Exotic $T_{csJ}^{\ast }$ and $T_{c\bar{s}J}^{\ast }$ 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 $T_{cs0}^{\ast }(2870{)}^0$ and $T_{c\bar{s}0}^{\ast }(2900)$, 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 Lüscher formalism. In the flavour $6$ 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 $T_{cs0}^{\ast }(2870{)}^0$ and $T_{c\bar{s}0}^{\ast }(2900)$, 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 $T_{cs0}^{\ast }(2870{)}^0$ and $T_{c\bar{s}0}^{\ast }(2900)$, 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 $\overline{15}$ sector, weak interactions are observed in $J^P=\{0,1,2,3,4{\}}^{+}$ with no well-determined poles in the energy region constrained.

Comments: 65 pages, 18 figures, 19 tables