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

TL;DR

This paper demonstrates a next-to-leading order equivalence between pT-broadening amplitudes and dipole/quadrupole scattering amplitudes in lightcone perturbation theory, revealing a complex relation involving graph classes and analytical continuation.

Contribution

It establishes a novel NLO relation between pT-broadening and dipole/quadrupole amplitudes, extending previous leading-order insights with a detailed graph analysis.

Findings

The relation holds at NLO for classes of graphs, not individual graphs.

Matching may require analytical continuation in longitudinal momentum.

The same relation applies to dijet and quadrupole production amplitudes.

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.