Lattice constraints on the thermal photon rate

Abstract

We estimate the photon production rate from an SU(3) plasma at temperatures of about $1.1{T}_{\mathrm{c}}$ and $1.3{T}_{\mathrm{c}}$. Lattice results for the vector current correlator at spatial momenta $k\ensuremath{\sim}(2\ensuremath{-}6)T$ are extrapolated to the continuum limit and analyzed with the help of a polynomial interpolation for the corresponding spectral function, which vanishes at zero frequency and matches to high-precision perturbative results at large invariant masses. For small invariant masses the interpolation is compared with the next-to-leading-order (NLO) weak-coupling result, hydrodynamics, and a holographic model. At vanishing invariant mass we extract the photon rate which for $k\ensuremath{\gtrsim}3T$ is found to be close to the NLO weak-coupling prediction. For $k\ensuremath{\lesssim}2T$ uncertainties remain large but the photon rate is likely to fall below the NLO prediction, in accordance with the onset of a strongly interacting behavior characteristic of the hydrodynamic regime.