0 Obtaining the Spin of the Proton from the Spins of the Quarks

Employing the experimental electro-weak interactions between quarks and leptons, the spin of the proton may easily be understood in terms of the spins of the constituent quarks. Before considering how one may obtain the spin of the proton from the spin of the constituitive qurks, let us recall a simple fact about total spin zero momentum space wave functions for any two spin one half particles; e.g. Ψ spin zero (k 1 , σ 1 , k 2 , σ 2) = 1 2 Φ(k 1 , k 2) (χ ↑ (σ 1)χ ↓ (σ 2) − χ ↑ (σ 2)χ ↓ (σ 1)). (1) The probability distribution in momentum and spin for one of the particles, for example P 1 (k 1 , σ 1) = σ 2 d 3 k 2 Such an equipartition of spin probability would certainly not hold true for a total spin one polarized wave function; e.g. Ψ spin one (k 1 , σ 1 , k 2 , σ 2) = Φ triplet (k 1 , k 2)χ ↑ (σ 1)χ ↑ (σ 2). Now, suppose that the proton is made up of three quarks (duu), and further suppose the quarks are distributed as a spin zero diquark [1,2] and a spin one half quark. Say (p) = (duu) = (du) (spinless diquark) + u (quark) tied together by a " string " as in conventional fragmentation models. Under the above hypothesis, the momentum probabilities are independent of spin for the quarks in the diquark, both d ∈ (du) and u ∈ (du), and only the isolated quark (u) may have a momentum probability which depends on polarization. From lepton-proton scattering polarization measurements of spin, s polarized = 1 2 η,