Bulk viscosity of quark-gluon plasma in strong magnetic fields

Abstract

We investigate the viscosities of the quark-gluon plasma in strong magnetic fields within the leading-log and lowest Landau level (LLL) approximations. We first show that the bulk viscosity in the direction parallel to the magnetic field is the only component that has a contribution from the quarks occupying the LLL. We then compute the bulk viscosity from the Kubo formula and find an intriguing quark-mass dependence as a consequence of a competition between the suppression of the bulk viscosity by conformal symmetry and an enhancement of the mean-free path by chirality conservation, which governs the behavior in the massless limit. The quark contribution to the viscosity along the magnetic field becomes larger than the one in the absence of a magnetic field. We also briefly estimate the other transport coefficients by considering the contribution of gluons. We show that the shear viscosities are suppressed compared to their values in the absence of a magnetic field.

One particle distribution function and shear viscosity in magnetic field: A relaxation time approach

“…Now we need to evaluate the tensor products like ξ (1) ijkl ξ (n) klmn and ξ (7) ijkl ξ (n) klmn which can be found from Eq. (17)(18)(19)(20)(21)(22)(23)(24). We have tabulated all such tensor products in table I.…”

“…For example, the phenomena of chiral magnetic effect (CME), chiral magnetic wave, and change in the photon and dilepton productions to name a few [4,[8][9][10][11][12]. Some other theoretical developments related to the magnetic field in heavy ion collisions includes magnetovortical evolution [13][14][15], calculation of Wigner functions for fermions in strong magnetic fields [17], shear viscosity in an anisotropic unitary Fermi gas [16], the shear and bulk viscosity of Quark-Gluon-Plasma (QGP) in strong magnetic fields [18][19][20] etc. On the other hand, several model studies in the last decade show that the QGP created in high energy heavy ion collisions possesses a very small value of shear viscosity to entropy density ratio.…”

Conductivities of magnetic quark-gluon plasma at strong coupling

“…Evaluation of anisotropic transport coefficients is needed for application of MHD. Viscosities in magnetic quark gluon plasma have been studied in [28,29]. Another interesting transport coefficient is the electric conductivity.…”

Calculation of anisotropic transport coefficients for an ultrarelativistic Boltzmann gas in a magnetic field within a kinetic approach

“…The electric field is neglected in [13,15] assuming that the electric field is much smaller than the magnetic field, which is a good approximation for QGP produced in heavy-ion collisions for instance. The constitutive equations in the Landau frame read [13,59]…”

“…M ≡ (∂P/∂B) T,µ is the magnetization. More details can be found in [13,59]. The coefficients involving magnetization in the definition of P and P ⊥ vanish for particles without dipole moment or spin, which is the case we consider in this work.…”