<p>At sufficiently low nuclear recoil energy, the scattering of dark matter (DM) in crystals gives rise to single phonon and multiphonon excitations. In anisotropic crystals, the scattering rate into phonons modulates over each sidereal day as the crystal rotates with respect to the DM wind. This gives a potential avenue for directional detection of DM. The daily modulation for single phonons has previously been calculated. Here we calculate the daily modulation for multiphonon excitations from DM in the mass range 1 MeV–1 GeV. We generalize previous multiphonon calculations, which made an isotropic approximation, and implement results in the DarkELF package. We find daily modulation rates up to 1%–10% for an <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Al</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>3</mn></msub></math> target and DM mass below 30 MeV, depending on the recoil energies probed. We obtain similar results for SiC, while modulation in Si, GaAs, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>SiO</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> is negligible.</p>

United States

Connor Stratman

Tongyan Lin

Daily modulation of low-energy nuclear recoils from sub-GeV dark matter

Direct detection experiments are looking for nuclear recoils from scattering of sub-GeV dark matter (DM) in crystals, and have thresholds as low as <math><mrow><mo>∼</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></mrow></math> or DM masses of <math><mo>∼</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. Future experiments are aiming for even lower thresholds. At such low energies, the free nuclear recoil prescription breaks down, and the relevant final states are phonons in the crystal. Scattering rates into single as well as multiple phonons have already been computed for a harmonic crystal. However, crystals typically exhibit some anharmonicity, which can significantly impact scattering rates in certain kinematic regimes. In this work, we estimate the impact of anharmonic effects on scattering rates for DM in the mass range <math><mo>∼</mo><mn>1</mn><mi>–</mi><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, where the details of multiphonon production are most important. Using a simple model of a nucleus in a bound potential, we find that anharmonicity can modify the scattering rates by up to two orders of magnitude for DM masses of <math><mi>O</mi><mo>(</mo><mi>MeV</mi><mo>)</mo></math>. However, such effects are primarily present at high energies where the rates are suppressed, and thus only relevant for very large DM cross sections. We show that anharmonic effects are negligible for masses larger than <math><mo>∼</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>.

Taiwan

Chia-Hsien Shen

Mukul Sholapurkar

Ethan Villarama

Anharmonic effects in nuclear recoils from sub-GeV dark matter

Dark matter (DM) could be a nonthermal relic that freezes in from extremely weak, sub-Hubble annihilation and decay of Standard Model (SM) particles. The case of Dirac DM freezing in via a dark photon mediator is a well-studied benchmark for DM direct detection experiments. Here, we extend prior work to take into account the possibility that DM is pseudo-Dirac with a small mass splitting. If the mass splitting is greater than twice the electron mass but less than the dark photon mass, there will be distinct cosmological signatures. The excited state <math><msub><mi>χ</mi><mn>2</mn></msub></math> is initially produced in equal abundance to the ground state <math><msub><mi>χ</mi><mn>1</mn></msub></math>. Due to the small couplings needed to explain the observed relic abundance, the excited state population can decay at late cosmological times, primarily via the three-body process <math><msub><mi>χ</mi><mn>2</mn></msub><mo>→</mo><msub><mi>χ</mi><mn>1</mn></msub><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math>. This injects energetic electrons into the ambient environment, providing observable signatures involving big bang nucleosynthesis, cosmic microwave background spectral distortions and anisotropies, and the Lyman-<math><mi>α</mi></math> forest. Furthermore, the ground state particles that are populated from the three-body decay receive a velocity kick, with implications for DM clustering on small scales. Inelastic freeze-in thus gives a motivated decaying DM candidate, where the long lifetimes are connected to the relic abundance mechanism.

Canada

Saniya Heeba

Katelin Schutz

Inelastic freeze-in

In most direct detection experiments, the free nuclear recoil description of dark matter scattering breaks down for masses <math><mo>≲</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, or when the recoil energy is comparable to a few times the typical phonon energy For dark matter lighter than 1 MeV, scattering via excitation of a single phonon dominates and has been computed previously, but for the intermediate mass range or higher detector thresholds, multiphonon processes dominate. We perform the first calculation of the scattering rate via multiphonon production for the entire keV-GeV dark matter mass range, assuming a harmonic crystal target. We provide an analytic description that connects the single phonon, multiphonon, and the nuclear recoil regimes. Our results are implemented in the public package darkelf.

