Jet quenching parameter of the quark-gluon plasma in a strong magnetic field: Perturbative QCD and AdS/CFT correspondence

We compute the jet quenching parameter (q) over cap of a quark-gluon plasma in the presence of a strong magnetic field using perturbative QCD (pQCD) in the weakly coupled regime, and AdS/CFT correspondence in the strongly coupled regime of N = 4 superYang-Mills. In the weakly coupled regime, we compute (q) over cap in pQCD at complete leading order (that is, leading log as well as the constant under the log) in the QCD coupling constant alpha(s), assuming the hierarchy of scales alpha(s)eB << T-2 << eB. We consider two cases of jet orientations with respect to the magnetic field: 1) the case of a jet moving parallel to the magnetic field; 2) the case of a jet moving perpendicular to the magnetic field. In the former case, we find (q) over cap similar to alpha(2)(s)(eB)T log(1/alpha(s)), while in the latter we have (q) over cap similar to alpha(2)(s) (eB)T log(T-2/alpha(s)eB). In both cases, this leading-order result arises from the scatterings with thermally populated lowest-Landau-level quarks. In the strongly coupled regime described by the AdS/CFT correspondence, we find (q) over cap similar to root lambda(eB)T or (q) over cap similar to root lambda root eBT(2) in the same hierarchy of T-2 << eB depending on whether the jet is moving parallel or perpendicular to the magnetic field, respectively, which indicates a universal dependence of (q) over cap on (eB)T in both regimes for the parallel case, the origin of which should be the transverse density of lowest-Landau-level states proportional to eB. Finally, the asymmetric transverse momentum diffusion in the case of a jet moving perpendicular to the magnetic field may give an interesting azimuthal asymmetry of the gluon bremsstrahlung spectrum in the Baier-Dokshitzer-Mueller-Peigne-Schiff and Zakharov (BDMPS-Z) formalism.