Abstract
We supply recently obtained results from lattice EQCD with the correct UV limit to construct the collisional broadening kernel C(b⊥) in a QCD plasma. We discuss the limiting behavior of C(b⊥) at small and large impact parameters b⊥, and illustrate how the results can be used to compute medium-induced radiation rates.
Highlights
Constantly emitting virtual collinear radiation; scattering of the particle or the emitted radiation with the medium can force the radiation to become real
Our results are cast into dimensionless ratios with the help of the three-dimensional coupling g32d, and plotted in figure 1, where we present CQCD(b⊥) at the two temperatures of further relevance for this work together with the limiting infrared and ultraviolet behavior that we will discuss further below
Numerical results for the medium-induced splitting rates are presented in figure 3, where we show the rates for the non-perturbative broadening kernel CQCD(b⊥) at T = 250, 500MeV, along with the corresponding results obtained for the leading order
Summary
Constantly emitting virtual collinear radiation; scattering of the particle or the emitted radiation with the medium can force the radiation to become real. As a high-energy particle propagates through a medium with a density matrix |p p|, a hard vertex generates an amplitude for the mixed state |p p − k, k|. This state forms at transverse separation b⊥ = 0 but as time evolves, it undergoes eikonalized propagation in the transverse plane, diffusing in b⊥ and receiving damping due to medium interactions; the strength of this damping at transverse separation b⊥, C(b⊥), is the Fourier transform of the rate of transverse momentum broadening:. It is common to make the approximation of many individually small scatterings, leading to transverse momentum diffusion: C(b⊥) =
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