Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Radiative energy loss of high energy quarks and gluons in a finite volume quark-gluon plasma

R. Baier, Yu. L. Dokshitzer, A. H. Mueller, S. Peigné, D. Schiff

TL;DR

This work extends the BDPS/BDMPS framework for medium-induced gluon radiation to a finite-length quark-gluon plasma. By modeling the medium with static scattering centers (Gyulassy–Wang approach) and deriving a Schrödinger-like equation for the radiation problem, the authors show that the induced energy loss scales as $L^2$ for finite media and connect this to the infinite-volume BDPS results in the appropriate limit. The analysis provides a detailed spectrum for gluon emission across different regimes (BH, LPM, and factorization), and yields explicit expressions for the differential spectrum and the total energy loss, highlighting the potential phenomenological impact for jet quenching in heavy-ion collisions. The formalism bridges finite- and infinite-length media in QCD and offers a practical method to estimate energy loss in quark-gluon plasmas.

Abstract

The medium induced energy loss spectrum of a high energy quark or gluon traversing a hot QCD medium of finite volume is studied. We model the interaction by a simple picture of static scattering centres. The total induced energy loss is found to grow as $L^2$, where $L$ is the extent of the medium. The solution of the energy loss problem is reduced to the solution of a Schrödinger-like equation whose ``potential'' is given by the single-scattering cross section of the high energy parton in the medium. These resuls should be directly applicable to a quark-gluon plasma.

Radiative energy loss of high energy quarks and gluons in a finite volume quark-gluon plasma

TL;DR

This work extends the BDPS/BDMPS framework for medium-induced gluon radiation to a finite-length quark-gluon plasma. By modeling the medium with static scattering centers (Gyulassy–Wang approach) and deriving a Schrödinger-like equation for the radiation problem, the authors show that the induced energy loss scales as for finite media and connect this to the infinite-volume BDPS results in the appropriate limit. The analysis provides a detailed spectrum for gluon emission across different regimes (BH, LPM, and factorization), and yields explicit expressions for the differential spectrum and the total energy loss, highlighting the potential phenomenological impact for jet quenching in heavy-ion collisions. The formalism bridges finite- and infinite-length media in QCD and offers a practical method to estimate energy loss in quark-gluon plasmas.

Abstract

The medium induced energy loss spectrum of a high energy quark or gluon traversing a hot QCD medium of finite volume is studied. We model the interaction by a simple picture of static scattering centres. The total induced energy loss is found to grow as , where is the extent of the medium. The solution of the energy loss problem is reduced to the solution of a Schrödinger-like equation whose ``potential'' is given by the single-scattering cross section of the high energy parton in the medium. These resuls should be directly applicable to a quark-gluon plasma.

Paper Structure

This paper contains 16 sections, 132 equations, 10 figures.

Table of Contents

  1. Introduction
  2. General expression of the medium induced radia-tion spectrum in QCD
  3. Model for multiple scattering
  4. Gluon emission induced by a single scattering
  5. Effective radiation amplitudes for double and multiple scat-te-ring
  6. Double scattering.
  7. Multiple scattering.
  8. Expression for the radiation spectrum induced by $N$ scatterings
  9. Heuristic discussion of the energy loss in finite length media
  10. General equation for the induced radiation spectrum
  11. Solution for the radiation spectrum in the small $\kappa$ limit
  12. Energy loss in a finite length medium
  13. Radiation amplitude induced by two scatterings
  14. Diagrammatic calculation of colour factors
  15. Expression of the medium induced spectrum
  16. ...and 1 more sections

Figures (10)

  • Figure 1: This gluon emission amplitude induced by the scattering of an energetic quark off two static centres 1 and 2 is negligible in the $\lambda \gg \mu^{-1}$ limit.
  • Figure 2: Gluon emission amplitude induced by one scattering.
  • Figure 3: Diagrammatic representation of the effective current (\ref{['EffCurrent1']}).
  • Figure 4: Radiation amplitude expressed in terms of effective currents.
  • Figure 5: Diagrams contributing to the effective emission amplitude induced by the transfer $\vec{q}_{i\bot}$.
  • ...and 5 more figures