Difference between revisions of "TF InclusiveDeltaDoverD"

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Using Isospin symmetry
 
Using Isospin symmetry
  
<math>u(x) \equiv u^p(x)\equiv d^n(x) \;\;\;\;\;</math> and <math>d(x) \equiv d^p(x)\equiv u^n(x) </math>
+
<math>u(x) \equiv u^p(x)\equiv d^n(x) \;\;\;\;\;</math> and <math>\;\;\;\;\;d(x) \equiv d^p(x)\equiv u^n(x) </math>
  
 
The unpolarized structure functions for the proton and neutron  may be written as  
 
The unpolarized structure functions for the proton and neutron  may be written as  

Revision as of 16:14, 22 September 2018

Delta_D_over_D

[math] q_i(x) \equiv q_i^{\parallel}(x) + q_i^{\perp}(x)[/math]

[math] \Delta q_i(x) \equiv q_i^{\parallel}(x) - q_i^{\perp}(x)[/math]



[math] F_1(x) \equiv \frac{1}{2} \sum_q e_i^2 q_i(x) [/math]


using the above definition to define the proton and neutron unpolarized structure function:

[math] F_1^p(x) \equiv \frac{1}{2} \sum_q e_i^2 q_i^p(x) = \frac{1}{2}\left [ \left( \frac{2}{3} \right)^2 u^p(x)+ \left( \frac{-1}{3} \right)^2 d^p(x)\right ] =\frac{1}{2} \left [\frac{4}{9}u^p(x) + \frac{1}{9}d^p(x)\right ][/math]

[math] F_1^n(x) \equiv \frac{1}{2} \sum_q e_i^2 q_i^p(x) = \frac{1}{2}\left [ \left( \frac{2}{3} \right)^2 u^n(x)+ \left( \frac{-1}{3} \right)^2 d^n(x)\right ] =\frac{1}{2} \left [\frac{4}{9}u^n(x) + \frac{1}{9}d^n(x)\right ][/math]


Using Isospin symmetry

[math]u(x) \equiv u^p(x)\equiv d^n(x) \;\;\;\;\;[/math] and [math]\;\;\;\;\;d(x) \equiv d^p(x)\equiv u^n(x) [/math]

The unpolarized structure functions for the proton and neutron may be written as

[math] F_1^p(x) =\frac{1}{2} \left [\frac{4}{9}u(x) + \frac{1}{9}d(x)\right ] \;\;\;\;\;[/math] [math] F_1^n(x)=\frac{1}{2} \left [\frac{4}{9}d(x) + \frac{1}{9}u(x)\right ][/math]



[math] g_1(x) \equiv \frac{1}{2} \sum_q e_i^2 \Delta q_i(x) [/math]

[math]g_1^d \approx \left ( 1 - 1.5 \omega_D \right ) \left ( g_1^n + g_1^p \right )[/math]<ref> Eq. 28 from https://arxiv.org/abs/1505.07877 which is based on https://arxiv.org/abs/0809.4308</ref>


<references />


Delta_D_over_D