Photon and Gluon Emission in Relativistic Plasmas

TL;DR

This paper provides a physically transparent derivation of the leading-order hard photon emission rate in ultra-relativistic plasmas, emphasizing the Landau-Pomeranchuk-Migdal interference arising from multiple soft scatterings. It formulates the problem with a Gaussian random background field and derives a ladder-resummation that reduces to a linear integral equation for a dressed current vertex, framed in a relativistic Schrödinger picture. The authors show how bremsstrahlung and pair annihilation contributions combine to give a final LPM rate for photons and then extend the formalism to gluon emission, incorporating non-Abelian color structure and three-rail correlations while ensuring infrared safety. The work connects to Migdal’s classical treatment in static media but provides a general, dynamic-background generalization appropriate for hot QCD plasmas, with implications for photon and gluon diagnostics in heavy-ion collisions.

Abstract

We recently derived, using diagrammatic methods, the leading-order hard photon emission rate in ultra-relativistic plasmas. This requires a correct treatment of multiple scattering effects which limit the coherence length of emitted radiation (the Landau-Pomeranchuk-Migdal effect). In this paper, we provide a more physical derivation of this result, and extend the treatment to the case of gluon radiation.

Figures (18)

• Figure 1: Two-to-two particle processes contributing to the leading order photon emission rate. Time may be viewed as running from left to right.
• Figure 2: Bremsstrahlung and pair production contributions to photon emission. The bottom line in each diagram can represent either a quark or a gluon.
• Figure 3: An interference term, involving amplitudes for photon emission before and after multiple scattering events, which contributes to the leading order emission rate.
• Figure 4: Orders of magnitude of various momentum, distance, and angular scales associated with bremsstrahlung of a photon with momentum of order $T$. $g$ stands for the strong coupling $g_{\rm s}$.
• Figure 5: The perturbative bremsstrahlung and annihilation processes of Fig. \ref{['fig:inelastic']}, with the soft gluon fields now interpreted as classical background fields.