Theory

Quark distribution Functions

Polarized

The inclusive double polarization asymmetries [math]A_N[/math] can be written in terms of polarized [math]\triangle q_v (x)[/math] and unpolarized [math] q_v (x)[/math] valence quark distributions,

[math]A_{1, p}[/math] = [math]\frac {4\triangle u_v (x) + \triangle d_v (x)} {4 u_v (x) + d_v (x)} [/math]
[math]A_{1, n}[/math] = [math]\frac {\triangle u_v (x) + 4\triangle d_v (x)} {u_v (x) + 4d_v (x)} [/math]

The semi-inclusive pion electro-production asymmetries can be written in terms of the valence quark distributions in the following way
[math]A_{1, p}\lt sup\gt (\pi +) - (\pi -)\lt /sup\gt [/math] = [math]\frac {4\triangle u_v (x) - \triangle d_v (x)} {4 u_v (x) - d_v (x)} [/math]

[math]A_{1, H}((\pi +) - (\pi -))[/math] = [math]\frac {\triangle u_v (x) + \triangle d_v (x)} { u_v (x) + d_v (x)} [/math]

where

[math]A ((\pi+) - (\pi-))[/math] = [math]\frac {\sigma} {3} [/math] A⁵