Abstract
We consider the scattering of dark matter particles from superfluid liquid $^4$He, which has been proposed as a target for their direct detection. Focusing on dark matter masses below ~1 MeV, we demonstrate from sum-rule arguments the importance of the production of single phonons with energies $\omega \lesssim 1$ meV. We show further that the anomalous dispersion of phonons in liquid $^4$He at low pressures [i.e., $d^2\omega(q)/dq^2>0$, where $q$ and $\omega(q)$ are the phonon momentum and energy] has the important consequence that a single phonon will decay over a relatively short distance into a shower of lower energy phonons centered on the direction of the original phonon. Thus the experimental challenge in this regime is to detect a shower of low energy phonons, not just a single phonon. Additional information from the distribution of phonons in such a shower could enhance the determination of the dark matter mass.
Highlights
The existence of dark matter has been conclusively established by multiple independent lines of gravitational evidence [1], its nature remains one of the outstanding mysteries in physics
We consider the scattering of dark matter particles from superfluid liquid 4He, which has been proposed as a target for their direct detection
Focusing on dark matter masses below ∼1 MeV, we demonstrate from sum-rule arguments the importance of the production of single phonons with energies ω ≲ 1 meV
Summary
The existence of dark matter has been conclusively established by multiple independent lines of gravitational evidence [1], its nature remains one of the outstanding mysteries in physics. Far fewer experiments have been proposed to detect dark matter in the challenging sub-MeV regime Such schemes generally involve systems with very low-energy gapped excitations—e.g., quasiparticles in superconductors [23], electrons in Dirac materials [24], and optical phonons in polar crystals [25]. Since the maximum phonon-roton energy (the maxon) is ∼1.1 meV, this cut effectively excludes single-phonon processes and requires multiphonon excitations They draw upon theoretical calculations of high-frequency density fluctuations [33] in estimating detection rates. Neighborhood of the Earth, and the excitations of superfluid 4He. We in Sec. III, review the kinematics of the interaction between dark matter particles and the helium, and we model their interaction in terms of a low-energy pseudopotential. Appendix A is devoted to a technical discussion of the relation of the helium structure function, Sðq; ωÞ, and the helium density-density correlation function, Appendix B discusses Sðq; ωÞ at nonzero temperature, and Appendix C discusses the q dependence of the rate of direct production of a pair of phonons
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