Two-parton scattering amplitudes in the Regge limit to high loop orders

TL;DR

This paper develops a method to compute high-order loop corrections to two-parton scattering amplitudes in QCD's Regge limit, revealing convergence properties and finite corrections across different color exchanges.

Contribution

It introduces a novel approach to solve the BFKL equation iteratively in momentum space, enabling high-loop order predictions for scattering amplitudes in perturbative QCD.

Findings

Computed amplitudes up to 13 loops.

Finite corrections have a finite radius of convergence.

Convergence depends on the color representation.

Abstract

We study two-to-two parton scattering amplitudes in the high-energy limit of perturbative QCD by iteratively solving the BFKL equation. This allows us to predict the imaginary part of the amplitude to leading-logarithmic order for arbitrary $t$-channel colour exchange. The corrections we compute correspond to ladder diagrams with any number of rungs formed between two Reggeized gluons. Our approach exploits a separation of the two-Reggeon wavefunction, performed directly in momentum space, between a soft region and a generic (hard) region. The former component of the wavefunction leads to infrared divergences in the amplitude and is therefore computed in dimensional regularization; the latter is computed directly in two transverse dimensions and is expressed in terms of single-valued harmonic polylogarithms of uniform weight. By combining the two we determine exactly both infrared-divergent and finite contributions to the two-to-two scattering amplitude order-by-order in perturbation theory. We study the result numerically to 13 loops and find that finite corrections to the amplitude have a finite radius of convergence which depends on the colour representation of the $t$-channel exchange.