Calculating the Jet Quenching Parameter

Models of medium-induced radiative parton energy loss account for the strong suppression of high-$p_T$ hadron spectra in $\sqrt{s_{NN}}=200\mathrm{GeV}$ Au-Au collisions at BNL RHIC in terms of a single “jet quenching parameter” $\widehat{q}$. We observe that $\widehat{q}$ can be given a model-independent, nonperturbative, quantum field theoretic definition in terms of the short-distance behavior of a particular lightlike Wilson loop. We then use the anti–de Sitter/conformal-field-theory correspondence to obtain a strong-coupling calculation of $\widehat{q}$ in hot $\mathcal{N}=4$ supersymmetric QCD, finding ${\widehat{q}}_{\mathrm{SYM}}=26.69\sqrt{{\alpha }_{\mathrm{SYM}}{N}_c}{T}^3$ in the limit in which both $N_c$ and $4\pi {\alpha }_{\mathrm{SYM}}{N}_c$ are large. Thus, at strong coupling $\widehat{q}$ is not proportional to the entropy density $s$, or to some “number density of scatterers” since, unlike the number of degrees of freedom, $\widehat{q}$ does not grow like $N_c^2$.