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

We present the first lattice investigation of coupled-channel $$ D\overline{D} $$ D D ¯ and $$ {D}_s{\overline{D}}_s $$ D s D ¯ s scattering in the JPC = 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 mπ ≃ 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 JPC = 0++ in the energy region ranging from slightly below 2mD up to 4.13 GeV. We find a so far unobserved $$ D\overline{D} $$ D D ¯ bound state just below threshold and a $$ D\overline{D} $$ D D ¯ resonance likely related to χc0(3860), which is believed to be χc0(2P). In addition, there is an indication for a narrow 0++ resonance just below the $$ {D}_s{\overline{D}}_s $$ D s D ¯ s threshold with a large coupling to $$ {D}_s{\overline{D}}_s $$ D s D ¯ s and a very small coupling to $$ D\overline{D} $$ D D ¯ . This resonance is possibly related to the narrow X(3915)/χc0(3930) observed in experiment also just below $$ {D}_s{\overline{D}}_s $$ D s D ¯ s . The partial wave l = 2 features a resonance likely related to χc2(3930). We work with several assumptions, such as the omission of J/ψω, ηcη 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.