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

The DD^* scattering phase shifts in the T_cc^+=ccu̅d̅ channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to m_π≃ 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_π >m_D^*-m_D. 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 m_c close to the physical value. They turn into a pair of virtual states at the largest m_c studied. With further increasing m_c, one virtual pole representing T_cc^+ is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the T_cc^+ pole is briefly discussed using the data on DD^* scattering from other lattice collaborations.