Inclusive Scattering
W
Semi-Inclusive Scattering
Quark distribution Functions
Unpolarized
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]I = [math]\frac {4\triangle u_v (x) + \triangle d_v (x)} {4 u_v (x) + d_v (x)} [/math]
[math]A_{1, n}[/math]I = [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
[math]A_{1, p}[/math][math]\pi^+ - \pi^-[/math] = [math]\frac {4\triangle u_v (x) - \triangle d_v (x)} {4 u_v (x) - d_v (x)} [/math]
[math]A_{1,2H}[/math][math]\pi^+ - \pi^-[/math] = [math]\frac {\triangle u_v (x) + \triangle d_v (x)} { u_v (x) + d_v (x)} [/math]
where
[math]A[/math][math]\pi^+ - \pi^-[/math] =[math]\frac {\sigma^{\pi^+ - \pi^-}_{\uparrow \downarrow} - \sigma^{\pi^+ - \pi^-}_{\uparrow \uparrow}} {\sigma^{\pi^+ - \pi^-}_{\uparrow \downarrow} + \sigma^{\pi^+ - \pi^-}_{\uparrow \uparrow}} [/math]
where [math]\sigma^{\pi^+ - \pi^-}[/math] is the measured difference of the yield from oppositely charged pions.
The semi - inclusive asymmetry can be expressed in the following way
[math]A_{1,2H}[/math][math]\pi^+ - \pi^-[/math] = [math]\frac {A^\pi^+} {1} [/math]