The dark Stodolsky effect: constraining effective dark matter operators with spin-dependent interactions

Abstract

Abstract We present a comprehensive discussion of the Stodolsky effect for dark matter (DM), and discuss two techniques to measure the effect and constrain the DM parameter space. The Stodolsky effect is the spin-dependent shift in the energy of a Standard Model (SM) fermion sitting in a bath of neutrinos. This effect, which scales linearly in the effective coupling, manifests as a small torque on the SM fermion spin and has historically been proposed as a method of detecting the cosmic neutrino background. We generalise this effect to DM, and give expressions for the induced energy shifts for DM candidates from spin-0 to spin-3/2, considering all effective operators up to mass dimension-6. In all cases, the effect scales inversely with the DM mass, but requires an asymmetric background. We show that a torsion balance experiment is sensitive to energy shifts of ΔE ≳ 10-28 eV, whilst a more intricate setup using a SQUID magnetometer is sensitive to shifts of ΔE ≳ 10-32 eV. Finally, we compute the energy shifts for a model of scalar DM, and demonstrate that the Stodolsky effect can be used to constrain regions of parameter space that are not presently excluded.