We compute the longitudinal electrical conductivity in the presence of strong background magnetic field in complete leading order of perturbative QCD, based on the assumed hierarchy of scales α s eB (m 2 q , T 2 ) eB. We formulate an effective kinetic theory of lowest Landau level quarks with the leading order QCD collision term arising from 1-to-2 processes that become possible due to 1+1 dimensional Landau level kinematics. In small m q /T 1 regime, the longitudinal conductivity behaves as σ zz ∼ e 2 (eB)T /(α s m 2 q log(T /m q )), where the quark mass dependence can be understood from the chiral anomaly with the axial charge relaxation provided by a finite quark mass m q . We also present parametric estimates for the longitudinal and transverse "color conductivities" in the presence of strong magnetic field, by computing dominant damping rates for quarks and gluons that are responsible for color charge transportation. We observe that the longitudinal color conductivity is enhanced by strong magnetic field, which implies that the sphaleron transition rate in perturbative QCD is suppressed by strong magnetic field due to the enhanced Lenz's law in color field dynamics. *

We present the quantum kinetic equation for spin polarization of massive quarks in leading log order of perturbative QCD, which describes time evolution of the spin density matrix in momentum space of a massive quark interacting with a background QCD plasma. We find that the time evolution operator of the spin density matrix, or the quantum kinetic collision terms, are universally of order α 2 s log(1/α s ) in terms of the QCD coupling constant α s = g 2 /(4π). Our quantum kinetic equation is valid for an arbitrary quark mass m m D ∼ gT , where m D is the Debye mass, and can be used to study relaxation dynamics of spin polarization of massive quarks in perturbative QCD

We compute the jet quenching parameterq of QCD plasma in the presence of strong magnetic field in both weakly and strongly coupled regimes. In weakly coupled regime, we computeq in perturbative QCD at complete leading order (that is, leading log as well as the constant under the log) in QCD coupling constant α s , assuming the hierarchy of scales α s eB T 2 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 findq ∼ α 2 s (eB)T log(1/α s ), while in the latter we havê q ∼ α 2 s (eB)T log(T 2 /α 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 findq ∼ √ λ(eB)T or q ∼ √ λ √ 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 ofq 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. *

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We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: eB ∼ g 4 logð1=gÞT 2 . We work in the assumption that the magnetic field is homogeneous and static, and the electrodynamics is nondynamical in a formal limit e → 0 while eB is kept fixed. We show that the shear viscosity takes a form η ¼ηðBÞT 3 =ðg 4 logð1=gÞÞ with a dimensionless functionηðBÞ in terms of a dimensionless variablēThe variableB corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions:B ∼ l mfp =l cyclo . We provide a full numerical result for the scaled shear viscosityηðBÞ.