Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Eikonal Evolution and Gluon Radiation

Alex Kovner, Urs Achim Wiedemann

TL;DR

The paper presents a transparent quantum mechanical formulation of eikonal propagation for high-energy hadronic processes, unifying several existing approaches. It shows how to compute total, elastic, inelastic and diffractive cross sections along with gluon production by propagating projectile partons through a frozen, Gaussian target field and averaging over target configurations. By deriving operator forms for the low-x evolution of both inelastic and diffractive DIS cross sections, it connects to the BK framework and extends it with all-order 1/N corrections, clarifying the role of diffractive channels and target correlations. The work provides explicit calculations for q+A and qqbar+A systems, elucidating the conditions under which projectile-biased observables differ from true cross sections and outlining the breakdown regimes at very small x due to Pomeron loop effects.

Abstract

We give a simple quantum mechanical formulation of the eikonal propagation approximation, which has been heavily used in recent years in problems involving hadronic interactions at high energy. This provides a unified framework for several approaches existing in the literature. We illustrate this scheme by calculating the total, elastic, inelastic and diffractive DIS cross sections, as well as gluon production in high energy hadronic collisions. From the q-qbar-g-component of the DIS cross sections, we straightforwardly derive low x evolution equations for inelastic and diffractive DIS distribution functions. In all calculations, we provide all order 1/N corrections to the results existing in the literature.

Eikonal Evolution and Gluon Radiation

TL;DR

The paper presents a transparent quantum mechanical formulation of eikonal propagation for high-energy hadronic processes, unifying several existing approaches. It shows how to compute total, elastic, inelastic and diffractive cross sections along with gluon production by propagating projectile partons through a frozen, Gaussian target field and averaging over target configurations. By deriving operator forms for the low-x evolution of both inelastic and diffractive DIS cross sections, it connects to the BK framework and extends it with all-order 1/N corrections, clarifying the role of diffractive channels and target correlations. The work provides explicit calculations for q+A and qqbar+A systems, elucidating the conditions under which projectile-biased observables differ from true cross sections and outlining the breakdown regimes at very small x due to Pomeron loop effects.

Abstract

We give a simple quantum mechanical formulation of the eikonal propagation approximation, which has been heavily used in recent years in problems involving hadronic interactions at high energy. This provides a unified framework for several approaches existing in the literature. We illustrate this scheme by calculating the total, elastic, inelastic and diffractive DIS cross sections, as well as gluon production in high energy hadronic collisions. From the q-qbar-g-component of the DIS cross sections, we straightforwardly derive low x evolution equations for inelastic and diffractive DIS distribution functions. In all calculations, we provide all order 1/N corrections to the results existing in the literature.

Paper Structure

This paper contains 18 sections, 113 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantum mechanics of eikonal propagation
  3. The projectile biased observables
  4. The target averages
  5. With due respect to the target
  6. Gluon production
  7. Gluon production in q+A
  8. Gluon production in $\pi(q\bar{q})$+$A$
  9. Small $x$ DIS in the target rest frame
  10. $q\bar{q}$-contribution to photoabsorption cross sections
  11. $q\bar{q}g$-Contributions to photoabsorption cross sections
  12. Eikonal low x evolution
  13. The inelastic cross section
  14. Diffractive cross section
  15. Summary
  16. ...and 3 more sections

Figures (2)

  • Figure 1: The target average of the product of two Wilson lines, denoted by thick lines. The fields $A^+$ in $W$'s are distributed with Gaussian weights local in the longitudinal coordinate according to (\ref{['2.18']}).
  • Figure 2: Schematic picture of a diffractive contribution to the $q\bar{q}$ scattering cross section which does contribute to the inelastic scattering cross section.