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The photon emission rate of a thermally equilibrated system is determined bythe imaginary part of the in-medium retarded correlator of the electromagneticcurrent transverse to the spatial momentum of the photon. In aLorentz-covariant theory, this correlator can be parametrized by a scalarfunction ${\cal G}_R(u\cdot {\cal K},{\cal K}^2)$, where $u$ is the fluidfour-velocity and ${\cal K}$ corresponds to the momentum of the photon. Wepropose to compute the analytic continuation of ${\cal G}_R(u\cdot {\calK},{\cal K}^2)$ at fixed, vanishing virtuality ${\cal K}^2$, to imaginaryvalues of the first argument, $u\cdot {\cal K}= i\omega_n$. At thesekinematics, the retarded correlator is equal to the Euclidean correlator$G_E(\omega_n, k=i\omega_n)$, whose first argument is the Matsubara frequencyand the second is the spatial momentum. The Euclidean correlator, which isdirectly accessible in lattice QCD simulations, must be given an imaginaryspatial momentum in order to realize the photon on-shell condition. Via aonce-subtracted dispersion relation that we derive in a standard way at fixed${\cal K}^2=0$, the Euclidean correlator with imaginary spatial momentum isrelated to the photon emission rate. The relation allows for a more directprobing of the real-photon emission rate of the quark-gluon plasma in latticeQCD than the dispersion relations which have been used so far, the latter beingat fixed spatial photon momentum $k$ and thus involving all possiblevirtualities of the photon.

Euclidean correlators at imaginary spatial momentum and their relation to the thermal photon emission rate