High Energy Resummation of Jet Observables

TL;DR

This paper extends high energy resummation techniques to jet observables, providing a gauge-invariant framework and demonstrating the resummation of all partonic channels with fixed-order validation up to third order.

Contribution

It introduces a novel approach to high energy resummation for jet observables, including a gauge-invariant method and a way to restore gluon indistinguishability at LLx accuracy.

Findings

Resummed transverse momentum distribution for gluon-initiated processes.

Validated resummation against fixed-order calculations up to a03.

Proposed a gauge-invariant framework using helicity techniques.

Abstract

In this paper we investigate the extension of high energy resummation at LLx accuracy to jet observables. In particular, we present the high energy resummed expression of the transverse momentum distribution of the outgoing parton in the general partonic process $g(q) + g(q) \to g(q) + X$. In order to reach this result, several new ideas are introduced and exploited. First we prove that LLx resummation is achieved by dressing with hard radiation an off-shell gluon initiated LO process even if its on-shell limit is vanishing or trivial. Then we present a gauge-invariant framework where these calculations can be performed by using the modern helicity techniques. Finally, we show a possible way to restore gluon indistinguishability in the final state, which is otherwise lost in the resummation procedure, at all orders in $\alpha_s$ at LLx. All partonic channels are then resummed and cross-checked against fixed-order calculations up to $\mathcal{O}(\alpha_s^3)$