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

TL;DR

In a medium with $k^2>0$, the paper analyzes nonperturbative production of millicharged scalars by reducing the Klein-Gordon equation in a background EM plane wave to a Mathieu equation, which exhibits instability bands that enable parametric resonance. It studies both running and standing wave configurations, distinguishing narrow ($q\ll1$) and broad ($q\gg1$) resonances to derive explicit instability conditions in terms of $E_0$, $\omega$, $n$, $e$, $m$, and $p_\perp$. The authors translate these resonances into laboratory constraints on millicharged particles and compare with existing bounds, highlighting metamaterial platforms with $n<1$ and standing-wave cavities to enhance sensitivity. The work provides a nonperturbative mechanism to probe millicharged scalars via resonant production in EM backgrounds and outlines experimental paths to surpass current limits in selected parameter regions.

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 exponentially growing solutions for certain parameter ranges. We show that this resonance indeed occurs for small scalar masses. We apply our results to derive constraints on millicharged particles and compare them with existing experimental data.

Figures (11)

• Figure 1: Mathieu equation stability chart. Vertical axis: $A_p$, Horizontal: $q$. Grey(white) area: stability(instability) regions of Mathieu equation. Blue solid line: Instability bound for narrow resonance regime. Black dashed line - line $A_p=2q$.
• Figure 2: The instability region (gray shadowed) for scaled perpendicular momentum $\pi_\perp$ as a function of scaled electric field $\mathcal{E}$. The boundaries of instability region determined by eq. \ref{['eq:NarrowBound']}. $n=\sqrt{0.9}$, $\mu=0$. The dashed curve represents $q=1$, the limitation for the narrow resonance approximation.
• Figure 3: Floquet exponent $\mu_{Fl}$ dependence on the scaled perpendicular momentum $\pi_\perp$ for first narrow resonance band and fixed $n=\sqrt{0.9}$, $\mu=0$, for several values of scaled electric field $\mathcal{E}$.
• Figure 4: Floquet exponent $\mu_{Fl}$ dependence on scaled electric field $\mathcal{E}$ for first narrow resonance band and fixed $n=\sqrt{0.9}$, $\mu=0$ and the average value of $\pi_{\perp}$ at fixed $\mathcal{E}$.
• Figure 5: The instability bounds of scaled perpendicular momentum $\pi_\perp$ as a function of scaled electric field $\mathcal{E}$. 3 curves: $\mu = 0$, $\mu=\sqrt{1-n^2}/2$, $\mu=0.2$. The boundaries of instability region determined by eq. \ref{['eq:NarrowBound']}. $n=\sqrt{0.9}$. The dashed curve represents $q=1$, the area of the narrow resonance regime is below the line.