The LPM effect in QCD and Radiative energy loss in a quark-gluon plasma

TL;DR

The paper analyzes the non-Abelian LPM effect in QCD by studying induced gluon radiation from a fast parton traversing a color-neutral QGP within a gauge-invariant potential framework. It introduces an effective formation time that depends on the parton’s color representation and derives an explicit expression for radiative energy loss that interpolates between the Bethe-Heitler and factorization limits, capturing color interference effects. The results show the radiative energy loss scales with the mean transverse momentum transfer and can dominate elastic loss at high energies, with gluon jets experiencing larger suppression due to non-Abelian interference. The work acknowledges underlying assumptions (weak coupling, small interaction range) and highlights plans to explore temperature-dependent screening and phenomenology near the deconfinement transition.

Abstract

The non-abelian analog of the Landau-Pomeranchuk-Migdal effect is investigated in perturbative QCD. Extending our previous studies, the suppression of induced soft bremsstrahlung due to multiple scatterings of quarks in the spinor representation is considered. The effective formation time of gluon radiation due to the color interference is shown to depend on the color representation of the emitting parton, and an improved formula for the radiative energy loss is derived that interpolates between the factorization and Bethe-Heitler limits.

Figures (4)

• Figure 1: Diagrams for induced gluon radiation from a single $qq$ scattering.
• Figure 2: Diagrams for gluon radiation from the quark line induced by double scatterings.
• Figure 3: The radiation formation factor $C_m(k)$, $m=5$, as a function of $\tau(k)/\lambda=2\cosh(y)/k_{\perp}\lambda$ for quarks (solid) and gluons (dashed).
• Figure 4: The energy dependence of energy loss, $dE/dz$, of a quark with energy $E$ inside a quark-gluon plasma at temperature $T=300$ MeV. A weak coupling $\alpha_s=0.3$ is used. The solid line is the full expression and the dashed line is the factorization limit of the radiative energy loss. The dot-dashed line is the elastic energy loss.