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A model-independent analysis of the infinite-momentum-frame charge density of partons in the transverse plane is presented for the nucleon.
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Our notation is that x ± ≡ ( x 0 ± x 3 ) / 2 , p ± ≡ ( p 0 ± p 3 ) / 2 x^{\pm}\equiv(x^{0}\pm x^{3})/\sqrt{2},p^{\pm}\equiv(p^{0}\pm p^{3})/\sqrt{2} , and p μ x μ = p − x + + p + x − − 𝐩 ⋅ 𝐛 p_{\mu}x^{\mu}=p^{-}x^{+}+p^{+}x^{-}-{\bf p}\cdot{\bf b} . The coordinates perpendicular to the 0 and 3 directions are denoted as 𝐛 {\bf b} and 𝐩 {\bf p}
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The momentum difference between the initial and final states appears via the use of derivatives of momentum-conserving delta functions in the moments computed by Ref. sachs
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The vector current q ¯ γ μ q \bar{q}\gamma^{\mu}q is conserved, so F 1 F_{1} is independent of the renormalization scale μ 2 \mu^{2} diehl2
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