Resumming double non-global logarithms in the evolution of a jet

TL;DR

This paper addresses the resummation of double non-global and collinear logarithms in jet evolution, proposing a collinearly-improved BMS equation to stabilize and enhance the accuracy of energy loss predictions in highly collimated jets.

Contribution

It introduces a collinearly-improved BMS equation that resums double collinear logs, extending the accuracy of non-global logarithm resummation beyond leading order.

Findings

Identifies the importance of anti-collinear emissions in jet evolution.

Constructs a collinearly-improved BMS equation for better resummation.

Demonstrates improved stability and accuracy in jet energy loss calculations.

Abstract

We consider the Banfi-Marchesini-Smye (BMS) equation which resums non-global energy logarithms in the QCD evolution of the energy lost by a pair of jets via soft radiation at large angles. We identify a new physical regime where, besides the energy logarithms, one has to also resum (anti)collinear logarithms. Such a regime occurs when the jets are highly collimated (boosted) and the relative angles between successive soft gluon emissions are strongly increasing. These anti-collinear emissions can violate the correct time-ordering for time-like cascades and result in large radiative corrections enhanced by double collinear logs, making the BMS evolution unstable beyond leading order. We isolate the first such a correction in a recent calculation of the BMS equation to next-to-leading order by Caron-Huot. To overcome this difficulty, we construct a collinearly-improved version of the leading-order BMS equation which resums the double collinear logarithms to all orders. Our construction is inspired by a recent treatment of the Balitsky-Kovchegov (BK) equation for the high-energy evolution of a space-like wavefunction, where similar time-ordering issues occur. We show that the conformal mapping relating the leading-order BMS and BK equations correctly predicts the physical time-ordering, but it fails to predict the detailed structure of the collinear improvement.