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arXiv · 2304.06750

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

Guillaume Rostagni·Jack D. Shergold
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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-$\frac 32$, 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 $\Delta E \gtrsim 10^{-28}\,\mathrm{eV}$, whilst a more intricate setup using a SQUID magnetometer is sensitive to shifts of $\Delta E \gtrsim 10^{-32}\,\mathrm{eV}$. 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.

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Guillaume Rostagni, Jack D. Shergold. 2023-04-13. The dark Stodolsky effect: constraining effective dark matter operators with spin-dependent interactions. https://doi.org/10.1088/1475-7516%2F2023%2F07%2F018

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