Quark distribution Functions
define and describeand here
Both models, pQCD and a hyperfine perturbed constituent quark model(CQD), show that as the scaling variable
The inclusive double polarization asymmetriesin the valence region, where the scaling variable can be written in terms of polarized and unpolarized valence quark distributions,
The semi-inclusive pion electro-production asymmetries can be written in terms of the valence quark distributions
where is the measured difference of the yield from oppositely charged pions. Using the first four equation (1), (2), (3) and (4) one can construct the valence quark distribution functions.
The semi - inclusive asymmetry can be rewritten in terms of the measured semi-inclusive and asymmetries:
where is the unpolarized structure function and the scaling polarized structure function.
The last equation can be expressed as
using the nomel