Abstract
We find the contribution of constituent quark loop mechanism to the branching ratio B_{4γ} = Γ_{4γ}/Γ_{4γ} \sim 5.45 \cdot 10^{-16} for the reasonable choice of constituent quark mass m \sim 280 MeV. This result is in agreement with vector-dominance approach result obtained years ago. Thus the main contribution arises from QED mechanism π^0 \to γ(γ^*) \to γ(3γ) including light-light scattering block with electron loop. This contribution was investigated in paper of one of us and gave B_{4γ} \sim 2.6 \cdot 10^{-11}.
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