Off-shell effects on the interaction of Nambu-Goldstone bosons and D mesons

The Bethe-Salpeter equation in unitarized chiral perturbation theory is usually solved with the so-called onshell approximation. The underlying argument is that the off-shell effects can be absorbed by the corresponding coupling constants and physical masses, which has been corroborated by the success of unitarized chiral perturbation theory in describing a variety of physical phenomena. Such an approximation needs to be scrutinized when applied to study the light-quark mass evolution of physical observables, as routinely performed nowadays. In the present work, we propose to solve the Bethe-Salpeter equation with the full off-shell terms of the chiral potentials and apply this formalism to the description of the latest n(f) = 2 + 1 lattice QCD (LQCD) data on the scattering lengths of Nambu-Goldstone bosons off D mesons. It is shown that the LQCD data can be better described in this formalism than in the widely used on-shell approximation. On the other hand, no qualitative difference between the on-shell and off-shell approaches is observed for the light-quark mass evolution of the scattering lengths, given the limited LQCD data and their relatively large uncertainties. We also show that the light-quark mass dependence of the D-s0* (2317) remains essentially the same in both approaches.