Parametrics of electromagnetic searches for axion dark matter

Open Access

Parametrics of electromagnetic searches for axion dark matter

Robert Lasenby

Phys. Rev. D 103, 075007 – Published 9 April 2021

Abstract

Light axionlike particles occur in many theories of beyond-Standard-Model physics, and may make up some or all of the Universe’s dark matter. One of the ways they can couple to the Standard Model is through the electromagnetic $F_{μ ν} {\tilde{F}}^{μ ν}$ portal, and there is a broad experimental program, covering many decades in mass range, aiming to search for axion dark matter via this coupling. In this paper, we derive limits on the absorbed power, and coupling sensitivity, for a broad class of such searches. We find that standard techniques, such as resonant cavities and dielectric haloscopes, can achieve $O (1)$ -optimal axion-mass-averaged signal powers, for given volume and magnetic field. For low-mass (frequency $≪ GHz$ ) axions, experiments using static background magnetic fields generally have suppressed sensitivity; we discuss the physics of this limitation, and propose experimental methods to avoid it, such as microwave up-conversion experiments. We also comment on the detection of other forms of dark matter, including dark photons, as well as the detection of relativistic hidden-sector particles.

Received 4 December 2020
Accepted 8 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.075007

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)

Axions Dark matter

Dark matter detectors

Particles & FieldsGravitation, Cosmology & Astrophysics

Authors & Affiliations

Robert Lasenby ^*

Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA

^*rlasenby@stanford.edu

Article Text

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Issue

Vol. 103, Iss. 7 — 1 April 2021

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Images

Figure 1
Theoretical sensitivity limits for experiments searching for axion DM through its coupling to photons, $L \supset g_{a γ γ} a E \cdot B$ . We assume that axion DM has a virialized velocity distribution with $δ v \sim 10^{- 3}$ , and density at Earth of $ρ_{a} ≃ 0.3 GeV {cm}^{- 3}$ . The red and dark green lines correspond to experiments using a static 4 T background magnetic field, with an experimental volume of $1 m^{3}$ , and an integration time of one year per $e$ -fold in axion mass. The blue lines correspond to up-conversion experiments, with a target frequency of 1 GHz, and taking a rms background magnetic field strength of 0.2 T in a volume of $1 m^{3}$ (with the same integration time assumptions). The $Q = 10^{6}$ SQL line (solid red) assumes a physical temperature of 10 mK, a quality factor of $10^{6}$ , and SQL-limited op-amp readout (we choose an expected SNR value of 3 as our sensitivity threshold, in this and other cases). The solid red line assumes that the experiment operates in the quasistatic regime, with a consequent suppression in sensitivity (see Sec. 4c), while the dot-dashed line shows the full sum-rule-limited sensitivity (e.g., from using an appropriate matching circuit). The thin red line at the bottom of the red shaded region corresponds to the PQL-limited sensitivity (assuming quasistatic suppression); for higher quality factors, SQL-limited readout can approach this. The $Q = 10^{6}$ QL line (solid green) takes the same assumptions as the SQL line, but with quantum-limited readout (see Sec. 3d), while the green dot-dashed line shows this without the quasistatic suppression. The $Q = 10^{11}$ SRF line (solid blue) corresponds to the isolated-linear-amplifier sensitivity for an up-conversion experiment with physical temperature 1.5 K, and mode quality factor $10^{11}$ [14]. The thin blue line at the bottom of the blue shaded region shows the PQL-limited sensitivity for these parameters—again, for higher quality factors, isolated amplifier readout can approach this [14]. The green diagonal band corresponds to the “natural” range of $g_{a γ γ}$ values at each QCD axion mass; if we write $g_{a γ γ} = \frac{α_{EM}}{2 π f_{a}} (\frac{E}{N} - 1.92)$ [4], then the upper edge of the band is at $E / N = 5$ [10], and the lower edge at $E / N = 2$ [4]. The gray diagonal lines indicate the Kim-Shifman-Vainshtein-Zakharov (upper, $E / N = 0$ ) and Dine-Fischler-Srednicki-Zhitnitsky (lower, $E / N = 8 / 3$ ) models. The gray shaded region corresponds to the parameter space excluded by ADMX [16, 17].
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Figure 2
Sensitivity projections for some existing and proposed dark photon DM detection experiments (solid lines), along with PQL sensitivity limits for the corresponding target volumes and integration times (dashed lines). See Sec. 5 for descriptions of the different projections. We assume that the dark photon DM has density at Earth of $ρ ≃ 0.3 GeV {cm}^{- 3}$ . The gray “stellar constraints” region corresponds to the bounds on energy loss from the Sun and from horizontal branch stars [71, 72, 73].
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Figure 3
Sensitivity of dark photon absorption experiments to the flux of longitudinal dark photons from the Sun. At $m ≪ 300 eV$ , this flux is dominated by longitudinal emission [110], so we only consider absorption of longitudinal dark photons. The “Xenon10” line shows the limits from dark photon absorption in the Xenon10 experiment [73]. The solid red line shows the sensitivity for a sapphire target, with $1 kg − yr$ exposure (as in Fig. 2). The dashed red line shows the constraints from an optimal incoherent absorber with the same volume [ $\sim (6 cm)^{3}$ ], illustrating that sapphire is an almost optimal absorber, and in particular, much more efficient than liquid xenon [Xenon10 uses an $\sim (17 cm)^{3}$ volume]. The dot-dashed line shows the maximum theoretical absorption rate for a cube of the same volume, taking advantage of coherent enhancement. As discussed in Sec. 6a, realizing this enhancement in a practical experiment would likely be very difficult. The gray regions correspond to existing constraints on dark photons from other observations [71, 72, 73, 98, 111, 112, 113, 114].
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