Testing Chameleon Theories with Light Propagating through a Magnetic Field

TL;DR

This work addresses the PVLAS anomaly by proposing chameleon scalar fields with environment-dependent mass as an alternative to standard ALPs. It develops a detailed framework for photon-chameleon mixing inside a magnetic-field cavity, accounting for confinement, coherence, and realistic phase shifts, and derives the modified rotation (dichroism) and ellipticity (birefringence) signals. A key result is that chameleons are trapped within the optical cavity, yielding ellipticity signals that typically exceed rotation, with the signal strength highly sensitive to cavity parameters and the chameleon potential (via $M$, $m_\phi$, and $n$). The paper then makes concrete predictions for PVLAS, QA, BMV, and BRFT, showing how current and upcoming experiments can test or constrain chameleon scenarios, potentially reconciling laboratory hints with astrophysical bounds by exploiting environmental mass screening.

Abstract

It was recently argued that the observed PVLAS anomaly can be explained by chameleon field theories in which large deviations from Newton's law can be avoided. Here we present the predictions for the dichroism and the birefringence induced in the vacuum by a magnetic field in these models. We show that chameleon particles behave very differently from standard axion-like particles (ALPs). We find that, unlike ALPs, the chameleon particles are confined within the experimental set-up. As a consequence, the birefringence is always bigger than the dichroism in PVLAS-type experiments.

Figures (6)

• Figure 1: Illustration of the difference between a sharp (step-like) change in the chameleon mass at the surface of the mirror and the more realistic $m_{\phi} \sim {\cal O}(1/d)$, for $d \gg 1/m_{c}$, behaviour, where $d$ is the distance from the surface of the mirror. In both of these sketches, $m_{c}$ is the chameleon mass inside the mirror and $m_{b}$ is the chameleon mass far from the mirror. The dotted line indicates the surface of the mirror.
• Figure 2: Predictions for rotation (upper plot) and ellipticity (lower plot) in the chameleon model as a function of $M$ and $m_\phi$. The PVLAS set-up is used ($L=100$ cm, $d=270$ cm, $\omega=1.2$eV, $B=5$ T and $\varphi=\pi/4$). Furthermore we have chosen $n=1$.
• Figure 3: Predictions for rotation (left) and ellipticity (right) in the chameleon model as a function of $M$ for $\Lambda = 2.3 \times 10^{-3}\,{\rm eV}$ and $n=1$. Predictions for the $2.3$ T PVLAS ($L=100$ cm, $d=270$ cm, $\omega=1.2$eV, $B=2.3$T, $\rho_{\rm gas} = 2\times 10^{-14}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) and Q$\&$A ($L=60$ cm,$d=145$ cm, $\omega=1.2$eV, $B=2.3$T, $\rho_{\rm gas} = 8.5 \times 10^{-9}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) set-ups are shown. The thin-dotted lines show the $95\%$ confidence upper bounds on both the rotation and the ellipticity.
• Figure 4: Predictions for rotation (left) and ellipticity (right) in the chameleon model as a function of $M$ for $\Lambda = 2.3 \times 10^{-3}\,{\rm eV}$ and $n=1$. Predictions for the $B=2.3$ T and $B=5.5$ T PVLAS ($L=100$ cm, $d=270$ cm, $\omega=1.2$ eV, $\rho_{\rm gas} = 2\times 10^{-14}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) and BMV ($L=50$ cm,$d=85$ cm, $\omega=1.2$ eV, $B=11.5$ T, $\rho_{\rm gas} \approx 10^{-14}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) set-ups are shown. The thin-dotted lines show the $95\%$ confidence upper bounds on both the rotation and the ellipticity.
• Figure 5: Predictions for rotation (left) and ellipticity (right) in the chameleon model as a function of $M$ for $\Lambda = 2.3 \times 10^{-3}\,{\rm eV}$ and $n=1$. Predictions for the $B=2.3$ T PVLAS ($L=100$ cm, $d=270$ cm, $\omega=1.2$ eV, $\rho_{\rm gas} = 2\times 10^{-14}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) and BRFT ($B = 2$ T, $L=800$ cm, $d=345$ cm, $\omega = 2.41$ eV, $\rho_{\rm gas} \approx 10^{-14}{\rm g cm}^{-3}$ and $\varphi=\pi/4$) set-ups are shown. The thin-dotted lines show the $95\%$ confidence upper bounds on both the rotation and the ellipticity.