$D_{s0}^{\ast }(2317)$ Meson and $D$-Meson-Kaon Scattering from Lattice QCD

Abstract

The scalar meson $D_{s0}^{\ast }(2317)$ is found 37(17)MeV below DK threshold in a lattice simulation of the $J^P=0^{+}$ channel using, for the first time, both DK as well as $\bar{s}c$ interpolating fields. The simulation is done on $N_f=2+1$ gauge configurations with $m_{\pi }\simeq 156$MeV, and the resulting $M_{D_{s0}^{\ast }}-\frac{1}{4}(M_{D_s}+3M_{D_s^{\ast }})=266(16)$ MeV is close to the experimental value 241.5(0.8)MeV. The energy level related to the scalar meson is accompanied by additional discrete levels due to DK scattering states. The levels near threshold lead to the negative DK scattering length $a_0=-1.33(20)$ fm that indicates the presence of a state below threshold.

Comments: 5 pages, 3 figures; version accepted for publication by PRL