Theory
Inclusive Scattering
W
Semi-Inclusive Scattering
Quark distribution Functions
Unpolarized
Polarized
The inclusive double polarization asymmetries [math]\displaystyle{ A_N }[/math] can be written in terms of polarized [math]\displaystyle{ \triangle q_v (x) }[/math] and unpolarized [math]\displaystyle{ q_v (x) }[/math] valence quark distributions,
[math]\displaystyle{ A_{1, p} }[/math]I = [math]\displaystyle{ \frac {4\triangle u_v (x) + \triangle d_v (x)} {4 u_v (x) + d_v (x)} }[/math]
[math]\displaystyle{ A_{1, n} }[/math]I = [math]\displaystyle{ \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]\displaystyle{ A_{1, p} }[/math][math]\displaystyle{ \pi^+ - \pi^- }[/math] = [math]\displaystyle{ \frac {4\triangle u_v (x) - \triangle d_v (x)} {4 u_v (x) - d_v (x)} }[/math]
[math]\displaystyle{ A_{1,2H} }[/math][math]\displaystyle{ \pi^+ - \pi^- }[/math] = [math]\displaystyle{ \frac {\triangle u_v (x) + \triangle d_v (x)} { u_v (x) + d_v (x)} }[/math]
where
[math]\displaystyle{ A }[/math][math]\displaystyle{ \pi^+ - \pi^- }[/math] =