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Comment by prof-dr-ir | Hacker News Reader

> there's a chance neutrinos are Majorana particles.

Pet peeve: don't say "are Majorana particles", say "have a Majorana mass term".

All spin 1/2 fermions in four spacetime dimensions can be constructed from the chiral (or Weyl) representation. A Dirac fermion is two independent chiral fermions. A Majorana fermion is just a chiral fermion written in a funny way. And people saying that chiral fermions cannot have mass are lying. (/rant)

By the way, a nicer explanation for the neutrino masses is the so-called seesaw mechanism:

https://en.wikipedia.org/wiki/Seesaw_mechanism

In this wiki article the Majorana mass is denoted B'. However, as the article explains, it must vanish by gauge invariance in the standard model.

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> And people saying that chiral fermions cannot have mass are lying

People usually say that in the context of the vanilla Standard Model. So far, experiments say we don't see right handed neutrinos and we also don't see lepton number violation. So we can't have masses there. This stuff only works if you start with the assumption that the Standard Model is an effective field theory and introduce higher dimension operators. Or if you go full BSM. The most simple expansion of the standard model that allows for Neutrino oscillations precisely needs them to be (pure) Majorana particles. Though that doesn't explain their weird masses as you say and the more complex expansion that results in seesaw (which adds a Dirac mass) seems a bit more natural. So your argument is mostly a case of missing context.

I kind of disagree on your statement about lepton violation. The standard model predicts lepton violating processes (sphalerons). The true symmetry of the standard model is B-L. Of course you are right, that these topological effects will not lead to majorana mass terms.

Well, while sphalerons theoretically break B+L in the non-perturbative regime, they are exponentially suppressed at the energy level of our colliders. At the same time, irrelevant operators that also violate it are suppressed by the GUT scale. So even if you take the minimal Standard Model at face value, you're out of luck finding any sign of the violation either way. But if Neutrinos get Majorana masses, that would be an additional explicit violation at the perturbative level. That would be something we can directly observe, as in neutrinoless double beta decay.

I agree, that neutrinoless double beta decay would be incredibly interesting, but it is very speculative (and depending on the neutrino mass hierarchy not really falsifiable).

My original point was just that lepton number is not a good symmetry as it is broken by rhe chiral anomaly, which is not speculative at all. Of course, the sphaleron effects are negligible in collider settings, but for cosmology they are crucial and might be indirectly observable.

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