Factorization and Resummation for Sequential Recombination Jet Cross Sections

TL;DR

This paper develops a theoretical framework for resumming logarithms in jet cross sections defined by sequential clustering, accounting for energy fractions and clustering effects, advancing precision in jet physics calculations.

Contribution

It extends factorization theorems to sequential jet clustering observables, deriving one-loop anomalous dimensions and analyzing clustering effects on resummation.

Findings

Derived the one-loop anomalous dimension for these observables.

Showed how clustering affects secondary emissions and gap size.

Performed resummation for various jet algorithms.

Abstract

We extend the class of factorization theorems for non-global observables from fixed angular constraints to cross sections defined in terms of sequential jet clustering. The associated hard and soft functions depend not only on the directions of the hard partons, but also on their energy fractions. We derive the one-loop anomalous dimension of the hard functions that drives the leading-logarithmic resummation. The anomalous dimension imposes energy ordering, which simplifies the clustering sequence. We perform resummations for gap-between-jet observables defined with different jet algorithms and explain the effects of the clustering on the importance of secondary emissions and on the effective gap size.