Fragmentation of a Jet with Small Radius

TL;DR

This paper develops a theoretical framework using soft-collinear effective theory to analyze and resum logarithms associated with small jet radius fragmentation, introducing the fragmentation function to a jet (FFJ) and deriving related evolution equations.

Contribution

It introduces the FFJ, relates it to standard jet functions, and demonstrates how to resum logarithms of jet radius R using renormalization group evolution.

Findings

Derived the FFJ at next-to-leading order.

Showed FFJs satisfy DGLAP evolution equations.

Proved a factorization theorem involving FFJs.

Abstract

In this paper we consider the fragmentation of a parton into a jet with small jet radius $R$. Perturbatively, logarithms of $R$ can appear, which for narrow jets can lead to large corrections. Using soft-collinear effective theory, we introduce the fragmentation function to a jet (FFJ), which describes the fragmentation of a parton into a jet. We discuss how these objects are related to the standard jet functions. Calculating the FFJ to next-to-leading order, we show that these objects satisfy the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations, with a natural scale that depends upon $R$. By using the standard renormalization group evolution, we can therefore resum logarithms of $R$. We further use the soft-collinear effective theory to prove a factorization theorem where the FFJs naturally appear, for the fragmentation of a hadron within a jet with small $R$. Finally, we also show how this formalism can be used to resum the ratio of jet radii for a subjet to be emitted from within a fat jet.