Dark Matter Detection with Bound Nuclear Targets: The Poisson Phonon Tail
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 DM momentum is comparable to the momentum spread of nuclei bound in a lattice, $$q_0 = \sqrt{2m_Nω_0}$$ where $$m_N$$ is the mass of the nucleus and $$ω_0$$ is the optical phonon energy, an intermediate scattering regime characterized by multiphonon 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 $$\textit{q}$$ is equal to the elastic value $$q^2 / (2m_N)$$, the phonon occupation number follows a Poisson distribution and thus the energy spread is Δ$$E = q\sqrt{ω_0/(2m_N)}$$. 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 multiphonon 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.
- Research Organization:
- Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- SC0015655; AC02-07CH11359
- OSTI ID:
- 1814529
- Alternate ID(s):
- OSTI ID: 1765959; OSTI ID: 2338315
- Report Number(s):
- FERMILAB-PUB-20-588-T; arXiv:2011.09477; PRLTAO; 081804
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Vol. 127 Journal Issue: 8; ISSN 0031-9007
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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