Search for $Υ(1S,2S) \to Z^{+}_{c}Z^{(\prime) -}_{c}$ and $e^{+}e^{-} \to Z^{+}_{c}Z^{(\prime) -}_{c}$ at $\sqrt{s}$ = 10.52, 10.58, and 10.867 GeV
The first search for $Z_{c}$ pair production in $Υ(1S)$ and $Υ(2S)$ decays and in $e^{+}e^{-}$ annihilation at $\sqrt{s}$ = 10.52, 10.58, and 10.867 GeV is conducted using data collected with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant signals are observed in any of the studied modes, and the 90\% credibility level upper limits on their product branching fractions in $Υ(1S)$ and $Υ(2S)$ decays (${\cal B}(Υ(1S,2S)\to Z^{+}_{c}Z^{(\prime) -}_{c})\times{\cal B}(Z^{+}_{c}\toπ^{+}+c\bar c)$ ($c\bar c=J/ψ$, $χ_{c1}(1P)$, $ψ(2S)$)) and the product of Born cross section and branching fraction for $e^{+}e^{-} \to Z^{+}_{c}Z^{(\prime) -}_{c}$ ($σ(e^+e^- \to Z^{+}_{c}Z^{(\prime) -}_{c})\times {\cal B}(Z^{+}_{c} \to π^+ +c\bar c)$) at $\sqrt{s}$ = 10.52, 10.58, and 10.867 GeV are determined. Here, $Z_{c}$ refers to the $Z_{c}(3900)$ and $Z_{c}(4200)$ observed in the $πJ/ψ$ final state, the $Z_{c1}(4050)$ and $Z_{c2}(4250)$ in the $πχ_{c1}(1P)$ state, and the $Z_{c}(4050)$ and $Z_{c}(4430)$ in the $πψ(2S)$ state.