Pi 0 Decay: Chances of e+ e- Gamma vs e+ e-

[Manel]

Hello everyone,
I found in the PDG booklet that pi 0 decay into e+ e- gamma is more likely to happen than to e+ e- only ..is there a reason that favorises the first decay?

 

[Orodruin]

The decay to a single electron-positron pair is suppressed because what would be the leading order contribution, the diagram with the exchange of one single photon, evaluates to zero.

 

[Manel]

the diagram with the exchange of one single photon, evaluates to zero.

I didn't understand what you mean here. Would you please clarify. Thanks a lot

 

[Orodruin]

The decays must happen via an intermediate state. The intermediate state which would be contributing the most to the electron-positron decay based on the couplings is not allowed.

 

[Manel]

Any resource detailing that ? So grateful

 

[Orodruin]

Complete understanding of this would require an introductory course in quantum field theory, usually given at universities somewhere in year 3-4.

 

[Manel]

Thanks a lot

 

[Hepth]

also helicity suppression probably plays a role. a pseudoscalar decaying to to leptons will be suppressed by the mass of the lepton, due to conservation of angular momentum requiring a spin flip on one lepton. adding the photon will allow the lepton to not have to flip, thus trading the mass suppression for alphaEM.