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Publication# Dark matter, dark photon and superfluid He-4 from effective field theory

Abstract

We consider a model of sub-GeV dark matter whose interaction with the Standard Model is mediated by a new vector boson (the dark photon) which couples kinetically to the photon. We describe the possibility of constraining such a model using a superfluid He-4 detector, by means of an effective theory for the description of the superfluid phonon. We find that such a detector could provide bounds that are competitive with other direct detection experiments only for ultralight vector mediator, in agreement with previous studies. As a byproduct we also present, for the first time, the low-energy effective field theory for the interaction between photons and phonons. (C) 2020 The Author(s). Published by Elsevier B.V.

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Effective field theory

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective

Dark matter

Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the elect

Standard Model

The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and cla

We study the response of a He-4 detector to the interaction of sub-GeV dark matter using an effective field theory for the superfluid. We compute the lifetime of the phonon, which agrees with what known from standard techniques, hence providing an important check of the effective field theory. We then study the process of emission of two phonons, and show how its rate is much more suppressed than the phase space expectations; this is a consequence of the conservation of the current associated to the superfluid symmetries. Talk presented at the TAUP 2019 conference.

We show how a relativistic effective field theory for the superfluid phase of 4 He 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 excitations in the phonon branch. 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.

We employ an effective field theory to study the detectability of sub-GeV dark matter through its interaction with the gapless excitations of superfluid 4He. 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.