Electrical conductivity of the quark-gluon plasma and soft photon spectrum in heavy-ion collisions

We extract the electrical conductivity $\sigma_0$ of the quark gluon plasma(QGP) and study the effects of magnetic field and chiral anomaly on soft photon azimuthal anisotropy, $v_2$, based on the thermal photon spectrum at $0.4GeV<p_{\perp}<0.6GeV$ at RHIC energy. As a basis for our analysis, we derive the behavior of retarded photon self energy of a strongly interacting neutral plasma in hydrodynamic regime in the presence of magnetic field and chiral anomaly. By evolving the resulting soft thermal photon production rate over the realistic hydrodynamic background and comparing the results with the preliminary data from the PHENIX Collaboration, we found that the electrical conductivity at QGP temperature is in the range: $0.4<\sigma_0/(e^{2}T) <1.1$, which is comparable with recent studies on lattice. We also compare the contribution from the magnetic field and chiral anomaly to soft thermal photon $v_{2}$ with the data. We argue that at LHC, the chiral magnetic wave would give negative contribution to photon $v_2$.