We report the results of a first search for a doubly charged $DDK$ bound state, denoted the $R^{++}$, in $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ inclusive decays and via direct production in $e^{+}{e}^{-}$ collisions at $\sqrt{s}=10.520$, 10.580, and 10.867 GeV. The search uses data accumulated with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. No significant signals are observed in the $D^{+}{D}_s^{*+}$ invariant-mass spectra of all studied modes. The 90% credibility level upper limits on their product branching fractions in $\mathrm{\Upsilon }(1S)$ and $\mathrm{\Upsilon }(2S)$ inclusive decays ($\mathcal{B}(\mathrm{\Upsilon }(1S,2S)\to R^{++}+\text{anything})\times \mathcal{B}({\mathrm{R}}^{++}\to {\mathrm{D}}^{+}{\mathrm{D}}_{\mathrm{s}}^{*+})$), the product values of Born cross section and branching fraction in $e^{+}{e}^{-}$ collisions ($\sigma (e^{+}{e}^{-}\to R^{++}+\text{anything})\times \mathcal{B}({\mathrm{R}}^{++}\to {\mathrm{D}}^{+}{\mathrm{D}}_{\mathrm{s}}^{*+})$) at $\sqrt{s}=10.520$, 10.580, and 10.867 GeV under different assumptions of $R^{++}$ masses varying from 4.13 to $4.17\mathrm{GeV}/c^2$ and widths varying from 0 to 5 MeV are obtained.

• Received 31 August 2020
• Accepted 29 October 2020

DOI:https://doi.org/10.1103/PhysRevD.102.112001

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Published by the American Physical Society