Electromagnetic decay of a neutral pion

Question

Why do neutral pions decay electromagnetically? Other neutral particles such as the neutron decay weakly, and charged pions decay weakly.

Answer 1

Pions and neutrons are hadrons, composite particles built from quarks:

• Neutrons are baryons, i.e. made of $udd$ combination of $u$ (up) and $d$ (down) quarks.
• Charged pions are mesons, i.e. they are made of quark and antiquark (denoted by bar above the letter) combination: $\pi^+ (u\bar d)$, $\pi^- (d\bar u)$, $\pi^0 (u\bar u \text{ or } d \bar d)$

From this information, and knowing that only one type of vertex is allowed in EM (photon, fermion in, fermion out), you can see how the neutral pion decays:

On the other hand, for charged pions you have a quark without the corresponding antiquark, you cannot get rid of them just by EM vertices, as the vertices have the same fermion on both legs.

Also think about the electric charge - photons carry no charge, but the initial charged pion does.