Masses and Mixing of $cq\bar{q}\bar{q}$ 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: $cq\bar{q}\bar{q}$. 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 SU(3)${}_{\mathrm{F}}$ representations are discussed: ${\overline{15}}_{\mathrm{S}}$, ${\bar{3}}_{\mathrm{S}}$, $6_{\mathrm{A}}$ and ${\bar{3}}_{\mathrm{A}}$. 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 D${}_{\mathrm{s}}^{+}$, 4 D${}^{+}$, 4 D${}^0$) and 16 explicit exotic states. We discuss D${}_{\mathrm{s}}$ 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 D${}_{\mathrm{s}}^{+}$(2632) in ${\overline{15}}_{\mathrm{S}}$ and with the same masses as D${}_{\mathrm{s}}^{+}$(2317) in $6_{\mathrm{A}}$ representation, which confirm the tetraquark nature of these states.

10 pages, 6 tables, 6 figures. Accepted for publication in Phys. Rev. D