Electromagnetic radiation in hot QCD matter: Rates, electric conductivity, flavor susceptibility, and diffusion

We discuss the general features of the electromagnetic radiation from a thermal hadronic gas as constrained by chiral symmetry. The medium effects on the electromagnetic spectral functions and the partial restoration of chiral symmetry are quantified in terms of the pion densities. The results are compared with the electromagnetic radiation from a strongly interacting quark-gluon plasma in terms of the leading gluon condensate operators. We use the spectral functions as constrained by the emission rates to estimate the electric conductivity, the light flavor susceptibility and diffusion constant across the transition from the correlated hadronic gas to a strongly interacting quark-gluon plasma.

Figure 1

Pion density parameter $\kappa$ vs temperature for different ${\mu }_{\pi }$.

Figure 2

Partial contributions of Eqs. (12) and (13) to the imaginary part of the correlator $-\mathrm{Im}{\mathbf{W}}^F$ at $T=190$ MeV for different $|\vec{q}|$ (${\mathrm{q}}_{\mathrm{vec}}$) and ${\mu }_{\pi }$. The thick black solid lines are the 0th order contribution without the pion. For the one pion contribution, labeled by $\pi$, the three lines in each figure correspond to the three lines in Eq. (13), respectively. PP represents the contribution from terms with the retarded pion propagator.

Figure 3

Dilepton rates for hadronic gas at $T=150$ and 190 MeV with various $|\vec{q}|$ and ${\mu }_{\pi }$.

Figure 4

Spectral function ${\rho }_V$ of the hadronic gas for $T=150$ and 190 MeV with various $|\vec{q}|$ and ${\mu }_{\pi }$.

Figure 5

${\rho }_V/MT$ of the hadronic gas at $T=190$ MeV and ${\mu }_{\pi }=0$. The left panel shows the $|\vec{q}|$ dependence and the right panel shows the contribution of the $A1$ meson which is included in $\mathrm{Im}{\Pi }_A$.

Figure 6

${\sigma }_E/T$ for the hadronic gas. The blue lines indicate the range of lattice results for two flavors [21, 31] and the green line indicates the lower bound [32].

Figure 7

Flavor susceptibilities of the pionic gas. Red thin solid line corresponds to the leading QGP result ${\chi }_{u,d}/T^2=N_c/3$. The black thick solid line corresponds to the leading contribution with $\int d^{3}kn(1+n)$ and the black thick dashed line corresponds to the susceptibilities with ${\mathcal{T}}_{\pi \pi }$ as in Appendix pp2.

Figure 8

Thermal dileptons. Left panel: sQGP and HTL. Right panel: $T$ and $|\vec{q}|$ dependence of the sQGP. $T$-independent $\langle B^2\rangle$ and $\langle E^2\rangle$ in Eq. (41) are used for the sQGP.

Figure 9

Vector spectral density. Left panel: comparison between sQGP and HTL results. Right panel: $|\vec{q}|$ dependence of sQGP. $T$-independent $\langle B^2\rangle$ and $\langle E^2\rangle$ in Eq. (41) are used for sQGP.

Figure 10

${\sigma }_E/T$ for sQGP. The blue lines indicate the range of lattice results for three flavors [21, 31] and the green line indicates the lower bound [32].

Figure 11

Dilepton rates and spectral function from the sQGP with $T$-dependent $\langle E^2\rangle$ and $\langle B^2\rangle$ in Eq. (43).