A New Limit on Possible Long-Range Parity-odd Interactions of the Neutron from Neutron Spin Rotation in Liquid $^{4}He$

Abstract: Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A parity-odd interaction between polarized nucleons and unpolarized matter proportional to $g_{V}g_{A}{\vec{s}} \cdot {\vec{p}}$ is one such possibility, where ${\vec{s}}$ and ${\vec{p}}$ are the spin and the momentum of the polarized nucleon, and $g_{V}$ and $g_{A}$ are the vector and axial vector couplings of an interaction induced by the exchange of a new light vector boson. We report a new experimental upper bound on such possible long-range parity-odd interactions of the neutron with nucleons and electrons from a recent search for parity violation in neutron spin rotation in liquid $^{4}He$. Our constraint on the product of vector and axial vector couplings of a possible new light vector boson is $g_{V}g_{A}^{n} \leq 10^{-32}$ for an interaction range of 1m. This upper bound is more than seven orders of magnitude more stringent than the existing laboratory constraints for interaction ranges below 1m, corresponding to a broad range of vector boson masses above $10^{-6}$ eV. More sensitive searches for a $g_{V}g_{A}^{n}$ coupling could be performed using neutron spin rotation measurements in heavy nuclei or through analysis of experiments conducted to search for nucleon-nucleon weak interactions and nuclear anapole moments.