Limits on Nonstandard Forces in the Submicrometer Range

We report the search for a nonstandard force by measuring the Casimir forces in the $0.48–6.5\mu \mathrm{m}$ range. By comparing the data and the theory of the Casimir force, we have obtained constraints for the parameter $\alpha$ of the Yukawa-type deviations from Newtonian gravity. The obtained limits are more stringent than previous limits in the $1.0–2.9\mu \mathrm{m}$ range. Furthermore, we have obtained lower limits for the fundamental scale $M_{*}$ for gauged baryon number in the bulk. In particular, for six extra dimensions, the limits on $M_{*}$ are stringent in the range $6.5\times {10}^{-6}<\rho <2.5\times {10}^{-4}$.

Figure 1

Schematic diagram of the instrument used herein. $P1$ and $P2$ indicate the spherical lens and the flat plate, respectively, that produce a macroscopic force. $P3$, $P4$, $P5$, and $P6$ indicate the plates forming actuators that are used to control the torsion angle. Plates $P1$, $P4$, and $P5$ are electrically grounded through the wire of the torsion balance.

Figure 2

(a) Data of the difference in force per constant step $\Delta F^{\exp }(z)/\Delta z$ as a function of distance after qualification cut (See text). The vertical error bars show statistical errors. The dotted, dashed, and solid curves show the residual electric force, the expected Casimir force after correction of the conductivity and roughness effects, and the total best-fit curve of the sum of the two functions, respectively. (b) Deviation between data of $\Delta F^{\exp }(z)/\Delta z$ and the best-fit of the sum of the residual electric force and the theoretical Casimir force $\Delta F^{\mathrm{fit}}(z)/\Delta z$.

Figure 3

Upper limits on the Yukawa parameter $\alpha$. These curves were obtained by experiments [12, 14, 15, 21, 22], respectively. The curve labeled ’this experiment’ shows the limits obtained at 95% C.L. The shaded area enclosed by solid lines and the shaded area enclosed by dashed lines show the predicted regions for $\beta =1$ and $\beta =2$, respectively, for gauged baryon number in the bulk [3]. The solid lines labeled 1 and 100 TeV and the dashed line labeled 10 TeV show the predicted line at the value of $M_{*}$ for $\beta =1$.

Figure 4

Lower limits on fundamental scale $M_{*}$ at 95% C.L. for $n=3$ (a) and $n=6$ (b), respectively, assuming $\beta =1$ or $\beta =2$. The solid curves, the dashed curves, and the dotted curves are the present data, and the limits calculated from 15, 21, respectively.