Open charm tetraquarks in broken ${\mathrm{SU}\left(3\right)}_F$ symmetry

Prompted by a recent lattice QCD calculation, we review the SU(3) light quark flavor structure of charmed tetraquarks with spin 0 diquarks. Fermi statistics forces the three light quarks to be in the representation $\overline{3}\otimes \overline{3}=3\oplus \overline{6}$. This agrees with the weak repulsion in the $15$ of the $3\otimes 8$ in $\overline{D}K$ scattering studied on the lattice. We analyze the $3\oplus \overline{6}$ multiplet broken by the strange quark mass and determine the five independent masses from the known masses of diquarks. The mass of $D_{s0}^{*}\left(2317\right)$ is predicted within 50 MeV accuracy. The recently observed ${\overline{D}}_s^{--}\left(2900\right)$ and ${\overline{D}}_s^0\left(2900\right)$, likely part of a $I=1$ multiplet, with flavor composition $\overline{c}\overline{q}{q}^{\prime }s$, and $X_0\left(2900\right)$, an isosinglet with flavor composition $\overline{c}\overline{s}ud$, fit naturally in a $3\oplus \overline{6}$ structure as the first radial excitations. We discuss also the decay modes of $D_{s0}^{*}\left(2317\right)$, of the radial excitations and of the predicted particles.