Charmonium-like resonances with JPC = 0++, 2++ in coupled D D ¯ $$ \mathrm{D}\overline{\mathrm{D}} $$ , D s D ¯ s $$ {\mathrm{D}}_{\mathrm{s}}{\overline{\mathrm{D}}}_{\mathrm{s}} $$ scattering on the lattice

Abstract

Abstract We present the first lattice investigation of coupled-channel D D ¯ $$ D\overline{D} $$ and D s D ¯ s $$ {D}_s{\overline{D}}_s $$ scattering in the J PC = 0++ and 2++ channels. The scattering matrix for partial waves l = 0, 2 and isospin zero is determined using multiple volumes and inertial frames via Lüscher’s formalism. Lattice QCD ensembles from the CLS consortium with m π ≃ 280 MeV, a ≃ 0.09 fm and L/a = 24, 32 are utilized. The resulting scattering matrix suggests the existence of three charmonium-like states with J PC = 0++ in the energy region ranging from slightly below 2 mD up to 4.13 GeV. We find a so far unobserved D D ¯ $$ D\overline{D} $$ bound state just below threshold and a D D ¯ $$ D\overline{D} $$ resonance likely related to χ c0(3860), which is believed to be χ c0(2P). In addition, there is an indication for a narrow 0++ resonance just below the D s D ¯ s $$ {D}_s{\overline{D}}_s $$ threshold with a large coupling to D s D ¯ s $$ {D}_s{\overline{D}}_s $$ and a very small coupling to D D ¯ $$ D\overline{D} $$ . This resonance is possibly related to the narrow X(3915)/χ c0(3930) observed in experiment also just below D s D ¯ s $$ {D}_s{\overline{D}}_s $$ . The partial wave l = 2 features a resonance likely related to χ c2(3930). We work with several assumptions, such as the omission of J/ψω, η c η and three-particle channels. Only statistical uncertainties are quantified, while the extrapolations to the physical quark-masses and the continuum limit are challenges for the future.

Keywords

• Lattice field theory simulation
• QCD Phenomenology