Fragmentation inside an identified jet

TL;DR

This paper introduces a new theoretical framework using Soft-Collinear Effective Theory to describe how a specific hadron fragments from a jet, providing a calculable function that links perturbative and non-perturbative aspects.

Contribution

It derives a novel fragmenting jet function G_i^h(s,z) that connects jet invariant mass and hadron momentum fraction, enabling semi-inclusive process analysis.

Findings

Derived the fragmenting jet function G_i^h(s,z).

Expressed G_i^h(s,z) in terms of perturbative coefficients and fragmentation functions.

Provided a rule to adapt existing jet-based factorization theorems for semi-inclusive processes.

Abstract

Using Soft-Collinear Effective Theory we derive factorization formulae for semi-inclusive processes where a light hadron h fragments from a jet whose invariant mass is measured. Our analysis yields a novel "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass \sqrt{s}, and on the fraction z of the large light-cone momentum components of the hadron and the parent parton i. We show that G_i^h(s,z) can be computed in terms of perturbatively calculable coefficients, J_{ij}(s,z/x), integrated against standard non-perturbative fragmentation functions, D_j^h(x). Our analysis yields a simple replacement rule that allows any factorization theorem depending on a jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h.