# Medium modified leading hadrons, jets and sub-jets in a single formalism

## TL;DR

This paper develops a unified formalism to describe medium modifications of hadrons, jets, and sub-jets in high-energy collisions, integrating theoretical models with hydrodynamic simulations and experimental data.

## Contribution

It introduces a comprehensive framework combining vacuum and medium-modified fragmentation functions within a higher-twist energy loss formalism, extended to complex jet sub-structures.

## Key findings

- Vacuum jet function aligns with PYTHIA simulations.
- Medium modifications are consistent with experimental data.
- Framework applicable to various collision energies.

## Abstract

Vacuum and medium modified fragmentation functions are used to study the properties of hadrons produced in hard interactions, in $p$-$p$ and $A$-$A$ collisions, respectively. We study the modification of reconstructed jets and high transverse momentum (high-$p_\mathrm{T}$) hadrons as they propagate through a dense medium. Jets and jet modification are studied within the framework of a factorized jet function. The vacuum jet function is found consistent with PYTHIA simulations. Both the modification of the fragmentation function and the jet function are carried out within the identical higher-twist energy loss formalism. This approach is then extended to di-hadron production within a jet. Its further extension to a "di-prong" function and its application to the soft-drop measurements are discussed. The methodology of extending these semi-analytical calculations to full Monte-Carlo simulations is outlined. All calculations are carried out within a (2+1)-D viscous hydrodynamic simulation and compared to experimental data from a variety of collision energies.