# Why can't neutral pion decay to two neutrino's

I know neutral pions mostly decay electromagnetically to two photons, but I don't understand why the decay to two neutrino's is not possible.

Perhaps they violate parity, but someone at the link https://www.physicsforums.com/threads/is-neutrino-spin-parity-1-2-or-1-2.934771/ said it does not make sense to talk about parity for neutrino's since they are produced only via the weak interaction, which does not conserve parity.

• The answer is clear, thank you. I thought it had to do with the helicities of the neutrino's causing the weak suppression. Apr 3, 2022 at 22:02
• Oh!, that too! You are right. In complete analogy to charged-pion decays, the weakly-interacting neutrino will be left-handed and the antineutrino right-handed, so, there will also be a helicity violation proportional to a power of the neutrino masses! The decay is triply doomed. Apr 3, 2022 at 22:10

Pion decay to two photons is electromagnetic (the original flavor chiral anomaly). But decay to two neutrinos could only go through a box diagram involving two Ws of opposite charge: the quarks or antiquarks hairpin of the pion wavefunction has to decay to a virtual $$W^+ ~ W^-$$ pair, which then connect to a similar hairpin involving a virtual charged lepton and a $$\nu ~\bar \nu$$ pair of decay product particles.

• That, then, entails a doubly weak suppression, by, at the very least, a factor of $$(m_\pi/M_W)^8$$ ... twenty two orders of magnitude. Hopeless.

As for parity, indeed, the doubly weak interaction blasts parity to vapor, but further consider that a neutrino-anti neutrino pair has the parity of a quark-antiquark pair…

• Hopeless, but not forbidden, so it's "possible" but super rare.
– rfl
Apr 1, 2022 at 11:04
• Wait until you start studying nucleon decay…. Apr 1, 2022 at 11:53
• hahahaha, LOL :)
– rfl
Apr 1, 2022 at 15:16