# How a particle's spin is decided?

• I
Gold Member
I'm taking a course in particle physics. One of the features different from particle to particle is the spin. For example Higgs boson has spin 0, muon and electron have spin 1/2, graviton has spin 2, and so on. How is this decided upon? Does it occur in the experiments or is it based on theoretical calculations?

mfb
Mentor
You can make theoretical predictions but you can also measure it. For stable or long-living charged particles you can directly measure how the particle react to electromagnetic radiation (e.g. for protons and electrons). For particles that live too short for this you can study the angular distributions and energy distributions of decay products as they depend on the particle spin. This is how the spin of the Higgs boson has been measured for example.

The graviton has never been seen as individual particle, but particles that lead to the polarization type we see with gravitational waves have to have spin 2.

phoenix95
Gold Member
The graviton has never been seen as individual particle, but particles that lead to the polarization type we see with gravitational waves have to have spin 2.
So I assume theoretical calculation of spin follows from the polarisation of the waves? How?

mfb
Mentor
If you rotate an electromagnetic wave around its propagation direction you have to rotate it by 360 degrees (2pi) until it matches the original wave. It has spin 1.
If you rotate the wave function of an electron in an analog way you have to rotate it by 720 degrees (4pi) until it matches the original wave. It has spin 1/2.
If you rotate a gravitational wave you have to rotate it by 180 degrees (pi) until it matches the original wave. It has spin 2.

Every particle physics textbook and good textbooks on quantum mechanics should cover that.

phoenix95