Pair production of light pseudoscalar particles in strong inhomogeneous fields by the Schwinger mechanism

The Schwinger mechanism is a non-perturbative process by which an infinite number of zero frequency photons can produce an electron-positron pair. For example a constant electric field larger than O(1011V/cm) will decay into electron-positron pairs, according to the Schwinger pair production probability formula [1]. In this paper we consider the pseudoscalar-two-photon coupling. We find that the pseudoscalar pair production probability is given by an expression w ∼ g exp−(O(m2/g)) in terms of the pseudoscalar-two-photon coupling g and the pseudoscalar mass m. This allows us to constrain the parameter space of {m, g} for any pseudoscalar model, based on the stability of electromagnetic fields. In axion models [2,3] the effective axion-two-photon coupling arise from axion couplings to charged fermions in a one loop diagram. This coupling is inversely proportional to the Peccei-Quinn symmetry beaking scale fa, and is independent of the mass of the fermion in the loop. The axion mass is inversely proportional to the square of fa. The pair production formula therefore can be expressed in terms of the single parameter fa. The generic electromagnetic interaction of a pseudoscalar φ can be written as (see Fig.1)