Position Space Interpretation for Generalized Parton Distributions

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¢ £¢ ¤ ¢ ¡ physical origin for ⊥ distortion Comparison of a non-rotating sphere that moves in z direction with a sphere that spins at the same time around the z axis and a sphere that spins around the x axis When the sphere spins around the x axis, the rotation changes the distribution of momenta in the z direction (adds/subtracts to velocity for y > 0 and y < 0 respectively). For the nucleon the resulting modification of the (unpolarized) momentum distribution is described by E(x, 0, −∆ 2 ⊥ ). Position Space Interpretation for Generalized Parton Distributions – p.20/55
simple model for E q (x, 0, −∆ 2 ⊥ ) For simplicity, make ansatz where E q ∝ H q with E u (x, 0, −∆ 2 ⊥) = κp u 2 H u(x, 0, −∆ 2 ⊥) E d (x, 0, −∆ 2 ⊥) = κ p d H d(x, 0, −∆ 2 ⊥) κ p u = 2κ p + κ n = 1.673 κ p d = 2κ n + κ p = −2.033. Satisfies: ∫ dxE q (x, 0, 0) = κ P q Model too simple but illustrates that anticipated distortion is very significant since κ u and κ d known to be large! Position Space Interpretation for Generalized Parton Distributions – p.21/55
Page 1 and 2: Position Space Interpretation for G
Page 3 and 4: (brief) Motivation generalization t
Page 5 and 6: Generalized Parton Distributions (G
Page 7 and 8: What is Physics of GPDs Definition
Page 9 and 10: Form Factors vs. GPDs operator forw
Page 11 and 12: Impact parameter dependent PDFs q(x
Page 13 and 14: Impact parameter dependent PDFs q(x
Page 15 and 16: Discussion: GPD ↔ q(x,b ⊥ ) GPD
Page 17 and 18: Discussion: GPD ↔ q(x,b ⊥ ) b
Page 19: The physics of E(x, 0, −∆ 2 ⊥
Page 23 and 24: connection with ⊥ SSA example: γ
Page 25 and 26: Summary DVCS allows probing GPDS
Page 27 and 28: extrapolating to ξ = 0 bad news:ξ
Page 29 and 30: QCD evolution So far ignored! Can b
Page 31 and 32: suppression of crossed diagrams ¡
Page 33 and 34: use translational invariance to rel
Page 35 and 36: density interpretation of q(x,b ⊥
Page 37 and 38: Boosts in nonrelativistic QM ⃗x
Page 39 and 40: Galilean subgroup of ⊥ boosts int
Page 41 and 42: Consequences many results from NRQM
Page 43 and 44: Poincaré algebra: [P µ , P ν ] =
Page 45 and 46: Together with [J z , P k ] = iε kl
Page 47 and 48: Proof that B ⊥ |p + ,R ⊥ = 0
Page 49 and 50: ¦ ¥ ¡ ¢ £¤ simple model for q
Page 51 and 52: ¡ £ ¡ ¢ back Figure 1: P + P
Page 53 and 54: ¢ ¡ ¡ Figure 2: Schematic view o
Page 55: ¡ ¢ ¢ £ ¡ £ ¤ ¢ ¢ ¥ ¦ §

Position Space Interpretation for Generalized Parton Distributions

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