Search for tetraquark states X${}_{cc\overline{ss}}$ in D${}_s$${}^{+}$ D${}_s$${}^{+}$ ( D${}_s$${}^{\ast +}$ D${}_s$${}^{\ast +}$) final states at Belle

A search for double-heavy tetraquark state candidates X${}_{cc\overline{ss}}$ decaying to D${}_s$${}^{+}$ D${}_s$${}^{+}$ and D${}_s$${}^{\ast +}$ D${}_s$${}^{\ast +}$ is presented for the first time using the data samples of 102×10${}^6$ Υ(1S) and 158×10${}^6$ Υ(2S) events, and the data samples at $\sqrt{s}$=10.52, 10.58, and 10.867 GeV corresponding to integrated luminosities of 89.5, 711.0, and 121.4 fb${}^{-1}$, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. The invariant-mass spectra of the D${}_s$${}^{+}$ D${}_s$${}^{+}$ and D${}_s$${}^{\ast +}$ D${}_s$${}^{\ast +}$D are studied to search for possible resonances. No significant signals are observed, and the 90% confidence level upper limits on the product branching fractions [B(Υ(1S,2S)→X${}_{cc\overline{ss}}$ anything)×B(X${}_{cc\overline{ss}}$ →D${}_s$${}^{+}$ D${}_s$${}^{+}$ D${}_s$${}^{\ast +}$ D${}_s$${}^{\ast +}$))]in Υ(1S,2S) inclusive decays and the product values of Born cross section and branching fraction [σ(e${}^{+}$e${}^{-}$→X${}_{cc\overline{ss}}$ + anything)×B(X${}_{cc\overline{ss}}$→ D${}_s$${}^{+}$ D${}_s$${}^{+}$ D${}_s$${}^{\ast +}$ D${}_s$${}^{\ast +}$))] in e${}^{+}$e${}^{-}$ collisions at $\sqrt{s}$=10.52, 10.58, and10.867 GeV under different assumptions of X${}_{cc\overline{ss}}$ masses and widths are obtained.