The Z → c(c)over-bar → γγ*, Z → b(b)over-bar → γγ* triangle diagrams and the Z → γψ, Z → γυ decays

The approach to the Z -> gamma psi and Z -> gamma I' decay study is presented in detail, based on the sum rules for the Z -> c -> gamma gamma* amplitudes and their derivatives. The branching ratios of the Z -> gamma psi and Z -> gamma I' decays are calculated for different hypotheses on saturation of the sum rules. The lower bounds of I pound (psi) BR(Z -> gamma psi) = 1.95 x 10(-7) and I ( pound upsilon) BR(Z -> gamma I') = 7.23 x 10(-7) are found. Deviations from the lower bounds are discussed, including the possibility of BR(Z -> gamma J/psi(1S)) similar to BR(Z -> gamma I'(1S)) similar to 10(-6), that could be probably measured in LHC. The angular distributions in the Z -> gamma psi and Z -> gamma I' decays are also calculated.