Interactions of Charmed Mesons with Light Pseudoscalar Mesons from Lattice QCD and Implications on the Nature of the D_{s0}^*(2317)

Abstract

We study the scattering of light pseudoscalar mesons ($\pi$, $K$) off charmed mesons ($D$, $D_s$) in full lattice QCD. The S-wave scattering lengths are calculated using Lüscher's finite volume technique. We use a relativistic formulation for the charm quark. For the light quark, we use domain-wall fermions in the valence sector and improved Kogut-Susskind sea quarks. We calculate the scattering lengths of isospin-3/2 $D\pi$, $D_s\pi$, $D_{s}K$, isospin-0 $D\bar{K}$ and isospin-1 $D\bar{K}$ channels on the lattice. For the chiral extrapolation, we use a chiral unitary approach to next-to-leading order, which at the same time allows us to give predictions for other channels. It turns out that our results support the interpretation of the $D_{s0}^{\ast }(2317)$ as a $DK$ molecule. At the same time, we also update a prediction for the isospin breaking hadronic decay width $\Gamma (D_{s0}^{\ast }(2317)\to D_s\pi )$ to $(133\pm 22)$ keV.

Comments: 22 pages, 5 figures; a typo in Table II corrected (for the coefficients of the NLO amplitudes)