Position Space Interpretation for Generalized Parton Distributions
Position Space Interpretation for Generalized Parton Distributions
Position Space Interpretation for Generalized Parton Distributions
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Impact parameter dependent PDFs<br />
q(x,b ⊥ ) ≡<br />
use translational invariance to relate to same matrix element that<br />
appears in def. of GPDs<br />
∫<br />
dx −〈 p + ,R ⊥ = 0 ⊥<br />
∣ ∣¯q(− x−<br />
2 ,b ⊥)γ + q( x−<br />
2 ,b ⊥) ∣ ∣p + ,R ⊥ = 0 ⊥<br />
〉<br />
e<br />
ixp + x −<br />
∫ ∫<br />
= |N | 2 d 2 p ⊥<br />
∫d 2 p ′ ⊥<br />
dx −〈 ∣<br />
p + ,p ′ ⊥<br />
∣¯q(− x−<br />
2 ,b ⊥)γ + q( x−<br />
2 ,b ⊥) ∣ 〉<br />
∣p + ,p ⊥ e<br />
ixp + x −<br />
<strong>Position</strong> <strong>Space</strong> <strong>Interpretation</strong> <strong>for</strong> <strong>Generalized</strong> <strong>Parton</strong> <strong>Distributions</strong> – p.11/55
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