Brian Campbell-Deem

CERN

Simon Knapen

Dark matter direct detection from the single phonon to the nuclear recoil regime

We present DarkELF, a python package to calculate interaction rates of light dark matter in dielectric materials, including screening effects. The full response of the material is parametrized in the terms of the energy loss function (ELF) of material, which DarkELF converts into differential scattering rates for both direct dark matter electron scattering and through the Migdal effect. In addition, DarkELF can calculate the rate to produce phonons from sub-MeV dark matter scattering via the dark photon mediator, as well as the absorption rate for dark matter comprised of dark photons. The package includes precomputed ELFs for Al, <math><mrow><msub><mrow><mi>Al</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math>, GaAs, GaN, Ge, Si, <math><msub><mi>SiO</mi><mn>2</mn></msub></math>, and ZnS, and allows the user to easily add their own ELF extractions for arbitrary materials.

Jonathan Kozaczuk

python Package for Dark Matter Scattering in Dielectric Targets

When a nucleus in an atom undergoes a collision, there is a small probability of an electron being excited inelastically as a result of the Migdal effect. In this Letter, we present the first complete derivation of the Migdal effect from dark matter-nucleus scattering in semiconductors, which also accounts for multiphonon production. The rate of the Migdal effect can be expressed in terms of the energy loss function of the material, which we calculate with density functional theory methods. Because of the smaller gap for electron excitations, we find that the rate for the Migdal effect is much higher in semiconductors than in atomic targets. Accounting for the Migdal effect in semiconductors can therefore significantly improve the sensitivity of experiments such as DAMIC, SENSEI, and SuperCDMS to sub-GeV dark matter.

Migdal Effect in Semiconductors

A number of direct detection experiments are searching for electron excitations created by the scattering of sub-GeV dark matter. We present an alternate formulation of dark matter-electron scattering in terms of the dielectric response of a material. For dark matter which couples to electrons, this approach automatically accounts for in-medium screening effects, which were not included in previous rate calculations for semiconductor targets. We show that the screening effects appear for both scalar and vector mediators. The result is a non-negligible reduction of reach for direct detection experiments which use dielectric materials as targets. We also explore different determinations of the dielectric response, including first-principles density functional theory (DFT) calculations and a data-driven analytic approximation using a Mermin oscillator model.

Dark matter-electron scattering in dielectrics

We propose the use of silicon carbide (SiC) for direct detection of sub-GeV dark matter. SiC has properties similar to both silicon and diamond but has two key advantages: (i) it is a polar semiconductor which allows sensitivity to a broader range of dark matter candidates; and (ii) it exists in many stable polymorphs with varying physical properties and hence has tunable sensitivity to various dark matter models. We show that SiC is an excellent target to search for electron, nuclear and phonon excitations from scattering of dark matter down to 10 keV in mass, as well as for absorption processes of dark matter down to 10 meV in mass. Combined with its widespread use as an alternative to silicon in other detector technologies and its availability compared to diamond, our results demonstrate that SiC holds much promise as a novel dark matter detector.

Sinéad M. Griffin

Israel

Yonit Hochberg

Katherine Inzani

Noah Kurinsky

To Chin Yu

Silicon carbide detectors for sub-GeV dark matter

We present a first calculation of the rate for plasmon production in semiconductors from nuclei recoiling against dark matter. The process is analogous to bremsstrahlung of transverse photon modes, but with a longitudinal plasmon mode emitted instead. For dark matter in the 10 MeV—1 GeV mass range, we find that the plasmon bremsstrahlung rate is 4–5 orders of magnitude smaller than that for elastic scattering, but 4–5 orders of magnitude larger than the transverse bremsstrahlung rate. Because the plasmon can decay into electronic excitations and has characteristic energy given by the plasma frequency <math><msub><mi>ω</mi><mi>p</mi></msub></math>, with <math><msub><mi>ω</mi><mi>p</mi></msub><mo>≈</mo><mn>16</mn><mtext> </mtext><mtext> </mtext><mi>eV</mi></math> in Si crystals, plasmon production provides a new signature and method to detect nuclear recoils from sub-GeV dark matter.

Plasmon production from dark matter scattering

For direct detection of sub-MeV dark matter, a promising strategy is to search for individual phonon excitations in a crystal. We perform an analytic calculation of the rate for light dark matter (<math><mrow><mi>keV</mi><mo>&lt;</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>DM</mi></mrow></msub><mo>&lt;</mo><mi>MeV</mi></mrow></math>) to produce two acoustic phonons through scattering in cubic crystals such as GaAs, Ge, Si, and diamond. The multiphonon rate is always smaller than the rate to produce a single optical phonon, whenever the latter is kinematically accessible. In Si and diamond, there is a dark matter mass range for which multiphonon production can be the most promising process, depending on the experimental threshold.