Jet Quenching Parameter in Medium with Chemical Potential from AdS/CFT

TL;DR

The paper addresses a nonperturbative determination of the jet quenching parameter in a hot, dense medium with nonzero chemical potential using the gauge/gravity duality. It computes $\hat{q}_{YM}$ from a lightlike Wilson loop via the on-shell Nambu–Goto action in a five-dimensional $R$-charged AdS black hole background, expressing the result as $\hat{q}_{YM}(κ,T_κ,λ)=\frac{π^2}{√2}√λT_0^3Q(κ)=\frac{π^2}{√2}√λ\left(\frac{2√{1+κ}}{2+κ}\right)^3T_κ^3Q(κ)$ with $Q(κ)=2√{1+κ}[\int_0^1 du/√(H^{-1/3}uf)]^{-1}$. It analyzes both small and large $κ$ regimes, showing that for $κ\ll1$ the ratio $\hat{q}_{YM}(κ)/\hat{q}_{YM}^{(0)}(T_0)=1+c_1κ+O(κ^2)$ with $c_1\approx0.5596$, while for $κ\gg1$, $Q(κ)\sim d_1κ^{7/6}$ and $\hat{q}_{YM} \sim const \cdot √λ T_κ^3 κ^{-1/3}$. A transition around $κ\approx2$ reflects thermodynamic instability of the background, with implications for holographic jet quenching and potential comparison to heavy-ion data.

Abstract

We calculate the jet quenching parameter in medium with chemical potential from AdS/CFT correspondence. Our result is summarized in a plot. Moreover, we extract the explicit form of the jet quenching parameter of medium with small chemical potential for phases of dual SYM corresponding to large and small black holes. For the former phase, the jet quenching is increased as the charge density increases, however, for the latter it is the opposite though the background is thermodynamically unstable.

Figures (1)

• Figure 1: The y-axis is the ratio between jet quenching parameters with and without chemical potential $\hat{q}_{YM}(\kappa,T_\kappa)/\hat{q}_{YM}^{(0)}(T_0)$ at $T_\kappa=T_0$, and the x-axis is the parameter $\kappa$ characterizing the charge-to-entropy density ratio.