Neutral Pion Decay: Why Can't it Produce Three Photons?

[akr]

Why is it not allowed for the neutral pion to decay to three photons? The PDG states that this mode violates charge conjugation, although obviously the two photon decay is the dominant decay of this particle, and I don't see how adding another neutral particle to the decay causes a violation of charge.

Thanks in advance!

 

[arivero]

Note that it is also forbidden to decay to two photons.

 

[Meir Achuz]

"Charge conjugation" invariance is different than charge conservation.
There is a quantum operator C which converts a particle into its antiparticle.
Particles like the photon and pizero are their own antiparticles.
They are eigenstates of the charge conjugation operator C.
The photon has eigenvalue C=-1, which is determined by how it enters QED.
The pizero has eigenvalue C=+1, which is determined experimentally by the fact that it decays into two photons and not three (The operator C is a multiplicative operator.), and theoretically by the quark model. A particle with C=+1 cannot decay into an odd number of photons.

 

[akr]

Thanks very much!