Reanalysis of lattice QCD spectra leading to the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\ast }(2460)$

Abstract

We perform a reanalysis of the energy levels obtained in a recent lattice QCD simulation, from where the existence of bound states of $KD$ and $K{D}^{\ast }$ are induced and identified with the narrow $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\ast }(2460)$ resonances. The reanalysis is done in terms of an auxiliary potential, employing a single-channel basis $K{D}^{(\ast )}$, and a two-channel basis $K{D}^{(\ast )},\eta D_s^{(\ast )}$. By means of an extended Lüscher method we determine poles of the continuum $t$-matrix, bound by about 40 MeV with respect to the $KD$ and $K{D}^{\ast }$ thresholds, which we identify with the $D_{s0}^{\ast }(2317)$ and $D_{s1}^{\ast }(2460)$ resonances. Using a sum rule that reformulates Weinberg compositeness condition we can determine that the state $D_{s0}^{\ast }(2317)$ contains a $KD$ component in an amount of about 70%, while the state $D_{s1}^{\ast }(2460)$ contains a similar amount of $K{D}^{\ast }$. We argue that the present lattice simulation results do not still allow us to determine which are the missing channels in the bound state wave functions and we discuss the necessary information that can lead to answer this question.

Comments: 22 pages, 2 figures; updated to match the published version