Radiative Energy Loss of High Energy Partons Traversing an Expanding QCD Plasma

TL;DR

This work extends the BDMPS framework for medium-induced radiation to a longitudinally expanding QCD plasma described by Bjorken scaling $T^3 \tau^\alpha = \text{const}$, with time-dependent $\mu$ and $\lambda$ and $\hat{q}(t)$. The authors derive the evolving transverse momentum broadening $p_{\perp W}^2(L)$ and the gluon radiation spectrum in the expanding medium, expressing the latter through a time-dependent harmonic-oscillator Green function and a parameter $\nu=1/(2-\alpha)$. They obtain analytic expressions for the radiative energy loss per unit length, showing it can be up to $6$ times the static value at $T(L)$ for $\alpha$ near unity, and provide relations tying energy loss to $p_{\perp W}^2(L)$. These results quantify how expansion dynamics amplify jet quenching and connect the energy loss to the evolving transport coefficient $\hat{q}$, with implications for interpreting jet suppression in heavy-ion collisions where the medium cools as it expands.

Abstract

We study analytically the medium-induced energy loss of a high energy parton passing through a finite size QCD plasma, which is expanding longitudinally according to Bjorken's model. We extend the BDMPS formalism already applied to static media to the case of a quark which hits successive layers of matter of decreasing temperature, and we show that the resulting radiative energy loss can be as large as 6 times the corresponding one in a static plasma at the reference temperature $T = T (L)$, which is reached after the quark propagates a distance $L$.

Figures (1)

• Figure :