Implementation of a medium-modified parton shower algorithm

TL;DR

This work addresses jet quenching by modeling medium-induced gluon radiation within a Monte Carlo final-state parton shower. The authors implement an additive correction to splitting functions, $P_{ m tot}(z)=P_{ m vac}(z)+\Delta P(z,t,\hat{q},L,E)$, inside the PYSHOW routine of PYTHIA, enabling energy-momentum conserving simulations of medium effects. They connect radiative energy loss and angular broadening through the transport coefficient $\hat{q}$ and a finite medium length $L$, using formation-time concepts to evolve the shower. Results for a 100 GeV jet in a 2 fm medium show depletion of high-$z$ and high-$p_T$ partons and enhancement at low/intermediate values, along with significant angular broadening; the low-$p_T$ rise is amplified by energy conservation and the lack of medium recoil in this implementation. The study provides a practical, differential framework for exploring medium-modified jet structure and lays the groundwork for future improvements, including recoil, elastic energy loss, color exchange, and broader applicability to other shower algorithms.

Abstract

We present a Monte Carlo implementation of medium-induced gluon radiation in the final-state branching process. Medium effects are introduced through an additive term in the splitting functions. We have implemented such modification within PYTHIA. We show the medium effects on the hump-backed plateau, and the transverse momentum and angular distributions with respect to the parent parton. As expected, with increasing medium densities there is an increase (decrease) of partons with small (large) momentum fraction, and angular broadening is observed. The effects on the transverse-momentum distributions are more involved, with an enhancement of low- and intermediate-$p_T$ partons and a decrease at large $p_T$, which is related to energy conservation, and to the lack of momentum exchange with the medium in our approach.

Figures (2)

• Figure 1: Intrajet parton distributions in $\xi=\ln{(E_{jet}/p)}$ (left), $p_{T}$ (middle) and $\theta={\rm acos}(p_z/p)$ (right) for a gluon of initial energy $E_{jet}=100$ GeV. PYTHIA default (black lines) and our results with $\hat{q}=0$ (blue lines) are compared.
• Figure 2: Intrajet parton distributions in $\xi$ (left), $p_{T}$ (middle) and $\theta$ (right) for a gluon of initial energy $E_{jet}=100$ GeV in a medium of length $L=2$ fm and for different transport coefficients $\hat{q}=0$ (black), 5 (red) and 50 (blue lines) GeV$^2$/fm.