Experimental Limits on Exotic Spin and Velocity Dependent Interactions Using Rotationally Modulated Source Masses and an Atomic-Magnetometer Array

Various theories beyond the standard model predict new interactions mediated by new light particles with very weak couplings to ordinary matter. Interactions between polarized electrons and unpolarized nucleons proportional to $g_V^N{g}_A^e\overrightarrow{\sigma }·\overrightarrow{v}$ and $g_A^N{g}_A^e\overrightarrow{\sigma }·\overrightarrow{v}\times \overrightarrow{r}$ are two such examples, where $\overrightarrow{\sigma }$ is the spin of the electrons, $\overrightarrow{r}$ and $\overrightarrow{v}$ are position and relative velocity between the polarized electrons and nucleons, $g_V^N/g_A^N$ is the vector or axial-vector coupling constant of the nucleon, and $g_A^e$ is the axial-vector coupling constant of the electron. Such interactions involving a vector or axial-vector coupling $g_V^N/g_A^N$ at one vertex and an axial-vector coupling $g_A^e$ at the polarized electron vertex can be induced by the exchange of spin-1 bosons. We report new experimental upper limits on such exotic spin-velocity-dependent interactions of the electron with nucleons from dedicated experiments based on a recently proposed scheme. We rotationally modulated two $\sim 6\mathrm{Kg}$ source masses at a frequency of 20 Hz. We used four identical atomic magnetometers in an array form to increase the statistics and cancel the common-mode noise. We applied a data processing method based on high precision numerical integration for the four harmonic frequencies of the signal. We reverse the rotation direction of the source masses to flip the signal due to the new interactions; thus, we can apply the $[+1,-3,+3,-1]$ weighting method to remove possible slow drifting. Our constraint on the product of vector and axial-vector couplings is $|g_V^N{g}_A^e|<2.1\times {10}^{-34}$ and on the product of axial-vector and axial-vector couplings is $|g_A^N{g}_A^e|<2.4\times {10}^{-22}$ for an interaction range of 10 m. The new constraints on vector-axial-vector interaction improved by as much as more than 4 orders of magnitude and on axial-axial interaction by as much as 2 orders of magnitude in the corresponding interaction range, respectively.

Figure 1

Schematic of the experimental setup. (a),(b) The top and end views of the setup, respectively. The servo motor rotates the two BGO cylinders as source masses which have a modulating frequency of 20 Hz, inducing pseudomagnetic field signals to the surrounding AMs if exotic spin- and velocity-dependent interactions exist. The AMs are magnetically shielded and placed on a platform sitting on pneumatic vibration isolators. A 1 cm thick aluminum plate shielding is applied to prevent possible air vibration caused by the rotating source masses. The encoder monitors the rotating angle and frequency in real time.

Figure 2

Noise-power-density measurement examples of the VA searching setup. $B_i$ is the magnetic field sensed by sensor ${\mathrm{AM}}_i$. $B_{\exp }=(-B_1-B_2+B_3+B_4)/4$ is plotted for the VA setup. The bottom plot is the Fourier transformation of the simulated signal $B_{\mathrm{VA}}^{\prime }$.

Figure 3

Constraints on the coupling constants $|g_V^N{g}_A^e|$ ($1\sigma$) as a function of interaction range $\lambda$ and new boson mass. The dashed line is from Ref. [26]. The solid line (dark area) is the present work.

Figure 4

Constraints on the coupling constants $|g_A^N{g}_A^e|$ ($1\sigma$) as a function of interaction range $\lambda$ and new boson mass. The dashed line is from Ref. [25]. The solid line (dark area) is the present work.