Quark Fragmentation within an Identified Jet

TL;DR

This paper develops a theoretical framework using Soft-Collinear Effective Theory to describe how specific hadrons fragment from jets with measured invariant mass, connecting perturbative calculations with non-perturbative fragmentation functions.

Contribution

It introduces the 'fragmenting jet function' G_i^h(s,z) and a simple replacement rule to extend inclusive jet factorization theorems to semi-inclusive processes involving identified hadrons.

Findings

Derived a factorization theorem for hadron fragmentation within jets.

Expressed the fragmenting jet function in terms of perturbative coefficients and fragmentation functions.

Applied the framework to processes like B -> X K gamma and e+e- dijet production.

Abstract

We derive a factorization theorem that describes an energetic hadron h fragmenting from a jet produced by a parton i, where the jet invariant mass is measured. The analysis yields a "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass s, and on the energy fraction z of the fragmentation hadron. We show that G^h_i 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). We also show that the sum over h of the integral over z of z G_i^h(s,z) is given by the standard inclusive jet function J_i(s) which is perturbatively calculable in QCD. We use Soft-Collinear Effective Theory and for simplicity carry out our derivation for a process with a single jet, B -> X h l nu, with invariant mass m_{X h}^2 >> Lambda_QCD^2. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h. We apply this rule to derive factorization theorems for B -> X K gamma which is the fragmentation to a Kaon in b -> s gamma, and for e^+e^- -> (dijets)+h with measured hemisphere dijet invariant masses.