A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$

In this exploratory study, near-threshold scattering of D and (D) over bar* meson is investigated using lattice QCD with N-f = 2+1+1 twisted mass fermion configurations. The calculation is performed in the coupled-channel Luscher finite-size formalism. The study focuses on the channel with I-G (J(PC)) = 1(+)(1(+-)) where the resonance-like structure Z(c)(3900) was discovered. We first identify the two most relevant channels and the lattice study is performed in the two-channel scattering model. Combined with the two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results for the scattering length parameters suggest that for the particular lattice parameters that we studied, the best fit parameters do not correspond to the peak in the elastic scattering cross-section near the threshold. Furthermore, in the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond the 3 sigma level.