Simple Formula for High-Energy Gluon Bremsstrahlung in a Finite, Expanding Medium

Abstract

Previous authors have considered the problem of the medium effects on single gluon bremsstrahlung associated with producing a high-energy particle in a finite, time-dependent QCD plasma. Working to leading logarithmic order, I show that the result for the bremsstrahlung gluon spectrum can be cast into a remarkably simple form in the general case. I similarly analyze the process of pair production. Also, I comment on the radius of convergence of the opacity expansion in cases where the leading-log approximation holds, showing that the opacity expansion does not converge when the thickness of the plasma is greater than roughly the bremsstrahlung formation time. Additionally, as a special bonus -- available for a limited time only while supplies last! -- I summarize translations between the notation used by a few of the groups who have worked on this and related problems.

arXiv comment25 pages, 1 figure [changes from v1: clarifications made as to range of validity of results for small medium size]

References in corpus (23)

• Radiative energy loss and $p_{\perp }$-broadening of high energy partons in nuclei
• Radiative energy loss of high energy quarks and gluons in a finite volume quark-gluon plasma
• Fully quantum treatment of the Landau--Pomeranchuk--Migdal effect in QED and QCD
• How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?
• Reaction Operator Approach to Non-Abelian Energy Loss
• Transport coefficients in high temperature gauge theories: (II) Beyond leading log
• Radiative energy loss of high energy quarks in finite-size nuclear matter and quark-gluon plasma
• Gluon Radiation off Hard Quarks in a Nuclear Environment: Opacity Expansion
• Bottom-up thermalization in heavy ion collisions
• Energy loss in perturbative QCD
• Photon and Gluon Emission in Relativistic Plasmas
• Calculating Quenching Weights
• Effective Kinetic Theory for High Temperature Gauge Theories
• Medium-induced radiative energy loss; equivalence between the BDMPS and Zakharov formalisms
• Radiative Energy Loss of High Energy Partons Traversing an Expanding QCD Plasma
• Energy Loss of Leading Partons in a Thermal QCD Medium
• Jet Quenching versus Jet Enhancement: A Quantitative Study of the BDMPS-Z Gluon Radiation Spectrum
• A simple sum rule for the thermal gluon spectral function and applications
• The Landau-Pomeranchuk-Migdal effect in QED
• On the Energy Loss of High Energy Quarks in a Finite-Size Quark-Gluon Plasma
• Reaction Operator Approach to Multiple Elastic Scatterings
• QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime
• Jet quenching and broadening: the transport coefficient $\hat{q}$ in an anisotropic plasma

Cited by in corpus (61)

• Jet physics in heavy-ion collisions
• Comparison of Jet Quenching Formalisms for a Quark-Gluon Plasma "Brick"
• Light quark energy loss in strongly-coupled N = 4 supersymmetric Yang-Mills plasma
• Jet Structure in Heavy Ion Collisions
• Jet quenching and medium response in high-energy heavy-ion collisions: a review
• Perturbative Thermal QCD: Formalism and Applications
• Finite-size effects on the radiative energy loss of a fast parton in hot and dense strongly interacting matter
• The First fm/c of Heavy-Ion Collisions
• The radiation pattern of a QCD antenna in a dense medium
• The radiation pattern of a QCD antenna in a dilute medium
• Deciphering the $z_g$ distribution in ultrarelativistic heavy ion collisions
• Predicting parton energy loss in small collision systems
• The LPM effect in sequential bremsstrahlung
• Jet quenching
• Gluon bremsstrahlung in finite media beyond multiple soft scattering approximation
• Improved opacity expansion for medium-induced parton splitting
• Equilibration of weakly coupled QCD plasmas
• The LPM effect in sequential bremsstrahlung 2: factorization
• Medium-induced radiative kernel with the Improved Opacity Expansion
• Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas
• Improved opacity expansion at NNLO for medium induced gluon radiation
• Medium-induced fragmentation and equilibration of highly energetic partons
• Medium-induced cascade in expanding media
• Non-perturbative determination of collisional broadening and medium induced radiation in QCD plasmas
• Jet radiation in a longitudinally expanding medium
• High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation
• Stopping distance for high energy jets in weakly-coupled quark-gluon plasmas
• Jet quenching parameter in an expanding QCD plasma
• Running coupling effects in the evolution of jet quenching
• Jet thermalization in QCD kinetic theory
• A modified in-medium evolution equation with color coherence
• Medium-induced radiation with vacuum propagation in the pre-hydrodynamics phase
• Precise description of medium-induced emissions
• A unified picture of medium-induced radiation
• Splitting rates in QCD plasmas from a non-perturbative determination of the momentum broadening kernel $C(q_{\perp })$
• In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers
• The medium-modified $g\to c\bar{c}$ splitting function in the BDMPS-Z formalism
• Jet quenching parameter in QCD kinetic theory
• Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss
• Parton energy loss in a hard-soft factorized approach
• Leading order, next-to-leading order, and non-perturbative parton collision kernels: effects in static and evolving media
• Parton Energy Loss and the Generalized Jet Transport Coefficient
• The LPM effect in sequential bremsstrahlung: from large-N QCD to N=3 via the SU(N) analog of Wigner 6-j symbols
• Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters $\hat{q}$
• Thermalization of mini-jets in a quark-gluon plasma
• Jet evolution in a dense QCD medium
• Heavy Quark Energy Loss in the Quark-Gluon Plasma in the Moller theory
• Transverse momentum broadening of medium-induced cascades in expanding media
• Heavy Quark Radiation in the Quark-Gluon Plasma in the Moliere Theory: Angular Distribution of the Radiation
• In-medium gluon radiation spectrum with all-order resummation of multiple scatterings in longitudinally evolving media
• Nonlocal wave turbulence in non-Abelian plasmas
• QCD antenna radiative spectrum in dense media within the Improved Opacity Expansion
• Jet quenching in out-of-equilibrium QCD matter
• Coherent gluon radiation: beyond leading-log accuracy
• Jet transport coefficients by elastic and radiative scatterings in the strongly interacting quark-gluon plasma
• Comparing parton energy loss models
• Hard gluon evolution in the last stage of the bottom-up thermalization
• Advancing QCD-based calculations of energy loss
• Hard gluon evolution in warming medium
• Gluon Bremsstrahlung in Weakly-Coupled Plasmas
• Jet quenching in expanding medium