Bulk viscosity of quark-gluon plasma in strong magnetic fields

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.

Figure 1

The contour in the complex-time plane. The part $C_{+}$ runs along the real axis and the part $C_{-}$ runs parallel to this axis, but is displaced by $-iϵ$.

Figure 2

The one-loop diagram for $G_{{\tilde{P}}_{\parallel }{\tilde{P}}_{\parallel }}^{(12)}$. The solid line is the quark propagator, and the blob is the vertex for ${\tilde{P}}_{\parallel }$, which is $k^3{\gamma }^3-{\mathrm{\Theta }}_{\beta }{k}^0{\gamma }^0$.

Figure 3

The solid (red) line is our result (${\zeta }_{\parallel }$), and the dotted (blue) line is ${\zeta }_{B=0}$. The red (blue) area on the right (left) is the temperature region $\sqrt{eB}<T$ ($T<\sqrt{{\alpha }_{s}eB}$) in which the LLL (leading-log) approximation is not reliable.

Figure 4

Schematic picture of the elliptic flow and the effect of the anisotropic bulk viscosity on it.