Dark Matter Detection With Bound Nuclear Targets: The Poisson Phonon Tail

Yonatan Kahn; Gordan Krnjaic; Bashi Mandava

doi:10.1103/PhysRevLett.127.081804

paper

Dark Matter Detection With Bound Nuclear Targets: The Poisson Phonon Tail

arXiv:2011.09477 · doi:10.1103/PhysRevLett.127.081804

Abstract

Dark matter (DM) scattering with nuclei in solid-state systems may produce elastic nuclear recoil at high energies and single-phonon excitation at low energies. When the dark matter momentum is comparable to the momentum spread of nuclei bound in a lattice, $q_{0} = 2 m_{N} ω_{0}$ where $m_{N}$ is the mass of the nucleus and $ω_{0}$ is the optical phonon energy, an intermediate scattering regime characterized by multi-phonon excitations emerges. We study a greatly simplified model of a single nucleus in a harmonic potential and show that, while the mean energy deposited for a given momentum transfer $q$ is equal to the elastic value $q^{2} / (2 m_{N})$ , the phonon occupation number follows a Poisson distribution and thus the energy spread is $Δ E = q ω_{0} / (2 m_{N})$ . This observation suggests that low-threshold calorimetric detectors may have significantly increased sensitivity to sub-GeV DM compared to the expectation from elastic scattering, even when the energy threshold is above the single-phonon energy, by exploiting the tail of the Poisson distribution for phonons above the elastic energy. We use a simple model of electronic excitations to argue that this multi-phonon signal will also accompany ionization signals induced from DM-electron scattering or the Migdal effect. In well-motivated models where DM couples to a heavy, kinetically-mixed dark photon, we show that these signals can probe experimental milestones for cosmological DM production via thermal freeze-out, including the thermal target for Majorana fermion DM.

arXiv comment6 pages, 3 figures, plus supplementary material

Dark Matter Detection With Bound Nuclear Targets: The Poisson Phonon Tail

Abstract

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