Difference between revisions of "Theory"

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==Unpolarized==
 
==Unpolarized==
 
==Polarized==
 
==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,
 
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,
 
      
 
      

Revision as of 19:42, 18 July 2007

Inclusive Scattering

W

Semi-Inclusive Scattering

Quark distribution Functions

describe qv(x) and Δqv(x) here

Unpolarized

Polarized

The inclusive double polarization asymmetries AN can be written in terms of polarized qv(x) and unpolarized qv(x) valence quark distributions,


A1,pI = 4uv(x)+dv(x)4uv(x)+dv(x)
A1,nI = uv(x)+4dv(x)uv(x)+4dv(x)


The semi-inclusive pion electro-production asymmetries can be written in terms of the valence quark distributions
A1,pπ+π = 4uv(x)dv(x)4uv(x)dv(x)


A1,2Hπ+π = uv(x)+dv(x)uv(x)+dv(x)


where

Aπ+π =σπ+π↑↓σπ+π↑↑σπ+π↑↓+σπ+π↑↑
where σπ+π is the measured difference of the yield from oppositely charged pions.
The semi - inclusive asymmetry can be expressed in the following way

Aπ+π1,2H=Aπ+1+1Rπ+/πp - Aπ1+Rπ+/πp

where Rπ+/π2H=σπ+σπ and

Aπ+(π)=σπ+(π)↑↓σπ+(π)↑↑σπ+(π)↑↓+σπ+(π)↑↑


An asymmetry Rπ++πnp=σπ++πpσπ++πnσπ++πpσπ++πn=gp1gn1Fp1Fn1(x,Q2)


The last equation can be expressed as
Rπ++πnp=Rn/p[Aπ+p1+1Rπ+/πp+Aπp1+Rπ+/πp]+Rp/n[Aπ+n1+1Rπ+/πn+Aπn1+Rπ+/πn]


Ri/j=1+(1y)22y(2y)1Rπ+i/j1+1Rπ+/πjRπ+i/j1+Rπ+/πj

Rπci/j=σπciσπcj