Casimir Geometry as a Probe of Short Range Forces

Abstract

Casimir force searches provide among the most sensitive laboratory probes of new short range interactions. Existing constraints rely almost exclusively on a single geometry. We show that Casimir geometry constitutes an independent observable, as Yukawa-type interactions and Casimir background exhibit different geometric scaling for bulk forces and surface quantum effects. We derive the first constraints from sphere-sphere and plate-plate geometries, thereby completing the canonical set of Casimir geometries, obtaining the most stringent Casimir-based bounds for $λ\lesssim 10^{-8}~\mathrm{m}$. Our results establish geometry as a new handle for systematic searches for short range forces.

Figures (3)

• Figure 1: Schematic illustrations of the Casimir force experimental configurations for Yukawa-type new force search: (a) sphere-plate (s-p) geometry, (b) plate-plate (p-p) geometry and (c) sphere-sphere (s-s) geometry. Scaling of Yukawa-type force gradient for each geometry is shown, with "corr." denoting correction effects. The distinct $\lambda$-scaling and corrections across geometries underlies the sensitivity to new forces demonstrated in this work.
• Figure 2: [Left] Constraints on the Yukawa coupling strength $\alpha$ as a function of characteristic force distance from the p-p Casimir geometry. Previous limits from s-p Casimir experiments Chen:2014odaBordag:2001qi, as well as sensitivity projections for the proposed p-p CANNEX experiment Sedmik:2020cfj are shown. The right axis corresponds to coupling strength $g_s$ of the scalar mediator with protons and neutrons assuming universal coupling, while the top axis denote the corresponding mediator mass. [Right] New constraints on the Yukawa coupling strength $\alpha$ from the s-s Casimir geometry. The solid line indicates our numerical calculations of the Yukawa-type force, while the dotted line shows the PFA results we obtained considering multilayered spheres. Example representative benchmarks from simplified models with gauged baryons, gluon-type modulus and strange modulus where effective $\alpha \gg 1$ can be predicted are displayed.
• Figure 3: Casimir pressure of the s-s setup from our computation (solid blue line) compared with the theoretical result (orange dashed line) from Ref. PhysRevLett.120.040401 [Fig. 3(c)], for the same experimental configuration.