Eikonal amplitudes and non-global logarithms from the BMS equation

TL;DR

This paper verifies the embedding of soft gluon emission amplitudes within the BMS equation, confirms non-global logarithm calculations up to fourth order, and explores the exponential structure of its solutions in QCD jet physics.

Contribution

It demonstrates the consistency of squared gluon emission amplitudes with the BMS equation and analyzes the exponential structure of its solutions in the context of non-global logarithms.

Findings

Squared amplitudes match previous results up to sixth order.

Non-global logarithms computed analytically up to fourth order.

Solution to the BMS equation expressed as a product of exponentials.

Abstract

The Banfi-Marchesini-Smye (BMS) equation accounts for non-global logarithms to all orders in perturbation theory in the large-Nc approximation. We show that the squared amplitudes for the emission of soft energy-ordered gluons are correctly embedded in this equation, and explicitly verify that they coincide with those derived in our previous work in the large-Nc limit up to sixth order in the strong coupling. We perform analytical calculations for the non-global logarithms up to fourth order for the specific hemisphere mass distribution in e+ e- collisions, thus confirming our previous semi-numerical results. We show that the solution to the BMS equation may be cast into a product of an infinite number of exponentials each of which resums a class of Feynman diagrams that manifest a symmetry pattern, and explicitly carry out the computation of the first of these exponentials.