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The Z\to c\bar c\toγγ^{\ast}, Z\to b\bar b\toγγ^{\ast} triangle diagrams and the Z\toγψ, Z\to γΥdecays

It is expounded the approach to the Z\toγΨand Z\toγΥdecay study, based on the sum rules for the Z\to c\bar c\toγγ^{\ast} and Z\to b\bar b\toγγ^{\ast} amplitudes and their derivatives. The branching ratios of the Z\toγψand Z\toγΥdecays are calculated for different guesses as to saturation of the sum rules. The lower bounds of \sum_ψ BR(Z\toγψ) = 1.95\cdot 10^{-7} and \sum_Υ BR(Z\toγΥ) = 7.23\cdot 10^{-7} are found. Deviations from the lower bounds are discussed, among them the possibility of BR(Z\toγJ/ψ(1S))\sim BR(Z\toγΥ(1S))\sim 10^{-6}, that could be probably measured in LHC. The angle distributions in the Z\toγψand Z\toγΥdecays are calculated also.