The $Z \to c\bar c \to \gamma \gamma *$, $Z \to b\bar b \to \gamma \gamma *$ triangle diagrams and the Z → γψ, Z → γγ decays

Abstract

We expounded an approach for studying the Z → γψ and Z → γγ decay based on the sum rules for the $Z \to c\bar c \to \gamma \gamma *$ and $Z \to b\bar b \to \gamma \gamma *$ amplitudes and their derivatives. We calculate the branching ratios of the Z → γψ and Z → γγ decays under different suppositions about the saturation of the sum rules. We find the lower bounds of Σ _ψ BR(Z → γψ) = 1.95 · 10 ⁻⁷ and Σ _γ BR(Z → γγ) = 7.23 · 10⁻⁷ and discuss deviations from the lower bounds including the possibility of BR[Z → γJ/ψ(1S)] ∼ BR[Z → γγ(1S)] ∼ 10 ⁻⁶, which is probably measurable at the LHC. Moreover, we calculate the angle distributions in the Z → γψ and Z → γγ decays.