Constraining short-range spin-dependent forces with polarized $^3$He

Abstract: We have searched for a short-range spin-dependent interaction using the spin relaxation of hyperpolarized $^3$He. Such a new interaction would be mediated by a hypothetical light scalar boson with \CP-violating couplings to the neutron. The walls of the $^3$He cell would generate a pseudomagnetic field and induce an extra depolarization channel. We did not see any anomalous spin relaxation and we report the limit for interaction ranges $\lambda$ between $1$ and $100~\rm{\mu m}$: $g_sg_p \lambda ^2 \leq 2.6\times 10^{-28}~\mathrm{m^2}\, ( 95~\%\, \mathrm{C.L.})$, where $g_s$($g_p$) are the (pseudo)scalar coupling constant, improving the previous best limit by 1 order of magnitude.