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In this paper we perform a detailed study of the masses and mixing of thesingle charmed scalar tetraquarks: $c q \bar{q} \bar{q}$. We also give asystematic analysis of these tetraquark states by weight diagrams, quantumnumbers and flavor wave functions. Tetraquark masses are calculated using fourdifferent fits. The following SU(3)$_\mathrm{F}$ representations are discussed:$\bar{15}_\mathrm{S}$, $\bar{3}_\mathrm{S}$, $6_\mathrm{A}$ and$\bar{3}_\mathrm{A}$. We use the flavor-spin Glozman-Riska interactionHamiltonian with SU(3) flavor symmetry breaking. There are 27 differenttetraquarks 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 16explicit exotic states. We discuss D$_\mathrm{s}$ and its isospin partners inthe same multiplet, as well as all the other four-quark states. Some explicitexotic states appear in the spectrum with the same masses asD$_\mathrm{s}^{+}$(2632) in $\bar{15}_\mathrm{S}$ and with the same masses asD$_\mathrm{s}^{+}$(2317) in $6_\mathrm{A}$ representation, which confirm thetetraquark nature of these states.

Masses and Mixing of $c q \bar{q} \bar{q}$ Tetraquarks Using Glozman-Riska Hyperfine Interaction