Quark mass dependence of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ resonances

Abstract

We determine the quark mass dependence - light and heavy - of the $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ properties, such as, mass, coupling to $DK$, scattering lengths and compositeness, from a global analysis of $DK$ energy levels from LQCD. In particular, we analyze the HSC energy levels for $DK$ scattering in $I=0$ for different boosts and two pion masses. The formalism is based in the local hidden-gauge interaction of Weinberg-Tomozawa type which respects chiral and heavy quark spin symmetries, supplemented by a term that takes into account the $D^{(\ast )}K$ coupling to a bare $c\bar{s}$ component. The isospin violating decay of the $D_{s0}^{\ast }(2317)\to D_s^{+}\ddot{I}{€}^0$ is also evaluated.