What are the fundamental violations in $\rm n \to p+e^-$?

Question

When the neutrino was postulated to complete the decay:

$$\rm n \to p+e^-+\bar{\nu}_e$$

if I'm not wrong, there was still not such a thing as lepton number violation. I know that the kinematic observed spectrum of the decay was only compatible with an additional particle taking part of the energy released in the decay, but is there any other fundamental violation taking place in this decay if the neutrino is not included?

I've deleted some pseudo-answers and related comments. – dmckee --- ex-moderator kitten Jun 05 '18 at 15:40 — dmckee --- ex-moderator kitten, Jun 05 '18 at 15:40

score 2 · Accepted Answer · answered Jun 05 '18 at 04:21

2

Just energy and momentum conservation. To be clear, the process $\rm n\to p+e^-$ could conserve momentum in principle, but the actual observed decays of the neutron violate momentum conservation if you ignore the neutrino.

answered Jun 05 '18 at 04:21

Chris

17,189

You mean the conservation of the momentum quadri-vector, right? – Juanjo Jun 05 '18 at 04:56
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Sort of. The conservation of four-momentum implies both energy conservation and three-momentum conservation. This decay violates both, not just one. – Chris Jun 05 '18 at 05:07
but isn't the total four-momentum the ones that needs to be conserved? – Juanjo Jun 05 '18 at 05:15
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No, each component is conserved separately. Energy is conserved, as is momentum in the x-direction, momentum in the y-direction, and momentum in the z-direction. – Chris Jun 05 '18 at 05:24
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It does not conserve spin. This is why the neutrino is added: the LHS has an odd half-spin, while the RHS is even. This is one of the things that brought down the hydrogen theory. – wendy.krieger Jun 05 '18 at 10:58
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It is worth looking at Pauli's "radioactive ladies and gentlemen" letter. Horse's mouth and all that. – dmckee --- ex-moderator kitten Jun 05 '18 at 17:16

What are the fundamental violations in $\rm n \to p+e^-$?

1 Answers1