Effective field theory for dark matter absorption on single phonons

Open Access

Effective field theory for dark matter absorption on single phonons

Andrea Mitridate, Kris Pardo, Tanner Trickle, and Kathryn M. Zurek

Phys. Rev. D 109, 015010 – Published 10 January 2024

Abstract

Single phonon excitations, with energies in the 1–100 meV range, are a powerful probe of light dark matter (DM). Utilizing effective field theory, we derive a framework to compute DM absorption rates into single phonons starting from general DM-electron, proton, and neutron interactions. We apply the framework to a variety of DM models: Yukawa coupled scalars, axionlike particles with derivative interactions, and vector DM coupling via gauge interactions or Standard Model electric and magnetic dipole moments. We find that GaAs or ${Al}_{2} O_{3}$ targets can set powerful constraints on a $U (1)_{B - L}$ model, and targets with electronic spin ordering are similarly sensitive to DM coupling to the electron magnetic dipole moment. Lastly, we make the code, phonodark-abs (an extension of the existing phonodark code which computes general DM–single phonon scattering rates), publicly available.

Received 5 October 2023
Accepted 10 December 2023

DOI:https://doi.org/10.1103/PhysRevD.109.015010

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Effective field theory Hypothetical particle physics models Particle dark matter Particle phenomena Quasiparticles & collective excitations

First-principles calculations

Particles & Fields

Authors & Affiliations

Andrea Mitridate ^1,*, Kris Pardo ^2,3,†, Tanner Trickle ^4,‡, and Kathryn M. Zurek ^2,§

¹Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany
²Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
³Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
⁴Theoretical Physics Division, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

^*andrea.mitridate@desy.de
^†kmpardo@usc.edu
^‡ttrickle@fnal.gov
^§kzurek@caltech.edu

Article Text

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Issue

Vol. 109, Iss. 1 — 1 January 2024

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Images

Figure 1
Comparison of the imaginary part of the dielectric function, $Im [ϵ (ω)]$ (top row), and energy loss function, $Im [- 1 / ϵ (ω)]$ (bottom row), from first principles calculation using Eq. (38) (solid lines) and measurements from Ref. [89] (dotted lines) for GaAs, ${Al}_{2} O_{3}$ (sapphire), and ${SiO}_{2}$ (quartz). Solid lines correspond to $γ_{ν} = 10^{- 2} ω_{ν}$ , and the boundaries of the shaded regions assume $γ_{ν} = 10^{- 1} ω_{ν}$ and $γ_{ν} = 10^{- 3} ω_{ν}$ .
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Figure 2
Projected 95% C.L. constraints (3 events) on $d_{e} = g_{e} Λ / m_{e}$ [Eq. (39), $Λ = M_{Pl} / \sqrt{4 π}$ ], utilizing single phonon excitations in GaAs (solid red), ${Al}_{2} O_{3}$ (solid blue), and ${SiO}_{2}$ (solid green) targets, assuming a $kg \cdot yr$ exposure and no backgrounds. Dashed lines correspond to projected constraints from absorption on electrons in small band-gap targets, i.e., Al superconductors (“Al-SC”, purple) [52, 57], and spin-orbit coupled targets ${ZrTe}_{5}$ (turquoise) [67]. Shaded regions correspond to constraints from fifth force experiments (teal) [125, 126] and stellar cooling bounds from red giants (“RG”, pink) [92] and white dwarfs (“WD”, orange) [124].
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Figure 3
Projected 95% C.L. constraints (three events) on the ALP couplings $g_{a e e}, g_{a n n}, g_{a p p}$ , Eq. (45), shown in the left, middle, and right panels, respectively, utilizing single phonon excitations in a variety of targets assuming a $kg \cdot yr$ exposure and no backgrounds. ${FeBr}_{2}$ (solid orange) is a ferromagnetic target with polarized electronic spins on the Fe site. In each panel, the dotted curves labeled ${GaAs}^{*}$ (blue) and ${Al}_{2} O_{3}^{*}$ (red) correspond to a GaAs and ${Al}_{2} O_{3}$ target whose total fermionic spin at each lattice site has been set to $S_{j, e} = [0, 0, 0.5], S_{j, p / n} = N_{j, p / n} [0, 0, 0.5]$ , where ${e, p, n}$ correspond to the left, middle, and right panels, respectively. Since these are not real targets, their purpose is to give an estimate of a target that does have nonzero spin ordering. As in Fig. 2, dashed lines correspond to projected constraints from absorption on electrons in small band-gap targets, i.e., Al superconductors (“Al-SC”, purple) [52, 57] and spin-orbit coupled targets ${ZrTe}_{5}$ (turquoise) [67]. In the left panel, the shaded gray region corresponds to constraints from solar axion searches with the XENONnT experiment [41], and the shaded light blue region corresponds to white dwarf (“WD”) cooling constraints [124]. The red line corresponds to constraints from red giant (“RG”) cooling [157, 158], which have come under recent scrutiny [162]. In the middle and right panels, the shaded teal region corresponds to neutron star (“NS”) cooling [159]. Tan lines correspond to the prototypical KSVZ and DFSZ QCD axion models [160], assuming $0.28 \leq \tan β \leq 140$ in the DFSZ model.
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Figure 4
Projected 95% C.L. constraints (three events) on $κ = - g_{e} / e = g_{p} / e$ (left panel) and $g_{B - L}$ , Eq. (50), in GaAs (solid red), ${Al}_{2} O_{3}$ (solid blue), and ${SiO}_{2}$ (solid green) targets utilizing single phonon excitations assuming a $kg \cdot yr$ exposure and no backgrounds. Projected constraints on the kinetically mixed dark photon model have also been shown in Ref. [89]; the purpose of the comparison here is to illustrate the good agreement between the first principles calculation performed here and the data-driven approach (dotted lines) utilizing the ELF [89], also compared in Fig. 1. Dashed lines are projected constraints from targets utilizing electronic absorption: doped Si (orange) [61], Al superconductors (“Al-SC”, purple) [52, 57], and the spin-orbit coupled target ${ZrTe}_{5}$ (turquoise) [67]. Fifth force constraints are from Ref. [163].
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Figure 5
Projected 95% C.L. constraints (three events) utilizing single phonon excitations on the MDM coupling to electrons, $d_{M}$ , and the EDM coupling to electrons, $d_{E}$ , in the left and right panels, respectively, assuming a $kg \cdot yr$ exposure and no backgrounds. Constraints from GaAs (solid red), ${Al}_{2} O_{3}$ (solid blue), and ${SiO}_{2}$ (solid green) targets are weak due to the response in a non-spin-ordered target coming at higher order. Similarly as in Fig. 3, we also consider a target with ferromagnetic ordering, ${FeBr}_{2}$ (solid orange), and use ${GaAs}^{*}$ (dotted red) and ${Al}_{2} O_{3}^{*}$ (dotted blue) as an example for other targets with ferromagnetic ordering. Projected constraints from small band-gap electronic absorption in Al superconductors (“Al-SC”, purple) [52, 57] and spin-orbit coupled target, ${ZrTe}_{5}$ , [67], shown as dashed lines, have been rescaled according to Ref. [90]. The shaded red region (“Therm.”) is excluded cosmologically; couplings in this region would overproduce DM via freeze-in, even at a reheat temperature of $\sim MeV$ [90, 165].
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