Small-x Parton Distributions of Large Hadronic Targets

TL;DR

This work analyzes small-x parton distributions in very large hadronic targets by comparing a target-rest-frame semiclassical calculation with the McLerran-Venugopalan model in the infinite momentum frame. Both frameworks reduce the interaction to the dipole cross section σ(ρ), with the large target size forcing dominance of small transverse-size fluctuations and yielding a perturbative description. The paper demonstrates frame equivalence through explicit expressions for σ(ρ) and q(ξ), and offers two Gaussian-based models to illustrate color-field averaging and its impact on σ(ρ). Overall, it provides a theoretical laboratory for studying small-x processes in QCD and clarifies how large targets introduce a new perturbative scale.

Abstract

A simple and intuitive calculation, based on the semiclassical approximation, demonstrates how the large size of a hadronic target introduces a new perturbative scale into the process of small-x deep inelastic scattering. The above calculation, which is performed in the target rest frame, is compared to the McLerran-Venugopalan model for scattering off large nuclei, which has first highlighted this effect in the infinite momentum frame. It is shown that the two approaches, i.e., the rest frame based semiclassical calculation and the infinite momentum frame based McLerran-Venugopalan approach are quantitatively consistent.

Figures (3)

• Figure 1: The Compton scattering amplitude within the semiclassical approach.
• Figure 2: Qualitative behaviour of the function $\sigma(\varrho)$.
• Figure 3: Space-time picture in the infinite momentum frame.