DK/Dπ 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 JP = 0+ is investigated in the flavour $$ \overline{\textbf{3}} $$ 3 ¯ , 6 and $$ \overline{\textbf{15}} $$ 15 ¯ 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 Lüscher method to provide constraints on infinite-volume scattering amplitudes. Examining the singularities of the amplitudes, the S-wave amplitude in the flavour $$ \overline{\textbf{3}} $$ 3 ¯ sector is found to contain a deeply bound state, strongly coupled to elastic threshold, corresponding to the $$ {J}^P={0}^{+}\ {D}_{s0}^{\ast }(2317) $$ J P = 0 + D s 0 ∗ 2317 . In the exotic flavour 6 sector a virtual bound state is found at $$ \sqrt{s_{\textrm{pole}}} $$ s pole = 2510 – 2610 MeV, roughly 40 – 140 MeV below threshold, whereas the $$ \overline{\textbf{15}} $$ 15 ¯ channel shows weak repulsion.