Resonant production of millicharged scalars in $k^2>0$ electromagnetic wave background

TL;DR

This paper studies the behavior of charged scalar particles in a medium with a plane electromagnetic wave, revealing resonant solutions and deriving constraints on millicharged particles.

Contribution

It reduces the Klein-Gordon equation to the Mathieu equation in a medium, identifying resonant solutions and providing new constraints on millicharged scalars.

Findings

Resonant solutions grow exponentially in certain parameter ranges.

Constraints on millicharged particles are derived from the resonant behavior.

Comparison with existing experimental data is performed.

Abstract

We investigate the solution of the Klein-Gordon equation for a charged scalar particle in an electromagnetic plane wave background with $k^2>0$, which can be realized in a medium with a refractive index $n<1$. We reduce the equation of motion to the Mathieu equation, which has resonant solutions that grow exponentially for certain parameter ranges. We apply our results to derive constraints on scalar millicharged particles and compare them with existing experimental data.