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 $sqrt{{s}_{NN}}=200text{ }text{ }mathrm{GeV}$ Au-Au collisions at BNL RHIC in terms of a single “jet quenching parameter” $stackrel{^}{q}$. We observe that $stackrel{^}{q}$ 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 $stackrel{^}{q}$ in hot $mathcal{N}=4$ supersymmetric QCD, finding ${stackrel{^}{q}}_{mathrm{SYM}}=26.69sqrt{{ensuremath{alpha}}_{mathrm{SYM}}{N}_{c}}{T}^{3}$ in the limit in which both ${N}_{c}$ and $4ensuremath{pi}{ensuremath{alpha}}_{mathrm{SYM}}{N}_{c}$ are large. Thus, at strong coupling $stackrel{^}{q}$ is not proportional to the entropy density $s$, or to some “number density of scatterers” since, unlike the number of degrees of freedom, $stackrel{^}{q}$ does not grow like ${N}_{c}^{2}$.