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Constraints on Possible Monopole-Dipole Interactions of WISPs from the Transverse Relaxation Time of Polarized $^3$He Gas

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A $P$-odd, $T$-odd, spin-dependent interaction between polarized and unpolarized matter is one such possibility. Such a monopole-dipole interaction can be induced by the exchange of spin-$0$ particles. The presence of a possible monopole-dipole interaction between fermion spins and unpolarized matter would cause an decreased transverse spin relaxation time $T_{2}$ for a confined gas of polarized nuclei. By reanalyzing previously existing data on the spin relaxation times of polarized $^3$He in gas cells with pressure in the millibar range and applying the well-established theory of spin relaxation for magnetic field gradients to gradients in a possible monopole-dipole field, we present new laboratory constraints on the strength and range of such an interaction. These constraints represent to our knowledge the best limits on such interactions for the neutron with ranges between $0.01$ cm and 1 cm.