Particle decay as asymptotic narrow parametric resonance

Parametric resonance can produce particles from oscillating scalar field, where an exponential growth of the particle number density can be developed. While it has been noticed that stimulated decay in Boltzmann equations exhibits similar parametric dependence of the exponential growth, it is not quantitatively clear yet under what circumstance can the two phenomena reconcile. We demonstrate that trilinear particle interaction in the Boltzmann equation can provide a good approximation to describe the distribution function and the number density in the asymptotic regime of narrow parametric resonance. We find that the crucial treatment leading to the quantitative agreement is a proper Gaussian simulation of the momentum spread inherited from nonrelativistic particle decay. With the simple particle picture, the analytic Boltzmann approximation can be applied to explosive photon production from axions/axion-like particles and to dark matter production from oscillating fields.