Vector and scalar charmonium resonances with lattice QCD

We perform an exploratory lattice QCD simulation of $D \bar D$ scattering, aimed at determining the masses as well as the decay widths of charmonium resonances above open charm threshold. Neglecting coupling to other channels, the resulting phase shift for $D \bar D$ scattering in p-wave yields the well-known vector resonance $\psi(3770)$. For $m_\pi = 156$ MeV, the extracted resonance mass and the decay width agree with experiment within large statistical uncertainty. The scalar charmonium resonances present a puzzle, since only the ground state $\chi_{c0}(1P)$ is well understood, while there is no commonly accepted candidate for its first excitation. We simulate $D \bar D$ scattering in s-wave in order to shed light on this puzzle. The resulting phase shift supports the existence of a yet-unobserved narrow resonance with a mass slightly below 4 GeV. A scenario with this narrow resonance and a pole at $\chi_{c0}(1P)$ agrees with the energy-dependence of our phase shift. Further lattice QCD simulations and experimental efforts are needed to resolve the puzzle of the excited scalar charmonia.