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If I've got an instance of a fundamental particle, how can I separate out the measurements of these three concepts?

(I think) I understand the theory behind them, and why the particles in the standard model are predicted to have the values they do. However, the process of validation of these numbers eludes me. How have they been historically measured?

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For spin measurements the original experiment was the Stern-Gerlach experiment in which you will see that a prior unpolarized beam will split up in two (Spin up and down) orientations.

see: http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment

For helicity, a very ingenious and fascinating experiment is the famours Goldhaber experiment that uses a very peculiar set of elements and also the Mößbauer effect to measure the helicity of neutrinos. The helicity is the projection of the Spin onto the momentum direction, and thus if you measure spin and momentum, you can compute helicity.

Link to original paper here: http://www.bnl.gov/nh50/

People often confuse helicity and chirality they are only the same in the case of massless particles. This is also the reason why we know that (at least interacting) neutrinos are always left-handed (the famous $$SU(2)_L$$ ), at least if we assume that neutrinos are massless (which is almost the case, but not strictly).

In contrast to helicity for massive particles (where you can always boost into a frame where you change the sign of the momentum direction and thus change helicity), chirality is a Lorentz-invariant property of the particle.

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This answer is fine +1, but the $SU(2)_L$ is before Higgs mechanism, where the neutrino is perfectly massless as well as the electron. –  Ron Maimon Apr 26 '12 at 4:54
    
one should also add that for decaying particles angular distributions of the decay products in the center of mass system can determine spin. –  anna v Apr 14 '13 at 10:50

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