Vector and scalar charmonium resonances with lattice QCD

We perform an exploratory lattice QCD simulation of D (D) over bar 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 (D) over bar 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 (D) over bar 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.