Structure of Relativistic States

QCD factorization in the Bjorken limit allows to separate the long-distance physics from the hard subprocess. At leading twist, only one parton in each hadron is coherent with the hard subprocess. Higher twist effects increase as one of the active partons carries most of the longitudinal momentum of the hadron, x → 1. In the Drell-Yan process πN → μ−μ+ + X, the polarization of the virtual photon is observed to change to longitudinal when the photon carries xF & 0.6 of the pion. I define and study the “Berger-Brodsky” limit of Q →∞ with Q(1− x) fixed. A new kind of factorization holds in the Drell-Yan process in this limit, in which both pion valence quarks are coherent with the hard subprocess, the virtual photon is longitudinal rather than transverse, and the cross section is proportional to a multiparton distribution. Generalized parton distributions contain information on the longitudinal momentum and transverse position densities of partons in a hadron. Transverse charge densities are Fourier transforms of the electromagnetic form factors. I discuss the application of these methods to the QED electron, studying the form factors, charge densities and spin distributions of the leading order |eγ〉 Fock state in impact parameter and longitudinal momentum space. I show how the transverse shape of any virtual photon induced process, γ∗(q) + i→ f , may be measured. Qualitative arguments concerning the size of such transitions have been previously made in the literature, but without a precise analysis. Properly defined, the amplitudes and the cross section in impact parameter space provide information on the transverse shape of the transition process.