# Jet fragmentation functions for $Z$-tagged jets

## TL;DR

This paper develops a QCD framework using Soft-Collinear Effective Theory to analyze jet fragmentation functions in $Z$-tagged jets, connecting experimental data with theoretical fragmentation functions.

## Contribution

It introduces a formalism that relates jet fragmentation functions to collinear and TMD fragmentation functions, providing a new method to analyze LHCb data.

## Key findings

- Good agreement with data for intermediate $z_h$ region
- Proposes binning in $z_h$ and $j_ot$ to probe TMD fragmentation functions
- Establishes a connection between fragmentation functions and jet substructure observables

## Abstract

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside $Z$-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction $z_h$ of the jet carried by the hadron and the transverse momentum $j_\perp$ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the $z_h$-dependence provides information on standard collinear fragmentation functions, while $j_\perp$-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate $z_h$ region. For $j_\perp$-dependence, we suggest binning in both $z_h$ and $j_\perp$, which would lead to a more direct probing of TMD fragmentation functions.