Scalar self-interactions loosen constraints from fifth force searches

TL;DR

This work analyzes a scalar field $\phi$ with quartic self-interaction and universal matter couplings, where the linear fifth-force potential has strength $\alpha = 2\beta^2$ and range $\lambda = m_\phi^{-1}$. The authors show that the chameleon mechanism, driven by the density-dependent minimum $\phi_{min}$ of $V_{eff}(\phi)$ and an environment-dependent mass $m_{eff}$, can screen the scalar force in dense media, allowing gravitational-strength couplings across laboratory and solar-system scales. Consequently, current laboratory and planetary tests can be satisfied with $\alpha \sim O(1)$, owing to thin-shell suppression, while modest improvements in experiments could detect a chameleon signal with a distinctive short-range, non-Yukawa signature. The paper also discusses naturalness concerns and proposes an isospin-triplet coupling as a way to mitigate radiative corrections, preserving a naturally light scalar without spoiling the phenomenology.

Abstract

The mass of a scalar field mediating a fifth force is tightly constrained by experiments. We show, however, that adding a quartic self-interaction for such a scalar makes most tests much less constraining: the non-linear equation of motion masks the coupling of the scalar to matter through the chameleon mechanism. We discuss consequences for fifth force experiments. In particular, we find that, with quartic coupling of order unity, a gravitational strength interaction with matter is allowed by current constraints. We show that our chameleon scalar field results in experimental signatures that could be detected through modest improvements of current laboratory set-ups.

Figures (6)

• Figure 1: Experimental constraints on the strength $\alpha$ and range $\lambda$(m) from all fifth force experiments to date. Note that $\alpha=1$ corresponds to gravitational strength. This plot neglects any self-coupling for the scalar field mediating the force. Reprinted from adellong.
• Figure 2: Small-scale blow-up of previous figure. Reprinted from adellong.
• Figure 3: Revised experimental constraints on the strength $\alpha$ and range $\lambda$(m) including the effects of a quartic self-interaction term with $\xi=1$. The main difference is for the E$\ddot{{\rm o}}$t-Wash adel and Irvine irvine experiments since their test masses have a thin shell. The test masses used in the Stanford stan and Colorado col experiments, on the other hand, are too small to have a thin shell. Thus the corresponding curves are the same as in Fig. \ref{['expconsb']}.
• Figure 4: Loop diagrams for the action (\ref{['DiracAction']}) which contribute to the scalar potential.
• Figure 5: Profile for the chameleon for an object with $m_cR_c\approx 65$. The solid curve is the result of numerical integration; the dotted line is the analytical approximation derived in the text.