Calculating the Jet Quenching Parameter from AdS/CFT

Abstract

Models of medium-induced radiative parton energy loss account for the strong suppression of high-pT hadron spectra in $\sqrt{s_{NN}}=200$ GeV Au-Au collisions at RHIC in terms of a single "jet quenching parameter'' $\hat{q}$. The available suite of jet quenching measurements make $\hat{q}$ one of the experimentally best constrained properties of the hot fluid produced in RHIC collisions. We observe that $\hat{q}$ can be given a model-independent, nonperturbative, quantum field theoretic definition in terms of the short-distance behavior of a particular light-like Wilson loop. We then use the AdS/CFT correspondence to obtain a strong-coupling calculation of $\hat{q}$ in hot N=4 supersymmetric QCD, finding ${\hat{q}}_{SYM}=26.69\sqrt{{\alpha }_{SYM}{N}_c}{T}^3$ in the limit in which both $N_c$ and $4\pi {\alpha }_{SYM}{N}_c$ are large. We thus learn that at strong coupling $\hat{q}$ is not proportional to the entropy density $s$, or to some "number density of scatterers'' since, unlike the number of degrees of freedom, $\hat{q}$ does not grow like $N_c^2$.

Version accepted for publication in Phys. Rev. Lett.; factor of Sqrt[2] error corrected, improving agreement between $\hat{q}$ in N=4 SYM and that extracted from RHIC data

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