Towards the quark mass dependence of T₂₂^+ from lattice QCD

The DD^* scattering phase shifts in the T₂₂^+=ccud channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to m_ 280 MeV. The phase shifts are analysed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrised by contact terms and a slight repulsion at long range mediated by one-pion exchange with m_ >m₃^*-mD. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for mc close to the physical value. They turn into a pair of virtual states at the largest mc studied. With further increasing mc, one virtual pole representing T₂₂^+ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the T₂₂^+ pole is briefly discussed using the data on DD^* scattering from other lattice collaborations.