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pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order

A. H. Mueller, S. Munier

TL;DR

<3-5 sentence high-level summary> The paper investigates the energy evolution of production observables in high-energy QCD, focusing on p_T-broadening and forward dipole amplitudes. It uses light-cone perturbation theory to perform a comprehensive comparison of next-to-leading order graphs, establishing an equivalence of the evolution kernels in the large-N_c limit. The authors show that the matching at NLO generally occurs at the level of graph classes and can require analytical continuation in longitudinal momentum, not a strict one-to-one graph correspondence. They further extend the framework to dijet production and quadrupole amplitudes, suggesting a universal NLO BFKL-type evolution description for these observables.

Abstract

Through the systematic inspection of graphs in the framework of lightcone perturbation theory, we demonstrate that an identity between the evolution of pT-broadening amplitudes with the energy and the evolution of forward scattering amplitudes of color dipoles off nuclei holds at next-to-leading order accuracy. In the general case, the relation is not a graph-by-graph correspondence, neither does it hold strictly speaking for definite values of the momenta: Instead, it relates classes of graphs of similar topologies, and in some cases, the matching requires an analytical continuation in the appropriate longitudinal momentum variable. We check that the same kind of relation is also true at next-to-leading order between amplitudes for the production of dijets and quadrupole forward amplitudes.

pT-Broadening and production processes versus dipole/quadrupole amplitudes at next-to-leading order

TL;DR

<3-5 sentence high-level summary> The paper investigates the energy evolution of production observables in high-energy QCD, focusing on p_T-broadening and forward dipole amplitudes. It uses light-cone perturbation theory to perform a comprehensive comparison of next-to-leading order graphs, establishing an equivalence of the evolution kernels in the large-N_c limit. The authors show that the matching at NLO generally occurs at the level of graph classes and can require analytical continuation in longitudinal momentum, not a strict one-to-one graph correspondence. They further extend the framework to dijet production and quadrupole amplitudes, suggesting a universal NLO BFKL-type evolution description for these observables.

Abstract

Through the systematic inspection of graphs in the framework of lightcone perturbation theory, we demonstrate that an identity between the evolution of pT-broadening amplitudes with the energy and the evolution of forward scattering amplitudes of color dipoles off nuclei holds at next-to-leading order accuracy. In the general case, the relation is not a graph-by-graph correspondence, neither does it hold strictly speaking for definite values of the momenta: Instead, it relates classes of graphs of similar topologies, and in some cases, the matching requires an analytical continuation in the appropriate longitudinal momentum variable. We check that the same kind of relation is also true at next-to-leading order between amplitudes for the production of dijets and quadrupole forward amplitudes.

Paper Structure

This paper contains 20 sections, 109 equations, 51 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Production cross sections and scattering amplitudes
  3. $p_\perp$ broadening in the McLerran-Venugopalan model
  4. $p_\perp$-broadening more generally
  5. Leading-order calculation
  6. Proof of the equivalence at next-to-leading order
  7. Two quark-gluon vertices
  8. $p_\perp$-broadening graphs
  9. Dipole graphs
  10. Proof of the correspondence
  11. Three quark-gluon vertices
  12. Initial state/initial and final state
  13. Initial state/final state
  14. Initial state/initial state
  15. Final state/final state
  16. ...and 5 more sections

Figures (51)

  • Figure 1: The three different types of interactions of a quark and a nucleus: inelastic (a), elastic in the amplitude (b) and elastic in the complex-conjugate amplitude (c). This illustrates the 3 terms in the r.h.s. of Eq. (\ref{['eq:S1']}).
  • Figure 2: Keldysh-Schwinger contour.
  • Figure 3: The Feynman amplitude described by Eq. (\ref{['eq:feynmanamp']}).
  • Figure 4: Graphical illustration of the r.h.s. of Eq. (\ref{['eq:disc']}).
  • Figure 5: Amplitude $A$ of Fig. \ref{['fig3']} viewed as a dipole scattering amplitude.
  • ...and 46 more figures