Difference between revisions of "Theory"

From New IAC Wiki
Jump to navigation Jump to search
Line 25: Line 25:
 
The semi - inclusive asymmetry can be expressed in the following way<br>
 
The semi - inclusive asymmetry can be expressed in the following way<br>
  
<math>A_{1,2H}</math><sup><math>\pi^+ - \pi^-</math></sup> = <math>\frac {A^{\pi^+}} {1} </math>
+
<math>A_{1,2H}</math><sup><math>\pi^+ - \pi^-</math></sup> = <math>\frac {A^{\pi^+}} {1 + \frac {1} {R_p^{\frac{\pi^+}{\pi^-}}} } </math>

Revision as of 18:07, 18 July 2007

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 + \frac {1} {R_p^{\frac{\pi^+}{\pi^-}}} } [/math]