Double Non-Global Logarithms In-N-Out of Jets

TL;DR

This paper derives and analyzes the leading non-global logarithms in jet mass ratios and energy vetoes for various jet algorithms, providing new relations and a factorized soft function form crucial for precise collider predictions.

Contribution

It presents the first detailed derivation of the algorithm- and radius-dependent leading non-global logarithms for jet observables, along with new relations among their coefficients and a factorized soft function form.

Findings

Derived the full algorithm and R dependence of leading NGLs.

Established new relations among NGL coefficients.

Proposed a factorized soft function form separating global and non-global logs.

Abstract

We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto \Lambda due to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form \alpha_s^2 \ln^2(\Lambda/m_{1,2}) or \alpha_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambridge-Aachen algorithms. In addition to determining the full algorithmic and R dependence of the leading NGLs, we derive new relations among their coefficients. We also derive to all orders in \alpha_s a factorized form for the soft function S(k_L,k_R,\Lambda) in the cross section \sigma(m_1,m_2,\Lambda) in which dependence on each of the global logs of \mu/k_L, \mu/k_R and \mu/\Lambda determined by the renormalization group are separated from one another and from the non-global logs. The same kind of soft function, its associated non-global structure, and the algorithmic dependence we derive here will also arise in exclusive jet cross sections at hadron colliders, and must be understood and brought under control to achieve precise theoretical predictions.