Sub-GeV dark matter in superfluid He-4: an effective theory approach

We employ an effective field theory to study the detectability of sub-GeV dark matter through its interaction with the gapless excitations of superfluid ${}^4$He. In a quantum field theory language, the possible interactions between the dark matter and the superfluid phonon are solely dictated by symmetry. We compute the rate for the emission of one and two phonons, and show that these two observables combined allow for a large exclusion region for the dark matter masses. Our approach allows a direct calculation of the differential distributions, even though it is limited only to the region of softer phonon excitations, where the effective field theory is well defined. The method presented here is easily extendible to different models of dark matter.