To my understanding the decay of a neutral pion into an electron-positron pair can only happen by the electromagnetic force and the mediation of two virtual photons in a triangle-diagram, so it is loop-suppressed.
What I'm failing to understand is: What is forbidding the direct decay into an electron-positron pair rather than 2 gamma rays? And why is the weak decay forbidden?
I assume I'm missing a conservation law, the question is which one?
Best Answer
In the pion reference frame the two outgoing leptons are very boosted, hence helicity and chirality almost coincide. The angular momentum conservation forces them to have opposite spins, since the pion spin is zero. Therefore, they will have the same helicity, which is highly suppressed in this kinematic regime, because of the vector nature of the QED interactions (see for example Thomson, Modern Particle Physics, chapter 6). Just my two cents.