Phonon background from gamma rays in sub-GeV dark matter detectors

High-energy photons with $\mathcal{O}(\mathrm{MeV})$ energies from radioactive contaminants can scatter in a solid-state target material and constitute an important low-energy background for sub-GeV dark matter direct-detection searches. This background is most noticeable for energy deposits in the 1–100 meV range due to the partially coherent scattering enhancement in the forward scattering direction. We comprehensively quantify the resulting single- and multiphonon background in Si, Ge, GaAs, SiC, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ target materials, which are representative of target materials of interest in low-mass dark matter searches. We use a realistic representation of the high-energy photon background, and contrast the expected background phonon spectrum with the expected dark matter signal phonon spectrum. An active veto is needed to suppress this background sufficiently in order to allow for the detection of a dark matter signal, even in well-shielded environments. For comparison we also show the expected single- and multiphonon event rates from coherent neutrino-nucleus scattering due to solar neutrinos, and find that they are subdominant to the photon-induced phonon background.

Figure 1

Total photon-ion scattering cross section and its respective contributions for a Si ion, for a photon energy of $E_{\gamma }=1461\mathrm{keV}$. In the left panel, the black solid line shows the total cross section. The purple, yellow, green, and blue dashed lines indicate the photon-electron Rayleigh (R), the nuclear Thomson (N), the Delbrück (D) and the nuclear resonance (NR) contributions, respectively. In the right panel, we show the photon-electron Rayleigh scattering cross section, with the innermost (K-shell) electrons (purple dotted), with the tightly-bound (K- and L-shell) electrons (yellow dashed), and with all electrons (black solid). The yellow-dashed line corresponds to photon-Si-ion scattering, while the black line corresponds to photon-Si-atom scattering; we see that the cross sections agree for $q\gtrsim 10\mathrm{keV}$.

Figure 2

Expected phonon spectrum from high-energy background photon scattering in silicon, germanium, gallium arsenide, silicon carbide, and sapphire. We assume a high-energy photon background flux that creates a Compton-scatter background rate of $0.042\mathrm{events}/\mathrm{kg}/\mathrm{day}/\mathrm{keV}$ in germanium at $\mathcal{O}(10\mathrm{keV})$ energies (see Appendix pp2). The displayed rates include multiphonon contributions up to $n=6$. The bin width corresponds to 2 meV.

Figure 3

Expected phonon spectrum in GaAs from high-energy background photon scattering compared with the phonon spectrum generated by three different DM candidates (dashed) for DM masses of 1 MeV on the left, and 10 MeV on the right. We assume a high-energy photon background flux that creates a Compton-scatter background rate of $0.042\mathrm{events}/\mathrm{kg}/\mathrm{day}/\mathrm{keV}$ in germanium at $\mathcal{O}(10\mathrm{keV})$ energies (see Appendix pp2 for details). The bin width corresponds to 2 meV. The three models shown correspond to DM coupling to nucleons via a heavy (hm, purple) and light (lm, beige) scalar mediator with a cross section of ${\sigma }_n={10}^{-43}{\mathrm{cm}}^2$ [84], as well as a light dark photon mediator model ($\mathrm{ld}\gamma$, green) that couples to the atomic constituents proportionally to the Standard Model photon [81]. Shown for comparison in gray is the solar neutrino background from coherent neutrino-nucleus scattering (see Appendix pp4 for details).

Figure 4

The cumulative multiphonon contributions to the total rate up to $n\le 6$ for GaAs, Si, Ge, and SiC (see Eq. (a28) for details). Shown spectra correspond to background rates assuming a single photon energy $E_{\gamma }=1.461\mathrm{MeV}$ ($n_{\gamma }=4.7\times {10}^{-16}{\mathrm{cm}}^{-3}$). Only including single phonons (dashed, large spacing) captures the peak of the spectra well below the cutoff of the phonon density ${\omega }_{\max }$ for a given material which corresponds to 0.35 meV, 0.68 meV, 0.38 meV, and 0.12 meV for GaAs, Si, Ge, and SiC, respectively. However, multiphonons can give sizeable contributions off peaks even below ${\omega }_{\max }$. Above the cutoff the spectrum is dominated by higher order multiphonons where each multiphonon can contribute up to a maximum energy of $\omega =n{\omega }_{\max }$. Higher orders are suppressed by additional Debye-Waller factors which together with the atomic form factors being only sizeable at small $q$ ($\lesssim 100\mathrm{keV}$) leads to a convergent expansion.

Figure 5

Comparison of the phonon background spectrum in GaAs generated by the realistic combination of photon energies and densities given in Table 1 (pale blue line) versus with the spectrum generated by a single photon energy $E_{\gamma }=1.461\mathrm{MeV}$ with a photon density $n_{\gamma }=1.3\times {10}^{-15}{\mathrm{cm}}^{-1}$ chosen such that the normalization of the overall background agrees in the low-energy bins (black dashed line).

Figure 6

The fraction, $f_{\mathrm{veto}}$, of phonon background events generated by high-energy photons that can be vetoed with the DM detector alone due to the high-energy photon Compton scattering or being absorbed by the DM detector. We consider a cubic target material consisting of either GaAs, Ge, Si, SiC, and ${\mathrm{Al}}_2{\mathrm{O}}_3$, and a detector mass of 1 gram (solid lines) and 1 kg (dashed lines).