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human
How do we know that the neutrinos have spin?

Neutrinos are neutrally charged particles that do not interact neither by strong force or electromagnetism. How do we know that neutrinos are spin 1/2 fermions? Could neutrinos have higher spin numbers?
gpt
Neutrinos were originally proposed as a way to explain the observed electron spectrum in beta decay:

n -> p + e + (anti)nu_e

Conservation of angular momentum for this reaction requires that the neutrino must be a fermion. The proton, neutron and electron are all spin-1/2. So the left-hand side of the reaction is spin 1/2, and the proton and electron together have a total spin of 1, only capable of generating states of integer spin in any given direction. It is therefore impossible for the neutrino to also have integer spin, since you would never be able to get a spin-1/2 state of the system on the right-hand side if that was the case. So the neutrino must have half-integer spin, i.e. it must be a fermion.

As to why it's specifically spin-1/2 and not some higher half-integer spin, this is more complicated. Fundamental particles in particular have more stringent limitations imposed on their possible spin from things like the Coleman-Mandula theorem, and in general a particle with spin higher than 1 will have unphysical scattering dynamics at high energies unless something very convoluted is done to fix things, that you wouldn't have to do if the neutrino was spin-1/2. The spin-1/2 model is sufficient to explain the data we have, so there's really no reason to have all of that extra complexity.