Transverse dynamics of hard partons in nuclear media and the QCD dipole Original Research Article

We derive the non-abelian generalization of the Furry approximation which describes the transverse dynamical evolution of a hard projectile parton inside a spatially extended colour target field. This provides a unified starting point for the target rest frame description of the nuclear dependence of a large class of observables. For the case of the virtual γ∗→qq̄ photoabsorption cross section, we investigate then in detail under which conditions the nuclear dependence encoded in the Furry wavefunctions can be parametrized by a qq̄ QCD dipole cross section. The important condition is colour triviality, i.e., the property that for arbitrary N-fold rescattering contributions the only non-vanishing colour trace is Nc CFN. We give proofs for the colour triviality of the inelastic, diffractive and total photoabsorption cross section measured inclusively or with one jet resolved in the final state. Also, we list examples for which colour interference effects remain. Colour triviality allows us to write the γ∗→qq̄ contribution to the DIS nuclear structure function F2 for small Bjorken xBj in terms of a path integral which describes the transverse size evolution of the qq̄ pair in the nuclear colour field. This expression reduces in an opacity expansion to the N=1 result of Nikolaev and Zakharov, and in the eikonal approximation to the Glauber-type rescattering formulas first derived by Mueller. In the harmonic oscillator approximation of the path integral, we quantify deviations from the eikonal limit. Their onset is characterized by the scales L/lf and E⊥tot L which relate the longitudinal extension L of the nuclear target to the coherence length lf and the total transverse energy E⊥tot accumulated by the q-q̄-pair.