Charmonium-like states with $J^{P}=1^{+}$ and isospin 1

TL;DR

This study uses lattice QCD to explore exotic charmonium-like mesons with specific quantum numbers and isospin, providing initial insights into their energy levels and scattering properties.

Contribution

First lattice QCD investigation of four-quark states with $J^{P}=1^{+}$ and isospin 1, including multiple volumes and momentum configurations.

Findings

Energy shifts near $Dar D^*$ threshold are very small.

Results are consistent with zero energy shift in the $1^{+-}$ channel.

Preliminary results suggest weak interaction effects in these channels.

Abstract

Many mesons with properties incompatible with a $\bar cc$ structure have already been discovered, e.g. the $Z_c$ mesons with isospin 1. We investigate the spectrum of exotic charmonium-like mesons using lattice QCD. The focus is on $\bar cc \bar qq$ states with $J^{PC}=1^{+\pm}$ and isospin 1. This is the first study of four-quark states with these quantum numbers, a non-zero total momentum and two different lattice volumes. We extract the energy levels and determine the scattering length for $D\bar D^*$ scattering close to the threshold using L\"uscher's formalism. Our preliminary results show that the energy shifts for eigenstates dominated by $D\bar{D}^*$ are very small in the $1^{++}$ channel and consistent with zero in the $1^{+-}$ channel.