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

We compute the jet quenching parameter $\widehat{q}$ of QCD plasma in the presence of strong magnetic field in both weakly and strongly coupled regimes. In weakly coupled regime, we compute $\widehat{q}$ in perturbative QCD at complete leading order (that is, leading log as well as the constant under the log) in QCD coupling constant ${\alpha }_s$, assuming the hierarchy of scales $\alpha_s eB\ll T^2\ll eB$. We consider two cases of jet orientations with respect to the magnetic field: 1) the case of jet moving parallel to the magnetic field, 2) the case jet moving perpendicular to the magnetic field. In the former case, we find $\widehat{q}\sim {\alpha }_s^2(eB)T\log (1\mathrm{/}{\alpha }_s)$, while in the latter we have $\widehat{q}\sim {\alpha }_s^2(eB)T\log (T^2\mathrm{/}{\alpha }_{s}eB)$. In both cases, this leading order result arises from the scatterings with thermally populated lowest Landau level quarks. In strongly coupled regime described by AdS/CFT correspondence, we find $\widehat{q}\sim \sqrt{\lambda }(eB)T$ or $\hat q\sim\sqrt{\lambda}\sqrt{eB}T^2$inthesamehierarchyof$T^2\ll eB$ depending on whether the jet is moving parallel or perpendicular to the magnetic field, respectively, which indicates a universal dependence of $\widehat{q}$ 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 jet moving perpendicular to the magnetic field may give an interesting azimuthal asymmetry of the gluon Bremsstrahlung spectrum in the BDMPS-Z formalism.