Spin of a proton from its parts.

[Spinnor]

Is there a simple way to see how all the spin and orbital angular momentum of a protons parts (quarks and gluons) sum precisely to that of a spin 1/2 fermion?

Thanks for any help!

 

[Drakkith]

All 3 quarks are spin 1/2. Since in a neutron and proton two of these quarks align oppositely of each other, they "cancel out" their spin and you have spin 1/2 left. Is that what you were asking?

 

[Spinnor]

All 3 quarks are spin 1/2. Since in a neutron and proton two of these quarks align oppositely of each other, they "cancel out" their spin and you have spin 1/2 left. Is that what you were asking?

That part I can see. My confusion is thinking of the proton as a sum of it's parts which include the gluons?

 

[Drakkith]

The gluons are virtual particles. They aren't real.

 

[SpectraCat]

The gluons are virtual particles. They aren't real.

That is incorrect .. direct experimental evidence of gluons has been observed. So they are just as real as any other particle in the "menagerie" that has been observed by it's decay products (i.e. most of them).

 

[Drakkith]

No, I mean the gluons that serve as the mediator of the strong force. Gluons are real particles, but in a proton they are virtual.

 

[tom.stoer]

@Drakkith: both quarks and gluons are "virtual" inside the nucleon. The naive picture of three constituent quarks carrying spin 1/2 each and adding these spins up to 1/2 fails when one tries to explain mass, spin etc. of nucleons based on QCD.

Experiments (deep inelastic scattering) show that the gluon contribution to the nucleon mass is large, and that quark and gluon spin together do not explain the spin 1/2. Instead the nucleon spin is something like the angular momentum of all its constituents (so-called nucleon spin crisis).

The physics of the nucleon can be understood based on lattice QCD calculations. In deep inelastic scattering experiments the contribution to mass, electric and magnetic moment, spin etc. is described using so-called structure functions which do not distinguish between "real" and "virtual".

The question why a nucleon (as a bound state of infinitly many elemenary particles) has spin 1/2 and not something totally different. The reason is
a) that a physical state must belong to some rep. of the Poincare group
b) and that the nucleon is simply the state with spin 1/2; of course there are others, ...

 

[Drakkith]

Ah, I see now. I didn't realize the situation was that complicated.