Searching for low mass dark matter via phonon creation in superfluid He 4

We consider the scattering of dark matter particles from superfluid liquid He4, 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. We show further that the anomalous dispersion of phonons in liquid He4 at low pressures [i.e., d2ω(q)/dq2>0, where q and ω(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.