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arXiv · 2309.14070

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

David J. Wilson·Christopher E. Thomas·Jozef J. Dudek·Robert G. Edwards
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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.

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David J. Wilson, Christopher E. Thomas, Jozef J. Dudek, Robert G. Edwards. 2023-09-25. Scalar and tensor charmonium resonances in coupled-channel scattering from QCD. https://doi.org/10.1103/physrevlett.132.241901

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