Off-forward Parton Distributions and Impact Parameter Dependent Parton Structure

where x = x±x and p = p+p refer to the usual light-cone components, p̄ = 1 2 (p+ p), ∆ = p− p, and t ≡ ∆. The “off-forwardness” (or skewedness) in Eqs. (1,2) is defined as ξ ≡ ∆ + p+ . From the point of view of parton physics in the infinite momentum frame, these OFPDs have the physical meaning of the amplitude for the process that a quark is taken out of the nucleon with longitudinal momentum fraction x and then inserted back into the nucleon with a four momentum transfer ∆ . OFPDs play dual roles and in a certain sense they interpolate between form factors and conventional parton distribution functions (PDFs) : for ξ = t = 0 one recovers conventional PDFs, i.e. longitudinal momentum distributions in the infinite momentum frame (IMF), while when one integrates H(x, ξ, t) over x, one obtains a form factor, i.e. the Fourier transform of a position space density (in the Breit frame!). One of the new physics insights that one can learn from these OFPDs is the angular