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We report the results of a first search for a doubly-charged $DDK$ boundstate, denoted the $R^{++}$, in $\Upsilon(1S)$ and $\Upsilon(2S)$ inclusivedecays 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 Belledetector at the KEKB asymmetric-energy $e^+e^-$ collider. No significantsignals are observed in the $D^{+}D_{s}^{*+}$ invariant-mass spectra of allstudied modes. The 90\% credibility level upper limits on their productbranching fractions in $\Upsilon(1S)$ and $\Upsilon(2S)$ inclusive decays(${\cal B}(\Upsilon(1S,2S) \to R^{++} + anything) \times {\cal B}(R^{++} \toD^{+} D_{s}^{*+})$), and the product values of Born cross section and branchingfraction in $e^+e^-$ collisions ($\sigma(e^+e^- \to R^{++} + anything) \times{\cal B}(R^{++} \to D^{+} D_{s}^{*+})$) at $\sqrt{s}$ = 10.520, 10.580, and10.867 GeV under different assumptions of $R^{++}$ masses varying from 4.13 to4.17 GeV/$c^2$, and widths varying from 0 to 5 MeV are obtained.

physical review. d/physical review. d.

Search for a doubly-charged $DDK$ bound state in $\Upsilon(1S,2S)$  inclusive decays and via direct production in $e^+e^-$ collisions at  $\sqrt{s}$ = 10.520, 10.580, and 10.867 GeV