Transverse Momentum Broadening Due to the Multiple Scattering

Most high energy collisions can be described by a single hard scattering. By studying the single scattering, we can extract the parton distribution functions and test the short-distance dynamics of strong interactions. The normal parton distributions have the interpretation of the probability distributions to find a parton within a hadron. On the other hand, in order to study quantum correlations of multi-partons inside a hadron, we need to investigate the multiple scattering. The multiple scattering is a high twist effect and is small compare to the single scattering. However, in collisions involve nucleus, the nucleus environment will enhance the multiple scattering effect. For example, when a parton propagates through a nuclear matter, the average transverse momentum is broadened due to the multiple scattering. Nuclear dependence of such broadening provides an excellent probe to study QCD dynamics beyond the single hard-scattering picture. A reliable calculation of the multiple scattering in QCD perturbation theory requires to extend the factorization theorem 1 beyond the leading power. Qiu and Sterman showed that the factorization theorem for hadron-hadron scattering holds at the first-nonleading power in momentum transfer , which is enough to study double scattering processes in hadronic collisions. Applying this generalized factorization theorem, Luo, Qiu and Sterman (LQS) developed a consistent treatment of the multiple scattering at the partonic level . LQS expressed the nuclear dependence of di-jet momentum imbalance in photo-nucleus collisions in terms of four-parton (twist-4) nuclear correlation functions . In the following, I will use the the deeply inelastic lepton-nucleus scattering (DIS) and the Drell-Yan process in hadron-nucleus collisions as examples to show that transverse momentum broadening is proportional to the similar four-parton correlation functions . The predictions of the multiple scattering effects rely on accurate infor-