Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2003-11-12
Nucl.Phys.A747:564-608,2005
Physics
High Energy Physics
High Energy Physics - Phenomenology
31 pages. To appear in Nucl. Phys. A. New section (VII) with response to and criticism of hep-ph/0312222
Scientific paper
10.1016/j.nuclphysa.2004.10.006
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.
Boyanovsky Daniel
de Vega Hector J.
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