$DK/D\pi$ scattering and an exotic virtual bound state at the $SU(3)$ flavour symmetric point from lattice QCD

Abstract

Elastic $S-$wave scattering of a charm meson with a light pseudoscalar meson in $J^P=0^{+}$ is investigated in the flavour $\bar{3}$, $6$ and $\overline{15}$ sectors at the $SU(3{)}_f$ flavour point using lattice QCD, working on three volumes with $m_{\pi }\approx 700$ MeV. Large bases of interpolating operators are employed to extract finite-volume spectra, which are subsequently used with the Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the $S-$wave amplitude in the flavour $\bar{3}$ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $J^P=0^{+}$ $D_{s0}^{\ast }(2317)$. In the exotic flavour $6$ sector a virtual bound state is found at $\sqrt{s_{\mathrm{pole}}}=2510-2610$ MeV, roughly $40-140$ MeV below threshold, whereas the $\overline{15}$ channel shows weak repulsion.

Comments: 41 pages, 15 figures, small changes to match published version