Search for tetraquark states $X_{cc\overline{s}\overline{s}}$ in $D_s^{+}{D}_s^{+}(D_s^{*+}{D}_s^{*+})$ final states at Belle

A search for double-heavy tetraquark state candidates $X_{cc\overline{s}\overline{s}}$ decaying to $D_s^{+}{D}_s^{+}$ and $D_s^{*+}{D}_s^{*+}$ is presented for the first time using the data samples of $102\times {10}^6$ $\mathrm{\Upsilon }(1S)$ and $158\times {10}^6$ $\mathrm{\Upsilon }(2S)$ 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 $121.4{\mathrm{fb}}^{-1}$, 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 $D_s^{*+}{D}_s^{*+}$ are studied to search for possible resonances. No significant signals are observed, and the 90% confidence level upper limits on the product branching fractions [$\mathcal{B}(\mathrm{\Upsilon }(1S,2S)\to X_{cc\overline{s}\overline{s}}+\text{anything})\times \mathcal{B}(X_{cc\overline{s}\overline{s}}\to D_s^{+}{D}_s^{+}(D_s^{*+}{D}_s^{*+}))$] in $\mathrm{\Upsilon }(1S,2S)$ inclusive decays and the product values of Born cross section and branching fraction [$\sigma (e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}+\text{anything})\times \mathcal{B}(X_{cc\overline{s}\overline{s}}\to D_s^{+}{D}_s^{+}(D_s^{*+}{D}_s^{*+}))$] in $e^{+}{e}^{-}$ collisions at $\sqrt{s}=10.52$, 10.58, and 10.867 GeV under different assumptions of $X_{cc\overline{s}\overline{s}}$ masses and widths are obtained.

Figure 1

The top (bottom) plots show the distribution of $M_{D_s^{+}}$ vs $M_{D_s^{+}}$ from the selected $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}\to D_s^{+}{D}_s^{+}(D_s^{*+}{D}_s^{*+})+\text{anything}$ candidates from data at $\sqrt{s}=10.58\mathrm{GeV}$, where the $D_s^{+}$ is reconstructed from $\varphi {\pi }^{+}$ or ${\overline{K}}^{*}(892{)}^0{K}^{+}$. The central solid boxes define the signal regions, and the red dash-dotted and blue dashed boxes show the $M_{D_s^{+}}$ sideband regions described in the text.

Figure 2

Distributions of $M_{D_s^{+}{D}_s^{+}}$ from data for processes (a) $\mathrm{\Upsilon }(1S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$, (b) $\mathrm{\Upsilon }(2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$, and $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$ at (c) $\sqrt{s}=10.52\mathrm{GeV}$, (d) $\sqrt{s}=10.58\mathrm{GeV}$, (e) $\sqrt{s}=10.867\mathrm{GeV}$. The cyan shaded histograms are from the normalized $M_{D_s^{+}{D}_s^{+}}$ sideband events.

Figure 3

Distributions of $M_{D_s^{*+}{D}_s^{*+}}$ from data for processes (a) $\mathrm{\Upsilon }(1S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$, (b) $\mathrm{\Upsilon }(2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$, and $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$ at (c) $\sqrt{s}=10.52\mathrm{GeV}$, (d) $\sqrt{s}=10.58\mathrm{GeV}$, (e) $\sqrt{s}=10.867\mathrm{GeV}$. The cyan shaded histograms are from the normalized $M_{D_s^{+}{D}_s^{+}}$ sideband events.

Figure 4

Distributions of $M_{D_s^{+}{D}_s^{+}}$ from data for processes (a) $\mathrm{\Upsilon }(1S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$, (b) $\mathrm{\Upsilon }(2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$, and $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$ at (c) $\sqrt{s}=10.52\mathrm{GeV}$, (d) $\sqrt{s}=10.58\mathrm{GeV}$, (e) $\sqrt{s}=10.867\mathrm{GeV}$. The cyan shaded histograms are from the normalized $M_{D_s^{+}{D}_s^{+}}$ sideband events.

Figure 5

Distributions of $M_{D_s^{*+}{D}_s^{*+}}$ from data for processes (a) $\mathrm{\Upsilon }(1S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$, (b) $\mathrm{\Upsilon }(2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$, and $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$ at (c) $\sqrt{s}=10.52\mathrm{GeV}$, (d) $\sqrt{s}=10.58\mathrm{GeV}$, (e) $\sqrt{s}=10.867\mathrm{GeV}$. The cyan shaded histograms are from the normalized $M_{D_s^{+}{D}_s^{+}}$ sideband events.

Figure 6

The 90% CL upper limits on the product branching fractions of $\mathrm{\Upsilon }(1S,2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{+}{D}_s^{+})+\text{anything}$ and the Born cross sections of $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}+\text{anything}$ at $\sqrt{s}=10.52$, 10.58, and 10.867 GeV with $M_{X_{cc\overline{s}\overline{s}}}$ varying from 4882 to $4922\mathrm{MeV}/c^2$ in steps of $5\mathrm{MeV}/c^2$ and ${\mathrm{\Gamma }}_{X_{cc\overline{s}\overline{s}}}$ varying from 0.54 to 6.54 MeV in steps of 1.0 MeV.

Figure 7

The 90% CL upper limits on the product branching fractions of $\mathrm{\Upsilon }(1S,2S)\to X_{cc\overline{s}\overline{s}}(\to D_s^{*+}{D}_s^{*+})+\text{anything}$ and the Born cross sections of $e^{+}{e}^{-}\to X_{cc\overline{s}\overline{s}}+\text{anything}$ at $\sqrt{s}=10.52$, 10.58, and 10.867 GeV with $M_{X_{cc\overline{s}\overline{s}}}$ varying from 4801 to $4841\mathrm{MeV}/c^2$ in steps of $5\mathrm{MeV}/c^2$ and ${\mathrm{\Gamma }}_{X_{cc\overline{s}\overline{s}}}$ varying from 2.58 to 8.58 MeV in steps of 1.0 MeV.