Multiple Collisions and Induced Gluon Bremsstrahlung in QCD

TL;DR

Gyulassy and Wang develop a perturbative QCD treatment of induced soft gluon radiation from a high-energy parton in a dense, color-neutral medium. They derive a non-abelian analogue of the LPM effect, encapsulated in a radiation formation factor that depends on color representation, formation time, and medium screening, and show how interference between multiple scatterings suppresses radiation in the soft regime. The formalism yields a saturated, approximately constant energy loss per unit length in the factorization limit and connects to the Bethe–Heitler linear regime in the dilute limit, with explicit interpolation formulas governed by the mean free path $oldsymbol{ extlambda}$ and screening scale $oldsymbol{oldsymbol{ extmu}}$. The results clarify how non-abelian color structure controls radiative energy loss and lay groundwork for transport models of parton cascades in dense QCD matter, while highlighting open questions for extending beyond the soft, eikonal regime.

Abstract

Induced soft gluon bremsstrahlung associated with multiple collisions is calculated via perturbative QCD. We derive the non-abelian analog of the Landau-Pomeranchuk effect that suppresses induced soft radiation with formation times exceeding the mean free path, $λ$. The dependence of the suppression effect on the $SU(N)$ representation of the jet parton as well as the kinematic variables is expressed through a radiation formation factor. Unlike in QED, the finite contribution from the small $x$ regime in QCD leads to an approximately constant radiative energy loss per unit length, $dE/dz\propto μ^2$, in the high energy limit that is sensitive to the infrared screening scale, $μ$, of the medium. As a function of the dimensionless parameter $ζ=λμ^2/E$, we show furthermore how the energy dependence of $dE/dz$ evolves from the above constant for $ζ\ll 1$ to the more familiar (Bethe-Heitler) linear dependence for $ζ\gg 1$.