W-D. Nowak - INFN

Wolf-Dieter Nowak, Perspectives in Hadronic Physics, May 15, 2008 – p. 3
3-dimensional Picture of the Proton
Nucleon momentum in Infinite Momentum Frame: (p γ
∗ + p nucl ) z → ∞
• Form factor
y
• Parton density
δ z
⊥
xp
y
• Generalized parton
distribution at =0
δ z
⊥
xp
y
b ⊥
z
b ⊥
x
z
x
z
x
f ( x)
f ( x, b )
⊥
ρ( b ⊥
)
0
b ⊥
x
1
0
x
1
0
b ⊥
Nucleon’s transv.
charge distribution
given by 2-dim.
Fourier transform
of Form Factor:
⇒ Parton’s
transverse
localization b ⊥
Probability density to
find partons of given
long. mom. fraction x
at resol. scale 1/Q 2
(no transv. inform.)
⇒ Parton’s longitudinal
momentum distribution
function (PDF) f(x)
Generalized Parton Distrib. s
(GPDs) probe simultaneously
transverse localization b ⊥
for a given longitudinal
momentum fraction x.
2nd moment by Ji relation:
J q,g = 1 2 lim t→0
R
x dx
[H q,g (x, ξ, t) + E q,g (x, ξ, t)]