The Zto cbar ctoγ γ^(ast), Zto bbar btoγ γ^(ast) triangle diagrams and the Ztoγ psi, Zto γ Upsilon decays

It is expounded the approach to the Z\to\gamma\Psi and Z\to\gamma\Upsilon decay study, based on the sum rules for the Z\to c\bar c\to\gamma\gamma^{\ast} and Z\to b\bar b\to\gamma\gamma^{\ast} amplitudes and their derivatives. The branching ratios of the Z\to\gamma\psi and Z\to\gamma\Upsilon decays are calculated for different guesses as to saturation of the sum rules. The lower bounds of \sum_{\psi} BR(Z\to\gamma\psi) = 1.95\cdot 10^{-7} and \sum_{\Upsilon} BR(Z\to\gamma\Upsilon) = 7.23\cdot 10^{-7} are found. Deviations from the lower bounds are discussed, among them the possibility of BR(Z\to\gamma J/\psi(1S))\sim BR(Z\to\gamma\Upsilon(1S))\sim 10^{-6}, that could be probably measured in LHC. The angle distributions in the Z\to\gamma\psi and Z\to\gamma\Upsilon decays are calculated also.