A How do we know the spins of elementary particles?

[Shen712]

How do we know the spin of an elementary particle? For example, a fermion has spin 1/2; a photon has spin 1; and even the ficticious graviton has spin 2. How do we know these spins? In other words, how are these spins determined?

 

[DrDu]

Spin is angular momentum and this can be measured, at least for electrons (https://en.wikipedia.org/wiki/Einstein–de_Haas_effect) and photons.
For gravitons, it is postulated from the form of the equations of general relativity.

 

[dextercioby]

To be a little nit-picking, fermions have spin 1/2, 3/2, 5/2, etc, not only 1/2. I would say that the graviton's spin is derived, not postulated.

 

[mfb]

For stable and long-living particles, we can put them in magnetic fields and watch the spin orientation change. In some cases we can also put them in inhomogeneous fields and measure the force directly (Stern-Gerlach experiment).

For unstable particles, we can study their decays: the angular and energy distributions of the decay products depend on the spin of the particles.

Gravitons have to couple to the stress-energy tensor to mediate gravity, and this is only possible with spin 2.

 

[DrDu]

For stable and long-living particles, we can put them in magnetic fields and watch the spin orientation change. In some cases we can also put them in inhomogeneous fields and measure the force directly (Stern-Gerlach experiment).

Yes, but this rather measures the magnetic moment than the spin.

 

[mfb]

Well, the two are related. You can predict the g-factor and the spin and check that the magnetic moment has the expected value. It works with electrons, although the measurements are typically interpreted as measurements of the g-factor. I don't know if protons and neutrons have a good theoretical prediction of their g-factor.

 

[Vanadium 50]

I don't know if protons and neutrons have a good theoretical prediction of their g-factor.

Depends on what you mean by "good". The naive static quark model gives μ(p) = 3 and μ(n) = -2 (in nuclear magnetons). Measured values are 2.793 and -1.913. QCD with perfect SU(2) flavor symmetry predicts μ(n)/μ(p) = -2/3. (It's essentially a Clebsch-Gordon coefficient) The measured value is -0.685.