Quark distribution Functions

describe and here

Polarized

Both models, pQCD and a hyperfine perturbed constituent quark model(CQD), show that as the scaling variable goes to one the double spin asymmetry is unity. On the other hand, CQM with SU(6) symmetry predicts that at = 1 = 5/9 for the proton, = 0 for the neutron and = 1/3 for the deuteron. The double spin asymmetry and the ratio of the polarized valence down quark distribution function to the unpolarized
The inclusive double polarization asymmetries can be written in terms of polarized and unpolarized valence quark distributions,

I =
I =

The semi-inclusive pion electro-production asymmetries can be written in terms of the valence quark distributions
=

=

where

=
where is the measured difference of the yield from oppositely charged pions.
The semi - inclusive asymmetry can be expressed in the following way

-

where and

An asymmetry

The last equation can be expressed as