of these interpolating currents indicates that: a) this state readily decays into the $P$-wave $[\rho J/\psi] / [\omega J/\psi ]$ channel but not into the $ [\rho \chi_{c2}]/[\omega \chi_{c2}]/[J/\psi f_2(1270)]$ channels, and b) it readily decays into the $[D^* \bar D_2^*]$ channel but not into the $P$-wave $[D^* \bar D^*]$ channel.