Search for $Upsilon(1S,2S) to Z^{+}_{c}Z^{(prime) -}_{c}$ 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 $Upsilon(1S)$ and $Upsilon(2S)$ 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 $Upsilon(1S)$ and $Upsilon(2S)$ decays (${cal B}(Upsilon(1S,2S)to Z^{+}_{c}Z^{(prime) -}_{c})times{cal B}(Z^{+}_{c}topi^{+}+cbar c)$ ($cbar c=J/psi$, $chi_{c1}(1P)$, $psi(2S)$)) and the product of Born cross section and branching fraction for $e^{+}e^{-} to Z^{+}_{c}Z^{(prime) -}_{c}$ ($sigma(e^+e^- to Z^{+}_{c}Z^{(prime) -}_{c})times {cal B}(Z^{+}_{c} to pi^+ +cbar c)$) 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 $pi J/psi$ final state, the $Z_{c1}(4050)$ and $Z_{c2}(4250)$ in the $pichi_{c1}(1P)$ state, and the $Z_{c}(4050)$ and $Z_{c}(4430)$ in the $pipsi(2S)$ state.