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.

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

References in corpus (2)

• 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

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• Non-perturbative determination of collisional broadening and medium induced radiation in QCD plasmas
• High-energy gluon bremsstrahlung in a finite medium: harmonic oscillator versus single scattering approximation
• Running coupling effects in the evolution of jet quenching
• Jet thermalization in QCD kinetic theory
• Precise description of medium-induced emissions
• Medium-induced radiation with vacuum propagation in the pre-hydrodynamics phase
• Splitting rates in QCD plasmas from a non-perturbative determination of the momentum broadening kernel $C(q_{\perp })$
• A unified picture of medium-induced radiation
• The medium-modified $g\to c\bar{c}$ splitting function in the BDMPS-Z formalism
• Universality (beyond leading log) of soft radiative corrections to $\hat{q}$ in $p_{\perp }$ broadening and energy loss
• Jet quenching parameter in QCD kinetic theory
• Leading order, next-to-leading order, and non-perturbative parton collision kernels: effects in static and evolving media
• Jet evolution in a dense QCD medium
• Transverse momentum broadening of medium-induced cascades in expanding media
• In-medium gluon radiation spectrum with all-order resummation of multiple scatterings in longitudinally evolving media
• 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
• Advancing QCD-based calculations of energy loss
• Hard gluon evolution in warming medium
• Jet quenching in expanding medium