Longitudinal conductivity in strong magnetic field in perturbative QCD: Complete leading order

Abstract

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. *

Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions

“…For example, the electrical conductivity will be an important input for the magnetohydrodynamics, which in turn will be relevant for the estimate of the magnetic-field profile. The techniques and ingredients developed in the computation of the heavy-quark diffusion coefficients have been applied in a few works for the jet quenching parameter [237] and the electrical conductivity [238,239] It would be instructive to see the computation of the coupling strength at the three-point vertex among two quarkonia and an external magnetic field by using the Bethe-Salpeter amplitudes obtained in the ladder approximation and the heavy-quark limit [240,241]. This computation involves a typical technique for the perturbation theory in the presence of a magnetic field.…”

Heavy-Quark Diffusion Dynamics in Quark–Gluon Plasma under Strong Magnetic Fields

“…After Ref. [3], a few works have been done for the jet quenching parameter [9] and the electrical conductivity [10,11] in the strong magnetic fields.…”

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

“…This has lead to attempts to estimate shear viscosity in various effective models [6][7][8][9][10][11][12] involving different approximation schemes. These include relaxation time approximations to the Boltzmann equation [13][14][15][16][17][18], Kubo formalism of evaluating equilibrium correlation functions [19][20][21][22][23][24][25], transport simulation of Boltzmann equation [6,[26][27][28], the perturbative QCD methods [29][30][31][32][33][34][35][36], as well as lattice methods [37,38].…”