Axions and "Light Shining Through a Wall": A Detailed Theoretical Analysis

TL;DR

This work analyzes photon-axion conversion in LSW experiments with a nonzero axion mass $m$ using three complementary methods: Green-function perturbation, WKB/eikonal, and an all-orders wave-matching $S$-matrix approach for a piecewise-constant magnetic field. A key finding is a threshold cusp at $\omega\approx m$ that enhances the photon-to-axion amplitude by a factor $\omega/k$ relative to the opposite conversion, while the all-orders treatment restores unitarity near threshold and yields exact ratio $\phi_T/a_T=\omega/k$ for piecewise-constant fields. The analysis also provides explicit expressions for near-threshold observables, estimates of light-through-a-wall and axion flux, and discusses magnetic-field penetration into the wall. The results clarify threshold effects, unitarity constraints, and the dependence on experimental geometry, informing future LSW search strategies and potential astrophysical implications of threshold enhancements.

Abstract

We give a detailed study of axion-photon and photon-axion conversion amplitudes, which enter the analysis of ``light shining through a wall'' experiments. Several different calculational methods are employed and compared, and in all cases we retain a nonzero axion mass. To leading order, we find that when the photon frequency $ω$ is very close to the axion mass $m$, there is a threshold cusp which significantly enhances the photon to axion conversion amplitude, by a factor $ω/\sqrt{ω^2-m^2}$ relative to the corresponding axion to photon conversion process. When $m=0$, the enhancement factor reduces to unity and the results of previous calculations are recovered. Our calculations include an exact wave matching analysis, which shows how unitarity is maintained near threshold at $ω=m$, and a discussion of the case when the magnetic field extends into the ``wall'' region.

Figures (1)

• Figure 1: Light shining through a wall setup. The wavy line indicates the photon field and the dashed line the axion field. In region I, there is only the photon wave, in region II the magnetic field gives rise to an axion wave, which exits with the photon wave into region III. In region IV, the "wall", the photon wave is absorbed, leaving only the axion wave in region V. In region VI, the magnetic field regenerates a photon wave from the axion, which exits into region VII, where the regenerated photon is detected.