Difference between revisions of "Theory"

From New IAC Wiki
Jump to navigation Jump to search
Line 33: Line 33:
  
  
An asymmetry <math>\triangle R_{np} ^{\pi^+ + \pi^-} = \frac {\triangle\sigma_p^{\pi^+ + \pi^-} - \triangle\sigma_n^{\pi^+ + \pi^-}} {\sigma_p^{\pi^+ + \pi^-} - \sigma_n^{\pi^+ + \pi^-}} = \frac {g_1^p - g_1^n} {F_1^p - F_1^n} (x, Q^2)</math>
+
An asymmetry <math>\triangle R_{np} ^{\pi^+ + \pi^-} = \frac {\triangle\sigma_p^{\pi^+ + \pi^-} - \triangle\sigma_n^{\pi^+ + \pi^-}} {\sigma_p^{\pi^+ + \pi^-} - \sigma_n^{\pi^+ + \pi^-}} = \frac {g_1^p - g_1^n} {F_1^p - F_1^n} (x, Q^2)</math><br>
 +
 
 +
 
 +
The last equation can be expressed as<br>
 +
<math>\triangle R_{np} ^{\pi^+ + \pi^-} = R_{n/p}[\frac {A_p^{\pi^+}} {1 + \frac {1} {R_p^{{\pi^+}/{\pi^-}}} } </math> - <math>\frac {A^{\pi^-}} {1 + R_p^{{\pi^+}/{\pi^-}} } ]
 +
+ R_{n/p}[\frac {A^{\pi^+}} {1 + \frac {1} {R_p^{{\pi^+}/{\pi^-}}} } </math> - <math>\frac {A^{\pi^-}} {1 + R_p^{{\pi^+}/{\pi^-}} } ]</math>

Revision as of 18:35, 18 July 2007

Inclusive Scattering

W

Semi-Inclusive Scattering

Quark distribution Functions

describe [math] q_v (x)[/math] and [math]\Delta q_v (x)[/math] here

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

where [math]R_{2H}^{\pi^+/\pi^-} = \frac{\sigma^{\pi^+}} {\sigma^{\pi^-}}[/math] and

[math]A^{\pi^+ (\pi^-)} = \frac {\sigma^{\pi^+ (\pi^-)}_{\uparrow \downarrow} - \sigma^{\pi^+(\pi^-)}_{\uparrow \uparrow}} {\sigma^{\pi^+ (\pi^-)}_{\uparrow \downarrow} + \sigma^{\pi^+(\pi^-)}_{\uparrow \uparrow}} [/math]


An asymmetry [math]\triangle R_{np} ^{\pi^+ + \pi^-} = \frac {\triangle\sigma_p^{\pi^+ + \pi^-} - \triangle\sigma_n^{\pi^+ + \pi^-}} {\sigma_p^{\pi^+ + \pi^-} - \sigma_n^{\pi^+ + \pi^-}} = \frac {g_1^p - g_1^n} {F_1^p - F_1^n} (x, Q^2)[/math]


The last equation can be expressed as
[math]\triangle R_{np} ^{\pi^+ + \pi^-} = R_{n/p}[\frac {A_p^{\pi^+}} {1 + \frac {1} {R_p^{{\pi^+}/{\pi^-}}} } [/math] - [math]\frac {A^{\pi^-}} {1 + R_p^{{\pi^+}/{\pi^-}} } ] + R_{n/p}[\frac {A^{\pi^+}} {1 + \frac {1} {R_p^{{\pi^+}/{\pi^-}}} } [/math] - [math]\frac {A^{\pi^-}} {1 + R_p^{{\pi^+}/{\pi^-}} } ][/math]