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Photon Emission from a Momentum Anisotropic Quark-Gluon Plasma

We compute the photon emission rate from a quark-gluon plasma with an anisotropic particle momentum distribution induced by a non-vanishing local shear pressure tensor. Our calculation includes photon production through Compton scattering and quark-antiquark annihilation at leading order in $α_s$, with all off-equilibrium corrections to leading order in the momentum anisotropy. For fermions we prove that the Kubo-Martin-Schwinger (KMS) relation holds in the hard loop regime for any particle momentum distribution function that is reflection-symmetric. This supports the equivalence, for 2 to 2 scattering processes, of the diagrammatic and kinetic approaches to calculating the photon emission rate. We compare the viscous rates from these two approaches at weak and realistic coupling strengths and provide parameterizations of the equilibrium and viscous photon emission rates for phenomenological studies in relativistic heavy-ion collisions.