Low-energy signals from the formation of dark-matter–nucleus bound states

Dark matter particles may bind with nuclei if there exists an attractive force of sufficient strength. We show that a dark photon mediator of mass $\sim (10–100)\mathrm{MeV}$ that kinetically mixes with Standard Model electromagnetism at the level of $\sim {10}^{-3}$ generates keV-scale binding energies between dark matter and heavy elements, while forbidding the ability to bind with light elements. In underground direct detection experiments, the formation of such bound states liberates keV-scale energy in the form of electrons and photons, giving rise to monoenergetic electronic signals with a time structure that may contain daily and seasonal modulations. We show that data from liquid-xenon detectors provides exquisite sensitivity to this scenario, constraining the galactic abundance of such dark particles to be at most $\sim {10}^{-18}–{10}^{-12}$ of the galactic dark-matter density for masses spanning $\sim (1–{10}^5)\mathrm{GeV}$. However, an exponentially small fractional abundance of these dark particles is enough to explain the observed electron recoil excess at XENON1T.

Figure 1

The minimum coupling $q_{\mathrm{eff}}$ required for dark matter to bind with various nuclei, as a function of dark-matter mass $m_{\chi }$, fixing $m_{A^{\prime }}=50\mathrm{MeV}$. A dark-matter–nuclear bound state exists with an element for values of $q_{\mathrm{eff}}$ above the corresponding line.

Figure 2

In the $\{m_{A^{\prime }},q_{\mathrm{eff}}\}$ plane, contours of fixed binding energy $E_B=2.5\mathrm{keV}$ of $(\chi {\mathrm{Xe}}^{+})$ for different choices of $m_{\chi }$. Along the dashed parts of the contours, $\chi$ also binds with Fe.

Figure 3

Left: limits derived from XENON1T (green) on the fractional abundance $f_{\chi }$, in the case that the binding energy between $\chi$ and xenon is $E_B=2.5\mathrm{keV}$ and $m_{A^{\prime }}=50\mathrm{MeV}$. The solid green line assumes an abundance of barium in the Gran Sasso overburden of $2\times {10}^{18}{\mathrm{cm}}^{-3}$, whereas the upper and lower dashed green lines assume a barium density that is larger or smaller by a factor of 3, respectively. Also shown are existing constraints (shaded gray) from searches for $\chi$-nuclear elastic scattering at CRESST [45], CDMS [46], and XENON1T [47]. Right: contours of $(\chi {\mathrm{Xe}}^{+})$ binding energy $2\mathrm{keV}\le E_B\le 3\mathrm{keV}$ for various choices of ${\alpha }_D$, fixing $m_{\chi }=1\mathrm{TeV}$, in the $\{m_{A^{\prime }},\epsilon \}$ plane. Along the dashed parts of the contours, $\chi$ also binds with Fe. The gray regions are currently excluded by accelerator and beam dump searches for visibly decaying dark photons [48]. Future accelerator searches, for instance APEX [49], FASER [50], HPS [51], LHCb [52, 53, 54, 55], NA64 [56, 57], and SeaQuest [58], will explore nearly all of the currently allowed parameter space shown.

Figure 4

The capture cross sections for the $s$-to-$s$ process (solid) and $p$-to-$s$ process (dashed), for capture of $\chi$ onto xenon (red), barium (green), and thallium (blue), as a function of dark matter mass $m_{\chi }$. Cross sections for Xe and Ba assume the existence of a $\chi -\mathrm{Xe}$ bound state with $E_B=2.5\mathrm{keV}$, while the calculation for Tl assumes that $\chi$ binds to Tl with $E_B=2.5\mathrm{keV}$.