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 />
∫ ∫<br />
= |N | 2 d 2 p ⊥<br />
∫d 2 p ′ ⊥<br />
= |N | 2 ∫<br />
d 2 p ⊥<br />
∫d 2 p ′ ⊥H<br />
dx −〈 p + ,p ′ ∣<br />
⊥ ¯q(− x−<br />
2 ,b ⊥)γ + q( x−<br />
2 ,b ⊥) ∣ 〉<br />
∣p + ,p ⊥ e<br />
ixp + x −<br />
dx −〈 p + ,p ′ ∣<br />
⊥ ¯q(− x−<br />
2 ,0 ⊥)γ + q( x−<br />
2 ,0 ⊥) ∣ ∣p + 〉<br />
,p ⊥ e<br />
ixp + x −<br />
×e ib ⊥·(p ⊥ −p ′ ⊥ )<br />
(<br />
x, 0, − (p ′ ⊥ − p ⊥ ) 2) e ib ⊥·(p ⊥ −p ′ ⊥ )<br />
↩→ q(x,b ⊥ ) =<br />
∫ d 2 ∆ ⊥<br />
(2π) 2 H(x, 0, −∆2 ⊥)e ib ⊥·∆ ⊥<br />
<strong>Position</strong> <strong>Space</strong> <strong>Interpretation</strong> <strong>for</strong> <strong>Generalized</strong> <strong>Parton</strong> <strong>Distributions</strong> – p.13/55