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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.

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    $\begingroup$ The answer is clear, thank you. I thought it had to do with the helicities of the neutrino's causing the weak suppression. $\endgroup$
    – MinecraftPlayer69
    Apr 3, 2022 at 22:02
  • $\begingroup$ 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. $\endgroup$
    – Cosmas Zachos
    Apr 3, 2022 at 22:10

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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…

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

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