Constraints on light dark matter from primordial black hole evaporation at dark matter direct detection experiments

Primordial black holes (PBHs) are able to produce light dark matter (DM) particles via Hawking radiation, and yield a flux of boosted DM that can be probed at underground DM direct detection experiments. We analyze both galactic and extragalactic contributions to the differential flux of light DM from PBH evaporation, and then compute the expected event rate from PBH boosted DM scattering off electrons or nuclei after taking into account the attenuation effect. Using recent data from DM direct detection experiments XENONnT, PandaX-4T and LZ, we set constraints on both DM-electron and DM-nucleus scattering cross sections, as well as the fraction of DM composed of PBHs $f_{\rm PBH}$ for $9\times10^{14}-1\times10^{16},\mathrm{g}$ PBHs that are not fully evaporated today. We also investigate the spectral evolution induced by Hawking evaporation throughout the evaporation and post-evaporation regimes. The constraints on the PBH mass are then extended into the $1\times10^{13}-6\times10^{14},\mathrm{g}$ window for fully evaporated PBHs.

💡 Research Summary

Primordial black holes (PBHs) with masses in the range (10^{13}–10^{16}) g evaporate via Hawking radiation and can emit any particle whose rest‑mass is below the Hawking temperature (T_{\rm PBH}=1.06~{\rm MeV},(10^{15}{\rm g}/M_{\rm PBH})). If a light dark‑matter (DM) particle (\chi) exists with mass (m_{\chi}\lesssim T_{\rm PBH}), it will be produced as a relativistic “boosted” component of the DM flux. The authors compute the differential flux of such PBH‑boosted DM (PBH‑BDM) from two distinct sources: (i) PBHs residing in the Milky Way halo (galactic component) and (ii) the cosmological population of PBHs (extragalactic component). The galactic contribution is obtained by integrating the Hawking spectrum over the line‑of‑sight density of PBHs, assuming a monochromatic PBH mass distribution and an NFW halo profile. The extragalactic flux is evaluated by integrating over cosmic time from the formation epoch ((t_{\rm min}=10^{11}) s) to the present, including red‑shift dilution of the emitted energy and the comoving PBH number density (n_{\rm PBH}=f_{\rm PBH}\rho_{\rm DM}/M_{\rm PBH}). Numerical spectra are generated with the BlackHawk v2.3 code, which implements the full grey‑body factors for fermionic emission.

A crucial ingredient is the attenuation of the relativistic DM as it traverses the Earth before reaching underground detectors. The authors model elastic scattering of (\chi) on electrons and nuclei, define a mean free path (\ell^{-1}= \sum_i n_i\sigma_{\chi i}) (with (n_e\simeq8\times10^{23},{\rm cm^{-3}}) and (n_N\simeq3.4\times10^{22},{\rm cm^{-3}})), and solve the energy‑loss differential equation (dT_{\chi}/dx=-\sum_i n_i\int_0^{T_{\max}^i}T_i,d\sigma_{\chi i}/dT_i). Analytic expressions for the transmitted kinetic energy (T_{d\chi}) as a function of the initial energy (T_{0\chi}) and the traversed depth (z) are derived (Eqs. 7‑12). The attenuation reshapes the spectrum: for small cross sections ((\sigma_{\chi e}\sim10^{-34}) cm(^2)) the flux at the detector is almost unchanged, whereas for larger cross sections ((\sigma_{\chi e}\sim10^{-28}) cm(^2)) the high‑energy tail is strongly suppressed and a pile‑up appears at lower energies.

With the attenuated flux in hand, the expected event rates in three leading liquid‑xenon direct‑detection experiments—XENONnT, PandaX‑4T and LZ—are computed for both electron‑recoil and nuclear‑recoil channels. The electron‑recoil analysis follows the standard ionisation‑yield formalism, while the nuclear‑recoil analysis uses the usual spin‑independent (SI) DM–nucleon cross section and the appropriate xenon nuclear response functions. The authors compare the predicted spectra with the most recent null results (exposure ≈ 5–6 t·yr) and derive 90 % C.L. exclusion curves in the ((m_{\chi},\sigma_{\chi e})) and ((m_{\chi},\sigma_{\chi N})) planes. For a fixed PBH mass, the limits improve dramatically over previous works that used older data sets (e.g. XENON1T, CDEX). In addition, by varying the PBH mass they translate the scattering‑cross‑section limits into bounds on the PBH abundance fraction (f_{\rm PBH}). For partially evaporating PBHs ((M_{\rm PBH}=9\times10^{14}–10^{16}) g) they obtain (f_{\rm PBH}\lesssim10^{-8})–(10^{-6}) (depending on the DM mass and interaction type), which is comparable to or stronger than constraints from the 21 cm EDGES anomaly, the extragalactic gamma‑ray background, and big‑bang‑nucleosynthesis.

A novel aspect of the paper is the treatment of fully evaporated PBHs ((M_{\rm PBH}<7.5\times10^{14}) g). Although such PBHs no longer exist today, the particles they emitted in the early universe survive as a relic relativistic DM background. The authors compute the cumulative contribution of these fully evaporated PBHs to the present‑day DM flux, taking into account the red‑shift of the emitted energies and the dilution of number density. By confronting this relic flux with the same direct‑detection data they extend the exclusion region down to (M_{\rm PBH}\sim10^{13}) g, thereby closing a gap left by cosmological probes.

In summary, the work provides a comprehensive and up‑to‑date analysis of light DM production from PBH Hawking evaporation, includes a realistic treatment of Earth‑matter attenuation, and exploits the latest liquid‑xenon data to set the strongest direct‑detection limits on the DM–electron, DM–nucleon cross sections and on the PBH fraction for a wide PBH‑mass window. The results demonstrate that underground detectors, originally designed for non‑relativistic WIMPs, are powerful probes of relativistic boosted DM scenarios and complement astrophysical and cosmological constraints on primordial black holes.