Masses and mixing ofcqq¯q¯tetraquarks using Glozman-Riska hyperfine interaction

Abstract

In this paper we perform a detailed study of the masses and mixing of the single charmed scalar tetraquarks: $cq\overline{q}\overline{q}$. We also give a systematic analysis of these tetraquark states by weight diagrams, quantum numbers, and flavor wave functions. Tetraquark masses are calculated using four different fits. The following $\mathrm{SU}(3{)}_{\mathrm{F}}$ representations are discussed: ${\overline{15}}_{S}$, ${\overline{3}}_{S}$, ${6}_{A}$, and ${\overline{3}}_{A}$. We use the flavor-spin Glozman-Riska interaction Hamiltonian with SU(3) flavor symmetry breaking. There are 27 different tetraquarks composed of a charm quark $c$ and of the three light flavors $u$, $d$, $s$: 11 cryptoexotic $(3{\mathrm{D}}_{s}^{+},4{\mathrm{D}}^{+},4{\mathrm{D}}^{0})$ and 16 explicit exotic states. We discuss ${\mathrm{D}}_{s}$ and its isospin partners in the same multiplet, as well as all the other four-quark states. Some explicit exotic states appear in the spectrum with the same masses as ${\mathrm{D}}_{s}^{+}(2632)$ in ${\overline{15}}_{S}$ and with the same masses as ${\mathrm{D}}_{s}^{+}(2317)$ in ${6}_{A}$ representation, which confirm the tetraquark nature of these states.