Vector and scalar charmonium resonances with lattice QCD

We perform an exploratory lattice QCD simulation of DD¯ 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 DD¯ scattering in p-wave yields the well-known vector resonance ψ(3770). For m_π = 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 χ_c0(1P) is well understood, while there is no commonly accepted candidate for its first excitation. We simulate DD¯ 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 χ_c0(1P) agrees with the energy-dependence of our phase shift. In addition, further lattice QCD simulations and experimental efforts are needed to resolve the puzzle of the excited scalar charmonia