Constraints on New Gravitylike Forces in the Nanometer Range

We report on a new constraint on gravitylike short-range forces, in which the interaction charge is mass, obtained by measuring the angular distribution of 5 Å neutrons scattering off atomic xenon gas. Around $10^7$ scattering events were collected at the 40 m small angle neutron scattering beam line located at the HANARO research reactor of the Korean Atomic Energy Research Institute. The extracted coupling strengths of new forces in the Yukawa-type parametrization are ${\widehat{g}}^2=(0.2\pm 6.8\pm 2.0)\times 10^{-15}{\mathrm{GeV}}^{-2}$ and ${\widehat{g}}^2=(-5.3\pm 9.0_{-2.8}^{+2.7})\times 10^{-17}{\mathrm{GeV}}^{-2}$ for interaction ranges of 0.1 and 1.0 nm, respectively. These strengths correspond to 95% confidence level limits of $g^2<(1.4\pm 0.2)\times 10^{-14}{\mathrm{GeV}}^{-2}$ and $g^2<(1.3\pm 0.2)\times 10^{-16}{\mathrm{GeV}}^{-2}$, improving the current limits for interaction ranges between 4 and 0.04 nm by a factor of up to 10.

Figure 1

Experimental limits at 95% C.L. for new gravitylike forces in the Yukawa-type parametrization space. Constraints $A$ and $B$ were obtained by measuring neutron-atom scattering [10, 11], while constraints $C$ to $I$ were obtained using macroscopic methods [12, 13, 14, 15, 16, 17, 18]. Theoretical expectations from an extra $U(1)$ gauge boson at different symmetry breaking scales ${\mathrm{\Lambda }}_{U(1)}$ ($\sim 246\mathrm{GeV}$ and 10 TeV) [1, 2] and from a baryon number gauge field in the bulk of extra space dimensions [3, 4] are shown as dashed lines and the hatched area, respectively.

Figure 2

A schematic view of the experimental setup (not to scale). Neutrons of wavelength 5 Å and a 12% spread were chosen by a velocity selector. Two collimators of diameter 22 mm produced a neutron beam with a 3 mrad divergence, which impinged on a xenon-filled target chamber of length 250 mm. Scattered neutrons were measured by a MWPC with pixel size $5.1\times 5.1{\mathrm{mm}}^2$ located 3.11 m downstream of the gas target. The xenon gas was purified to better than 10 ppm by a getter system using a carefully controlled flow rate.

Figure 3

(a) Simulated corrected differential cross sections for the constant term $h_c(\theta )$, the electromagnetic interaction term $h_{\text{em}}(\theta )$, and the new interaction term $h_{\text{new}}(\theta ;\mathrm{ƛ}=1\mathrm{nm})$. They are normalized to ${\int }_{S}h(\theta )d\theta =1$ over the signal acceptance $S$ of 16.1 mrad $<\theta <160.8\mathrm{mrad}$. Within this signal region, the distribution due to the new interaction term for $\mathrm{ƛ}\sim 1\mathrm{nm}$ is clearly different from the known interaction terms. (b) Measured distributions for the xenon-filled [$g_{\text{sam}}(\theta )$] and empty [$g_{\text{emp}}(\theta )$] chamber. The contribution from beam background $g_{\text{bg}}(\theta )$, not shown in the figure, has a flat distribution, with around $3\mathrm{counts}/\mathrm{bin}$. (c) Residuals from the reference distribution due to known interactions. The data, shown as crosses, are consistent with the case of no new forces (${\chi }^2$ par degree of freedom is 1.4).

Figure 4

(a) Evolution of the best fit values ${\widehat{g}}^2$ as a function of the fraction of collected events $\kappa$ for $\mathrm{ƛ}=1\mathrm{nm}$. The full data set corresponds to $\kappa =1$. (b) Evolution of the estimated ${\widehat{g}}^2$ uncertainty ${\sigma }_{{\widehat{g}}^2}(\kappa )$. It is well described by the simple model ${\sigma }_{{\widehat{g}}^2}(\kappa )=(t/\sqrt{\kappa })\oplus u$, with $t=7.6\times 10^{-17}{\mathrm{GeV}}^{-2}$ and $u=4.8\times 10^{-17}{\mathrm{GeV}}^{-2}$, shown as the dashed curve.

Figure 5

Comparison of the 95% C.L. limits presented in this Letter with those given in Refs. [10, 11, 12]. The results improve the previous constraints by a factor of up to 10 for interaction ranges between 4 and 0.04 nm. The dashed line shows the theoretical prediction due to extra $U(1)$ gauge bosons with symmetry braking scales of ${\mathrm{\Lambda }}_{U(1)}\sim 246\mathrm{GeV}$ and $\sim 1\mathrm{TeV}$ [1, 2].