The DN, πΣc interaction in finite volume and the Λc(2595) resonance

In this work the interaction of the coupled channels DN and πΣ c in an SU(4) extrapolation of the chiral unitary theory, where the Λ c (2595) resonance appears as dynamically generated from that interaction, is extended to produce results in finite volume. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the phase shifts in the infinite volume from the lattice results is solved. We observe that it is possible to obtain accurate πΣ c phase shifts and the position of the Λ c (2595) resonance, but it requires the explicit consideration of the two coupled channels. We also observe that some of the energy levels in the box are attached to the closed DN channel, such that their use to induce the πΣ c phase shifts via Luescher's formula leads to incorrect results. (orig.)