High energy scattering in Quantum Chromodynamics

TL;DR

The work surveys high-energy hadronic scattering in QCD, tracing a path from the parton model and Bjorken scaling to the small-$x$ regime where gluon saturation dominates. It presents the eikonal picture and linear (BFKL) evolution, then introduces nonlinear saturation via the BK equation and the Color Glass Condensate, including the JIMWLK formalism and MV initial conditions. The third part applies CGC to nucleus-nucleus collisions, showing how inclusive gluon and quark spectra can be computed from classical Yang–Mills dynamics and how LO+NLO corrections can be organized and factorized, with attention to initial-state instabilities and their resummation. The framework aims to connect early-time glasma dynamics to subsequent thermalization and hydrodynamics in heavy-ion collisions.

Abstract

In this series of three lectures, we discuss several aspects of high energy scattering among hadrons in Quantum Chromodynamics. The first lecture is devoted to a description of the parton model, Bjorken scaling and the scaling violations due to the evolution of parton distributions with the transverse resolution scale. The second lecture describes parton evolution at small momentum fraction x, the phenomenon of gluon saturation and the Color Glass Condensate (CGC). In the third lecture, we present the application of the CGC to the study of high energy hadronic collisions, with emphasis on nucleus-nucleus collisions. In particular, we provide the outline of a proof of high energy factorization for inclusive gluon production.

Figures (23)

• Figure 1: Generic hard process in the scattering of two hadrons. Left: Leading Order. Right: Next-to-Leading Order correction involving gluon radiation in the initial state.
• Figure 2: Kinematical variables in the Deep Inelastic Scattering process. $k$ and $P$ are known from the experimental setup, and $k^\prime$ is obtained by measuring the deflected lepton.
• Figure 3: SLAC results on DIS.
• Figure 4: Cartoons of the valence partons of a proton, and their interactions and fluctuations. Left: proton at low energy. Right: proton at high energy.
• Figure 5: Region of $y^\mu$ that dominates in the Bjorken limit.