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

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 $\omega$ 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 $\omega/\sqrt{\omega^2-m^2}$ 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 $\omega=m$, and a discussion of the case when the magnetic field extends into the ``wall'' region.