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

Elastic $S-$wave scattering of a charm meson with a light pseudoscalar meson in JP =0⁺ is investigated in the flavour 3̄, 6 and 15̄ sectors at the SU(3)f flavour point using lattice QCD, working on three volumes with mπ ≈ 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 3̄ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the JP = 0⁺ Dₛ₀^*(2317). In the exotic flavour 6 sector a virtual bound state is found at √sₚₒₗₑ = 2510 - 2610 MeV, roughly $40-140$ MeV below threshold, whereas the 15̄ channel shows weak repulsion.