Photon production from a thermalized quark gluon plasma: quantum kinetics and nonperturbative aspects

We study the production of photons from a quark gluon plasma in local thermal equilibrium by introducing a non-perturbative formulation of the real time evolution of the density matrix. The main ingredient is the real time effective action for the electromagnetic field to $\mathcal{O}(\alpha_{em})$ and to all orders in $\alpha_s$. The real time evolution is completely determined by the solution of a \emph{classical stochastic} non-local Langevin equation which provides a Dyson-like resummation of the perturbative expansion. The Langevin equation is solved in closed form by Laplace transform in terms of the thermal photon polarization. A quantum kinetic description emerges directly from this formulation. We find that photons with $k \lesssim 200 ~{Mev}$ \emph{thermalize} as plasmon quasiparticles in the plasma on time scales $t \sim 10-20 ~{fm}/c$ which is of the order of the lifetime of the QGP expected at RHIC and LHC. We then obtain the direct photon yield to lowest order in $\alpha_{em}$ and to leading logarithmic order in $\alpha_s$ in a \emph{uniform} expansion valid at all time. The yield during a QGP lifetime $t \sim 10 ~{fm}/c$ is systematically larger than that obtained with the equilibrium formulation and the spectrum features a distinct flattening for $k \gtrsim 2.5 ~{Gev}$. We discuss the window of reliability of our results, the theoretical uncertainties in \emph{any} treatment of photon emission from a QGP in LTE and the shortcomings of the customary S-matrix approach.