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 $$ D\overline{D} $$DD¯ and $$ {D}_s{\overline{D}}_s $$DsD¯s scattering in theJ^PC= 0⁺⁺and 2⁺⁺channels. The scattering matrix for partial wavesl= 0,2 and isospin zero is determined using multiple volumes and inertial frames via Lüscher’s formalism. Lattice QCD ensembles from the CLS consortium withm_π≃ 280 MeV,a≃ 0.09 fm andL/a= 24,32 are utilized. The resulting scattering matrix suggests the existence of three charmonium-like states withJ^PC= 0⁺⁺in the energy region ranging from slightly below 2_mDup to 4.13 GeV. We find a so far unobserved $$ D\overline{D} $$DD¯ bound state just below threshold and a $$ D\overline{D} $$DD¯ resonance likely related toχ_c0(3860), which is believed to beχ_c0(2P). In addition, there is an indication for a narrow 0⁺⁺resonance just below the $$ {D}_s{\overline{D}}_s $$DsD¯s threshold with a large coupling to $$ {D}_s{\overline{D}}_s $$DsD¯s and a very small coupling to $$ D\overline{D} $$DD¯ . This resonance is possibly related to the narrowX(3915)/χ_c0(3930) observed in experiment also just below $$ {D}_s{\overline{D}}_s $$DsD¯s . The partial wavel= 2 features a resonance likely related toχ_c2(3930). We work with several assumptions, such as the omission ofJ/ψω,η_cηand 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.