$DK/D\pi$ 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 $\bar{\mathbf{3}}$, $\mathbf{6}$ and $\overline{\mathbf{15}}$ 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 L\"uscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the $S-$wave amplitude in the flavour $\bar{\mathbf{3}}$ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $J^P = 0^+$ $D_{s0}^*(2317)$. In the exotic flavour $\mathbf{6}$ sector a virtual bound state is found at $\sqrt{s_{\rm{pole}}} = 2510 - 2610$ MeV, roughly $40-140$ MeV below threshold, whereas the $\overline{\mathbf{15}}$ channel shows weak repulsion.