# Sub-MeV Dark Matter and the Goldstone Modes of Superfluid Helium

## TL;DR

This paper applies an effective field theory approach to superfluid helium-4 to analyze sub-MeV dark matter interactions, revealing suppressed phonon emission rates and potential experimental signatures for dark matter detection.

## Contribution

It introduces a relativistic effective field theory framework for superfluid helium-4 to compute dark matter scattering rates, highlighting the suppression of two-phonon emission at low energies and the importance of phonons.

## Key findings

- Two-phonon emission rates are strongly suppressed for sub-MeV dark matter.
- The dominant contribution to emission comes from phonons.
- Angular distributions can help determine dark matter mass.

## Abstract

We show how the relativistic effective field theory for the superfluid phase of helium-4 can replace the standard methods used to compute the production rates of low momentum excitations due to the interaction with an external probe. This is done by studying the scattering problem of a light dark matter particle in the superfluid, and comparing to some existing results. We show that the rate of emission of two phonons, the Goldstone modes of the effective theory, gets strongly suppressed for sub-MeV dark matter particles due to a fine cancellation between two different tree-level diagrams in the limit of small exchanged momenta. This phenomenon is found to be a consequence of the particular choice of the potential felt by the dark matter particle in helium. The predicted rates can vary by orders of magnitude if this potential is changed. We prove that the dominant contribution to the total emission rate is provided by the phonons. Finally, we analyze the angular distributions for the emissions of one and two phonons, and discuss how they can be used to measure the mass of the hypothetical dark matter particle hitting the helium target.