Exotic $T^*_{csJ}$ and $T^*_{c\bar{s}J}$ states and coupled-channel scattering at the $SU(3)$ flavour symmetric point from lattice QCD

Abstract

Motivated by recent experimental observations of the flavour-exotic $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, we present the first lattice QCD study of coupled-channel scattering of a charm meson with a light meson in the flavour-exotic sectors at the $SU(3)_f$ flavour symmetric point. Utilising five volumes with $m_\pi \approx 700$ MeV and employing large bases of meson-meson operators, finite-volume spectra are extracted and used to constrain infinite-volume scattering amplitudes with $J^P = \{0, 1, 2, 3, 4\}^+$ via the L\"uscher formalism. In the flavour $\mathbf{6}$ sector, each $S$-wave channel considered is found to be attractive with the scattering amplitudes having an associated pole singularity on an unphysical sheet below threshold, giving six flavour-exotic poles in the energy region constrained. In $J^P = 0^+$ there is a virtual bound state and a resonance. The latter is identified with the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, appearing as one state in the $SU(3)_f$ flavour symmetric limit, and suggests the existence of an isospin-$\frac{1}{2}$ partner. In $J^P =1^+$ there are three poles, one of which is identified as a $J^P =1^+$ partner of the $T^*_{cs0}(2870)^0$ and $T^*_{c\bar{s}0}(2900)$, and $J^P =2^+$ contains one pole which is identified as their $J^P =2^+$ partner. Only mild interactions and no poles are seen in the $J^P = \{3, 4\}^+$ scattering amplitudes. In the flavour $\overline{\mathbf{15}}$ sector, weak interactions are observed in $J^P = \{0, 1, 2, 3, 4\}^+$ with no well-determined poles in the energy region constrained.