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

I 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 $0.4\mathrm{GeV}<p_{\perp }<0.6\mathrm{GeV}$ at the Brookhaven Relativistic Heavy Ion Collider energy. As a basis for my analysis, I 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 data from the PHENIX Collaboration, I found that the electrical conductivity at QGP temperature is in the range: $0.4<{\sigma }_0/\left(e^{2}T\right)<1.1$, which is comparable with recent studies on lattice. I also compare the contribution from the magnetic field and chiral anomaly to soft thermal photon $v_2$ with the data. I argue that at the CERN Large Hadron Collider, the chiral magnetic wave would give negative contribution to photon $v_2$.

Figure 1

${\langle \sigma /e{T}^2\rangle }_{QGP}$ (red dots), the average of $\sigma /e^{2}T$ in QGP as computed from Eq. (26) using photon production at $p_{\perp }$ bin $0.4\mathrm{GeV}<p_{\perp }<0.6\mathrm{GeV}$ for three different centrality bins ($0–20\%$, $20–40\%$, $40–60\%$) [2]. Blue dotted lines are corresponding to the upper and lower bound for $\sigma /e^{2}T$ as quoted in the abstract and in Eq. (3). Dashed horizontal lines are corresponding to the range of $\sigma /\left(e^{2}T\right)$ as estimated by lattice simulation in Ref. [18] with $C_{\text{EM}}=(2/3)e^2$.

Figure 2

PHENIX results of direct photon $v_2$ [3]. (Figure is reproduced from Ref. [26].)

Figure 3

The contribution of magnetic field to photon $v_2,v_2\left(B\right)$ [cf. Eq. (29)], at $p_{\perp }=0.5$ GeV vs the lifetime of magnetic field ${\tau }_B$. Photon production is computed based on Eqs. (20) and (27) for four different $\lambda =2,4,6,8$ (red solid, blue dashed, green dot-dashed, orange dotted curves, respectively). Here $\lambda$ is a parameter appearing in Eq. (33) which parametrizes the ${\omega }_B{\tau }_{\text{rel}}$ in the plasma. Two dashed horizontal lines correspond to the upper and lower bound of direct photon $v_2$ at $p_{\perp }=0.5$ GeV from the data (c.f. Fig. 2). Panels (a), (b), (c) correspond to centrality bins $0–20\%,20–40\%,40–60\%$, respectively.