The High-Energy Limit of 2-to-2 Partonic Scattering Amplitudes

TL;DR

This paper advances the understanding of 2-to-2 partonic scattering amplitudes at high energies by deriving a closed-form solution for the soft part and providing an iterative method for the hard contributions, with numerical analysis.

Contribution

It introduces a new closed-form solution for the soft amplitude in dimensional regularization and an algorithmic approach for the hard contributions using BFKL equation in two dimensions.

Findings

Wavefunction is infrared finite.

Soft anomalous dimension fixed at NLL accuracy.

Hard contributions determined iteratively.

Abstract

Recently, there has been significant progress in computing scattering amplitudes in the high-energy limit using rapidity evolution equations. We describe the state-of-the-art and demonstrate the interplay between exponentiation of high-energy logarithms and that of infrared singularities. The focus in this talk is the imaginary part of 2 to 2 partonic amplitudes, which can be determined by solving the BFKL equation. We demonstrate that the wavefunction is infrared finite, and that its evolution closes in the soft approximation. Within this approximation we derive a closed-form solution for the amplitude in dimensional regularization, which fixes the soft anomalous dimension to all orders at NLL accuracy. We then turn to finite contributions of the amplitude and show that the remaining hard contributions can be determined algorithmically, by iteratively solving the BFKL equation in exactly two dimensions within the class of single-valued harmonic polylogarithms. To conclude we present numerical results and analyse large-order behaviour of the amplitude.