Thermal axion production in QCD from the lattice

Abstract: Thermal axion production in the early Universe is controlled by the QCD topological-charge-density spectral function evaluated on the light-cone as a function of momentum k. We show how weighted integrals of this quantity can be computed using Euclidean lattice QCD without any analytic continuation, similar to what Harvey Meyer and collaborators have recently done for the photon production rate. We then test the approach in pure-glue QCD at T=1.5 Tc, finding that it is feasible to extract at least one and possibly two finite weighted k-integrals of the k-dependent production rate. This opens the possibility for extractions in full QCD at temperatures around and somewhat above the crossover temperature, where other methods are not reliable.