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.
Highlights
The presence of dark matter is one of the most compelling evidences for physics beyond the Standard Model, but the question about its nature remains unanswered
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
From the comparison with that obtained with time-honored standard techniques, especially in the low dark matter mass region, we show that the effective field theory (EFT) description of the phonon dynamics is impressively successful
Summary
The presence of dark matter is one of the most compelling evidences for physics beyond the Standard Model, but the question about its nature remains unanswered. We confirm the results of our previous analysis [25] and study the case of dark matter particles with masses as low as a few keV. [19,20], but from the EFT we are able to understand that the predicted suppression is due to a precise cancellation between two tree-level diagrams [25], which occurs in the limit of small momentum transfers This turns out to be the consequence of integrating out highly off-shell phonons. We observe that this mechanism does not take place if the interaction between the dark matter and the bulk of 4He happens via a coupling different from the simple number density. Conventions.—Throughout this paper, we set ħ 1⁄4 c 1⁄4 1 and work with a metric signature ημν 1⁄4 diagð−1; 1; 1; 1Þ
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