Axion emission from a hot plasma

We give the technics for the calculation of production and energy loss rates for axion-like particles (scalar or pseudo-scalar coupling to the gauge boson) from a hot QED (or QCD) heat bath. We compute the contribution coming from, the decay mode of a transverse to a longitudinal photon (or gluon). The energy loss rate for this process behaves asT ⁷. Considering the supernova SN1987A event, this behaviour could improve the upper bound on the coupling constant between asions and photons.