Calculating Quenching Weights

TL;DR

The paper develops and compares two leading theoretical frameworks for medium-induced parton energy loss—BDMPS-Z multiple soft scattering and GLV opacity—by computing quenching weights P(ΔE) and the related observables, for static and expanding QCD media and with angular radiation considerations. It provides a CPU-efficient numerical subroutine and demonstrates applications to hadronic spectra suppression and medium-modified fragmentation functions, showing qualitative agreement with RHIC data while clarifying the role of finite path length and kinematic constraints. A key finding is that, with appropriate parameter mappings, the two approaches yield broadly similar quenching weights and can be related to the transport properties of the medium, such as the transport coefficient hat{q} and the Debye mass, even in dynamically evolving environments. The work highlights the importance of realistic geometry and phase-space constraints and offers a practical toolset for interpreting jet quenching phenomena at RHIC and LHC, while acknowledging potential additional physics beyond parton energy loss in the current data.

Abstract

We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peigné-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint resulting from finite in-medium path length reduces significantly the transverse momentum dependence of the nuclear modification factor, thus leading to consistency with the data measured at the Relativistic Heavy Ion Collider (RHIC).

Figures (20)

• Figure 1: The medium-induced gluon energy distribution $\omega \frac{dI}{d\omega}$ in the multiple soft scattering approximation for different values of the kinematic constraint $R = \omega_c\, L$.
• Figure 2: The multiplicity of additional medium-induced gluons (\ref{['2.14']}) radiated with energy large than $\omega$. Calculation done in the multiple soft scattering approximation.
• Figure 3: The medium-induced gluon energy distribution $\omega \frac{dI}{d\omega}$ for a hard quark in the single hard scattering approximation, calculated for different values of the kinematic constraint $\bar{R}$.
• Figure 4: The multiplicity of additional medium-induced gluons (\ref{['2.14']}) radiated with energy larger than $\omega$. Calculation done in the single hard scattering approximation.
• Figure 5: The gluon energy distribution without kinematic constraint ($R$, $\bar{R} \to \infty$) as calculated in the multiple soft scattering approximation, and in the single hard scattering approximation for $n_0L = 0.5, 1, 2, 4$. Results for the single hard scattering approximation are plotted for $(L/\lambda)\, \bar{\omega}_c = \omega_c$.