The Drell-Yan Process and Factorization in Impact Parameter Space
S. J. Brodsky, A. Hebecker, E. Quack
TL;DR
This paper develops an impact-parameter space formulation of the Drell–Yan process at small $x_{ ext{target}}$, expressing DY cross sections as convolutions of a universal color-dipole cross section $σ(ρ)$ with DY-specific photon wave functions, paralleling the established DIS framework. By analyzing the DY process in the target rest frame, it shows that the same $σ(ρ)$ governs both DIS and DY, with the two time-orderings of photon emission encoded in the $q\bar{q}$-interference that defines this cross section. The work provides explicit expressions for transverse and longitudinal DY cross sections and extends to rich angular structures (θ, φ), including TT and LT interference terms, offering new observables (azimuthal correlations) to extract information about $σ(ρ)$ and small-$x$ dynamics. It also discusses the implications for nuclear targets via shadowing and highlights future directions for incorporating higher-order corrections and broader QCD effects within this coherent framework.
Abstract
The cross section for Drell-Yan pair production in the limit of small $x$-target is derived in the rest frame of the target hadron. Our calculation is based on the fundamental quantity $σ(ρ)$, the cross section for the scattering of a $q\bar{q}$-pair with fixed transverse separation $ρ$ off a hadronic target. As in deep inelastic scattering the result can be given in terms of integrals of $σ(ρ)$. This is consistent with well known factorization theorems and also relates higher-twist terms in both processes. An analysis of the angular distribution of the produced lepton shows that additional integrals of $σ(ρ)$ can be obtained in the Drell-Yan process, which are not measurable in inclusive deep inelastic scattering.