Scalar and tensor charmonium resonances in coupled-channel scattering from QCD

TL;DR

This study uses lattice QCD to analyze charmonium resonances in the 0++ and 2++ channels, revealing specific resonances and their couplings in the energy region up to 4100 MeV, providing first-principles insights into their properties.

Contribution

First lattice QCD determination of coupled-channel scattering amplitudes for charmonium resonances in the 0++ and 2++ sectors, identifying resonance poles and their couplings.

Findings

Identified a single χc0 and χc2 resonance near 4000 MeV.

Resonances have widths around 70 MeV and strong couplings to D*D* channels.

No additional scalar bound-states or near-threshold resonances were found.

Abstract

We determine $J^{PC}=0^{++}$ and $2^{++}$ hadron-hadron scattering amplitudes in the charmonium energy region up to 4100 MeV using lattice QCD, a first-principles approach to QCD. Working at $m_\pi\approx 391$ MeV, more than 200 finite-volume energy levels are computed and these are used in extensions of the L\"uscher formalism to determine infinite-volume coupled-channel scattering amplitudes. We find that this energy region contains a single $\chi_{c0}$ and a single $\chi_{c2}$ resonance. Both are found as pole singularities on the closest unphysical Riemann sheet, just below 4000 MeV with widths around 70 MeV. The largest couplings are to kinematically-closed $D^* \bar{D}^*$ channels in $S$-wave, and couplings to several decay channels consisting of pairs of open-charm mesons are found to be large and significant in both cases. Above the ground state $\chi_{c0}$, no other scalar bound-states or near-$D\bar{D}$ threshold resonances are found, in contrast to several theoretical and experimental studies.