Photon production from a thermalized quark–gluon plasma: quantum kinetics and non-perturbative aspects

Abstract

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 O ( α em ) and to all orders in α s . The real time evolution is completely determined by the solution of a 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 ≲ 200 MeV thermalize as plasmon quasiparticles in the plasma on time scales t ∼ 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 α em and to leading logarithmic order in α s in a uniform expansion valid at all time. The yield during a QGP lifetime t ∼ 10 fm / c is systematically larger than that obtained with the equilibrium formulation and the spectrum features a distinct flattening for k ≳ 2.5 GeV . We discuss the window of reliability of our results, the theoretical uncertainties in any treatment of photon emission from a QGP in LTE and the shortcomings of the customary S-matrix approach.