Charmonium $\chi_{c0}$ and $\chi_{c2}$ resonances in coupled-channel scattering from lattice QCD

TL;DR

This study uses lattice QCD to analyze charmonium resonances, identifying scalar and tensor states around 4000 MeV with strong couplings to open-charm channels, and compares findings with experimental and theoretical results.

Contribution

First lattice QCD analysis of coupled-channel scattering in the charmonium energy region identifying scalar and tensor resonances near 4000 MeV.

Findings

Identified a scalar resonance near 4000 MeV with strong couplings to Dar{D} and D_sar{D}_s

Found a tensor resonance at similar mass with strong couplings to multiple D meson channels

Did not observe significant features between the ground state χ_{c0}(1P) and the resonance

Abstract

In order to explore the spectrum of hidden-charm scalar and tensor resonances, we study meson-meson scattering with $J^{PC}=0^{++}, 2^{++}$ in the charmonium energy region using lattice QCD. Employing a light-quark mass corresponding to $m_\pi \approx 391$ MeV, we determine coupled-channel scattering amplitudes up to around 4100 MeV considering all kinematically relevant channels consisting of a pair of open-charm mesons or a charmonium meson with a light meson. A single isolated scalar resonance near 4000 MeV is found with large couplings to $D\bar{D}$, $D_s \bar{D}_s$ and the kinematically closed $D^* \bar{D}^*$ channel. A single tensor resonance at a similar mass couples strongly to $D\bar{D}$, $D\bar{D}^*$ and $D^* \bar{D}^*$. We compare the extracted resonances to contemporary experimental candidate states, previous lattice results and theoretical modeling. In contrast to several other studies, we do not find any significant feature in the scalar amplitudes between the ground state $\chi_{c0}(1P)$ and the resonance found around 4000 MeV.