Parton shower evolution in a 3-d hydrodynamical medium

TL;DR

The paper investigates jet quenching in heavy-ion collisions by simulating a pQCD parton shower evolving inside a realistic 3-d hydrodynamic medium, characterized by a local transport coefficient $\hat{q}$ that increases parton virtuality and induces extra radiation. A Monte Carlo implementation modifies the vacuum shower (based on PYSHOW) to include medium-induced virtuality growth, resulting in a medium-modified fragmentation function (MMFF) whose path-averaged form is used to predict $R_{AA}$ and other jet observables. Comparison with central Au-Au data at $200\ \text{A GeV}$ yields a best-fit $K$-factor around 1.5, implying $\hat q_0 \simeq 7.8\ \text{GeV}^2$/fm, but the approach struggles to reproduce the observed rise of $R_{AA}$ with $P_T$, signaling that soft physics and hydrodynamic responses may need to be coupled to the shower evolution. The work clarifies the role of radiative energy loss via modified shower dynamics and highlights the limitations of a purely perturbative, shower-based description in the soft sector, motivating hybrid frameworks for a complete description of jet quenching.

Abstract

We present a Monte Carlo simulation of the perturbative Quantum Chromodynamics (pQCD) shower developing after a hard process embedded in a heavy-ion collision. The main assumption is that the cascade of branching partons traverses a medium which (consistent with standard radiative energy loss pictures) is characterized by a local transport coefficient qhat which measures the virtuality per unit length transferred to a parton which propagates in this medium. This increase in parton virtuality alters the development of the shower and in essence leads to extra induced radiation and hence a softening of the momentum distribution in the shower. After hadronization, this leads to the concept of a medium-modified fragmentation function. On the level of observables, this is manifest as the suppression of high transverse momentum (PT) hadron spectra. We simulate the soft medium created in heavy-ion collisions by a 3-d hydrodynamical evolution and average the medium-modified fragmentation function over this evolution in order to compare with data on single inclusive hadron suppression and extract the qhat which characterizes the medium. Finally, we discuss possible uncertainties of the model formulation and argue that the data in a soft momentum show evidence of qualitatively different physics which presumably cannot be described by a medium-modified parton shower.

Figures (8)

• Figure 1: Transport coefficient $\hat{q}$ encountered by a quark travelling into $+x$ direction through the hydrodynamical medium in a 200 AGeV collision at impact paramter $b=2.4$ fm for different initial hard vertex position in the transverse $(x,y)$ plane (in all cases $y=0$). Values have been extracted for $K=1.5$ (see Eq. (\ref{['E-qhat']}), which represents the best fit to the data.
• Figure 2: Longitudinal momentum distribution of hadrons in a jet originating from a 20 GeV quark in vacuum and in medium. The medium results are given for two different values of line-integrated virtuality $\Delta Q^2$ for scenarios (A,B,C) describing three different characteristic paths through the medium (see text for details).
• Figure 3: The Hump-backed plateau distribution $dN/d\xi$ for a jet originating from a 20 GeV quark shown both in vacuum and medium modified at two different values of line-integrated virtuality $\Delta Q^2$.
• Figure 4: Momentum distribution of hadrons in the jet transverse to the direction of the shower initiating parton for a 20 GeV quark, both in vacuum and in medium for two different values of the line-integrated virtualtiy $\Delta Q^2$.
• Figure 5: Angular distribution of hadrons with respect to the jet axis for a shower initiated by a 20 GeV quark, both in vacuum and in medium for two different values of the line-integrated virtualtiy $\Delta Q^2$.