The electrical conductivity and soft photon emissivity of the QCD plasma

Abstract

The electrical conductivity in the hot phase of the QCD plasma is extracted from a quenched lattice measurement of the Euclidean time vector correlator for 1.5 < T/T_c < 3. The spectral density in the vicinity of the origin is examined using a method specially adapted to this region, and a peak at small energies is seen. The continuum limit of the electrical conductivity, and the closely related soft photon emissivity of the QCD plasma, are then extracted from a fit to the Fourier transform of the temporal vector correlator.

Figures (3)

• Figure 1: Bayesian fits to $\Delta G_{ V}(t)$ at $T=2T_c$ for $m/T_c= 0.03$ and $N_t=8$ (circles) 10 (squares) and 12 (pentagons). The fits were made with $N_\omega=16$ and $0\le\omega\le4\pi T$, choosing ${\cal L}=1$. Changes in the fits due to variations in these algorithmic quantities are indistinguishable on the scale of this figure.
• Figure 2: $\Delta\rho_{ V}(\omega)$ obtained from fits to $\Delta G_{ V}(t)$ at $T=2T_c$ determined on a $12\times26^2\times48$ lattice with $m/T_c=0.03$. Statistical errors obtained with $N_\omega=32$ are denoted by the bars, while the lines span thrice the range allowed by various systematic uncertainties as discussed in the text.
• Figure 3: The electrical conductivity of the QCD plasma, $\sigma$, as a function of the temperature, $T$. The dimensionless quantity related to the soft photon emission rate shown on the right hand y-axis equals $6\sigma/T$deltafoot. The bars denote statistical errors in the fit to the form in eq. (\ref{['model']}) with $M=2$ and $N=1$.