A Dynamical Scaling Law for Jet Tomography

TL;DR

A scaling law is established which relates medium effects in a collision of arbitrary dynamical expansion to that in an equivalent static scenario, and is calculated for typical kinematical values of the RHIC and LHC heavy ion programming medium-modified fragmentation functions for collisions with realistic dynamical Expansion.

Abstract

Medium modifications of parton fragmentation provide a novel tomographic tool for the study of the hot and dense matter created in ultrarelativistic nucleus-nucleus collisions. Their quantitative analysis, however, is complicated by the strong dynamical expansion of the collision region. Here, we establish for the multiple scattering induced gluon radiation spectrum a scaling law which relates medium effects in a collision of arbitrary dynamical expansion to that in an equivalent static scenario. Based on this scaling, we calculate for typical kinematical values of the RHIC and LHC heavy ion programs medium-modified parton fragmentation functions for heavy ion collisions with realistic dynamical expansion.

Figures (3)

• Figure 1: The two contributions to the probability (\ref{['eq2']}) that a parton looses $\Delta E$ of its energy in the medium: Continuous part (upper figure) and the discrete probability $p_0$ in (\ref{['eq6']}) that the hard parton escapes the medium without interaction (lower figure).
• Figure 2: The medium-induced gluon radiation spectrum $\omega\, \frac{dI}{d\omega}$ for different dynamical expansion parameters $\alpha$=0 (solid line), $\alpha$=0.5 (dotted-dashed), $\alpha$=1 (dashed) and $\alpha$=1.5 (dotted). The scaling law (\ref{['eq8']}) is shown for R=400 and R=4000.
• Figure 3: The LO BKK Binnewies:1994ju fragmentation function $u\to \pi$ for no medium and the medium-modified fragmentation functions for different gluon rapidity densities (see eq. (\ref{['eq12']})) and $L=7$ fm.