Photon emissivity of the quark-gluon plasma: a lattice QCD analysis of the transverse channel

We present results for the thermal photon emissivity of the quark-gluon plasma derived from spatially transverse vector correlators computed in lattice QCD at a temperature of 250 MeV. The analysis of the spectral functions, performed at fixed spatial momentum, is based on continuum-extrapolated correlators obtained with two flavours of dynamical Wilson fermions. We compare the next-to-leading order perturbative QCD correlators, as well as the ${\cal N}=4$ supersymmetric Yang-Mills correlators at infinite coupling, to the correlators from lattice QCD and find them to lie within $\sim10\%$ of each other. We then refine the comparison, performing it at the level of filtered spectral functions obtained model-independently via the Backus-Gilbert method. Motivated by these studies, for frequencies $\omega\lesssim2.5\,$GeV we use fit ans\"atze to the spectral functions that perform well when applied to mock data generated from the NLO QCD or from the strongly-coupled SYM spectral functions, while the high-frequency part, $\omega\gtrsim 2.5\,$GeV, is matched to NLO QCD. We compare our results for the photon emissivity to our previous analysis of a different vector channel at the same temperature. We obtain the most stringent constraint at photon momenta around $k\simeq0.8\,$GeV, for which we find a differential photon emission rate per unit volume of $d\Gamma_\gamma/d^3k = (\alpha_{\rm em}/(\exp(k/T)-1))\times (2.2 \pm 0.8 ) \times 10^{-3}\,{\rm GeV}$.