Study of the K D, ηD_s coupled system in a finite volume and the D_s*0 (2317) resonance

An SU(4) extrapolation of the chiral unitary theory in coupled channels is utilized to study the scalar mesons in the charm sector, and it is further extended to produce results in finite volume. The theory in the infinite volume produces dynamically the Ds*0(2317) resonance by means of the coupled channels K D,η Ds. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is solved. We observe that it is possible to obtain accurate K D phase shifts and the position of the Ds*0 (2317) state, but it requires the explicit consideration of the two coupled channels in the analysis if one goes close to the ηDs threshold. We also show that a careful analysis of the finite volume data can shed some light on the nature of the Ds*0 (2317) resonance as a K D molecule or otherwise.