Quark loop contribution to ${\pi }^0\to 4\gamma$

We find the contribution of constituent quark-loop mechanism to the branching ratio of ${\pi }^0\to 4\gamma$ process to be $B_{4\gamma }^{\mathrm{hadr}}={\Gamma }_{{\pi }^0\to 4\gamma }/{\Gamma }_{{\pi }^0\to 2\gamma }\approx 5.45·{10}^{-16}$ for the reasonable choice of constituent quark mass $m\approx 280\mathrm{MeV}$. This result is in agreement with the vector-dominance approach result obtained years ago. Thus the main contribution arises from the QED mechanism ${\pi }^0\to \gamma ({\gamma }^{*})\to \gamma (3\gamma )$ including light-light scattering block with electron loop. This contribution was investigated in the paper of one of us and gave $B_{4\gamma }^{\mathrm{QED}}\sim 2.6·{10}^{-11}$.

Figure 1

Diagrams of hadronic contribution within Vector-Dominance model (VDM).

Figure 2

Diagrams of hadronic contribution within constituent quark-loop approach.