# Quark intrinsic angular momentum and the Proton Spin Crisis

According to recent results regarding the "Proton Spin Crisis", apparently only about 30% of the total angular momentum of the proton comes from the intrinsic angular momentum of its constituent quarks, the rest apparently being the result of gluon spin, sea quarks and orbital angular momentum.

I understand that sum rules for angular momentum only apply in weakly bound, perturbative composites such as atoms in which angular momentum coupling occurs and as such is an approximation that fails in strongly bound composites such as hadrons.

But what I don't understand is that I have been taught from the beginning that in quantum physics, angular momentum is a fundamentally discrete quantity that only comes in integer or half integer multiples of the reduced Planck constant and that this applies to mesons and baryons just as much as it applies to the elementary particles. The theory of the nucleus requires that protons and neutrons are fermions with exactly 1/2\h spin so that they follow the the Pauli exclusion principle. Also, the need for color charge is motivated by the use of the spin of mesons and baryons to demonstrate that quarks are fermions and the consequent necessity of color charge to allow quarks to have an antisymmetric collective wavefunction to avoid the contradiction entailed by the (ostensibly) symmetric wave function of the delta baryon. If the angular momentum sum rules don't apply to baryons and mesons, doesn't that make this argument for the existence of color charge logically questionable?

Basically, what's constraining the spin of the proton to be discrete and exactly one half the reduced Planck constant if it's produced by a strong interaction between large numbers of gluons and sea quarks?

(Please don't mistake me for a crank. I know I've totally misunderstood something basic about the theory, I'm not trying to argue with scientists who are probably a million times smarter than me.)

• It is not a crisis about the sum rule of angular momentum. It is rather a puzzle about the intrinsic spin distribution of partons (quarks and gluons) which turns out not to be the same as the protons as a whole. So, there should be other contributions to the total spin. Some proposals were made in the sense that the orbital angular momentum of partons are responsible to have a different distribution than expected. – Oktay Doğangün Apr 22 '18 at 11:17
• Hi. Thank you for your comment, it's very helpful. So, although the total spin of the proton must always be quantized and discrete - one half times the reduced planck constant - the distribution of this discrete spin amongst the constituents of the proton can be very complex - perhaps fractional or continuous, in a sense? This just seems a little odd given how fermionic quarks are motivated in the books I've read as the necessary components of mesons (baryons) since their integer (half-integer) spins are explained by the fact that they contain 2 (3) constituent quarks. – G. Summers Apr 22 '18 at 18:37