New Bounds on Exotic Long-Range Spin-Spin Interactions

Many proposed extensions to the Standard Model of particle physics introduce new bosons that can mediate forces which couple to particle spin. Here we describe a search for such forces coupling spin-polarized neutrons and protons in our magnetometer to spin-polarized electrons within Earth. We measure these interactions by varying the orientation of an optical $^{199}$Hg-$^{133}$Cs free-precession comagnetometer mounted upon a precision rotation platform. From these measurements, we establish upper bounds on the dimensionless coupling constants associated with the axial-axial potential $V_2$ and the axial-vector potential $V_{11}$ as a function of the force's range $\lambda$. For the electron-neutron and electron-proton potential $V_2$ at infinite range, we find $|g_A^eg_A^n| \leq 3.0 \times 10^{-48}$ and $|g_A^eg_A^p| \leq 3.0 \times 10^{-47}$. For $V_{11}$, we find our most stringent bounds to be $|g_A^eg_V^n| \leq 2.2 \times 10^{-25}$ and $|g_A^eg_V^p| \leq 2.2 \times 10^{-24}$ at $\lambda \approx 10^3$ km. Our results represent an improvement over previous results by up to a factor of 17 and set the most stringent bounds on long-range axial-axial and axial-vector couplings between electron spins and neutron and proton spins.