NLO thermal dilepton rate at non-zero momentum

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The vector channel spectral function and the dilepton production rate from a QCD plasma at a temperature above a few hundred MeV are evaluated up to next-to-leading order (NLO) including their dependence on a non-zero momentum with respect to the heat bath. The invariant mass of the virtual photon is taken to be in the range $ {{\mathcal{K}}^2} $ ~ (πT)2 ~ (1GeV)2, generalizing previous NLO results valid for $ {{\mathcal{K}}^2} $ ≫ (πT)2. In the opposite regime 0 < $ {{\mathcal{K}}^2} $ ≪ (πT)2 the loop expansion breaks down, but agrees nevertheless in order of magnitude with a previous result obtained through resummations. Ways to test the vector spectral function through comparisons with imaginary-time correlators measured on the lattice are discussed.