Theory

Quark distribution Functions

Polarized

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

$A_{1, p}$ = $\frac {4\triangle u_v (x) + \triangle d_v (x)} {4 u_v (x) + d_v (x)}$
$A_{1, n}$ = $\frac {\triangle u_v (x) + 4\triangle d_v (x)} {u_v (x) + 4d_v (x)}$

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

$A_{1, H}((\pi +) - (\pi -))$ = $\frac {\triangle u_v (x) + \triangle d_v (x)} { u_v (x) + d_v (x)}$

where

$A ((\pi+) - (\pi-))$ = $\frac {\sigma} {3}$ A⁵