Constraints on Spin-Independent Nucleus Scattering with sub-GeV Weakly Interacting Massive Particle Dark Matter from the CDEX-1B Experiment at the China Jinping Underground Laboratory

We report results on the searches of weakly interacting massive particles (WIMPs) with sub-GeV masses ($m_{\chi }$) via WIMP-nucleus spin-independent scattering with Migdal effect incorporated. Analysis on time-integrated (TI) and annual modulation (AM) effects on CDEX-1B data are performed, with 737.1 kg day exposure and 160 eVee threshold for TI analysis, and 1107.5 kg day exposure and 250 eVee threshold for AM analysis. The sensitive windows in $m_{\chi }$ are expanded by an order of magnitude to lower DM masses with Migdal effect incorporated. New limits on ${\sigma }_{\chi N}^{\mathrm{SI}}$ at 90% confidence level are derived as $2\times {10}^{-32}\sim 7\times {10}^{-35}{\mathrm{cm}}^2$ for TI analysis at $m_{\chi }\sim 50–180\mathrm{MeV}/c^2$, and $3\times {10}^{-32}\sim 9\times {10}^{-38}{\mathrm{cm}}^2$ for AM analysis at $m_{\chi }\sim 75\mathrm{MeV}/c^2–3.0\mathrm{GeV}/c^2$.

Figure 1

(a) Expected measureable spectra of the $\chi \text{−}N$ elastic SI-scattering (gray dash line), $\chi \text{−}N$ inelastic SI-scattering due to Migdal effect with N shell ($n=4$) electron, M shell ($n=3$) electron and L shell ($n=2$) electron ionized (blue, red and cyan regions, respectively), and the Migdal signal used in this analysis ($(n=2)+(n=3)$, black soild line). The target nucleus is Ge, the mass of WIMPs is set to $1\mathrm{GeV}/c^2$, and ${\sigma }_{\chi N}^{\mathrm{SI}}$ is set to ${10}^{-36}{\mathrm{cm}}^2$. The analysis energy threshold is marked by the black dash-dotted line. Energy resolution is not taken into account in this plot. (b) The measured spectrum for TI analysis (black point) [11], with L/M-shell x-ray contributions from the cosmogenic nuclides in the germanium crystal subtracted. The bin width is 50 eVee, and the energy range is 0.16–2.16 keVee. The blue dash-dotted line and red dash line are the expected $\chi \text{−}N$ spectra due to Migdal effect at $m_{\chi }$ equal to $50\mathrm{MeV}/c^2$ and $1.0\mathrm{GeV}/c^2$, at cross section corresponding to the upper limit at 90% confidence level, derived by binned poisson method.

Figure 2

Upper limits at 90% C.L. on ${\sigma }_{\chi N}^{\mathrm{SI}}$ derived by Binned Poisson method in TI analysis using the CDEX-1B experiment data, with several benchmark experiments [5, 6, 11, 12, 13, 32, 33, 34, 35] superimposed. Limits from nuclear recoil-only analysis with the same data set is shown (black dash line) as comparison. This analysis incorporating Migdal effect (red solid line) provides the best sensitivities for $m_{\chi }\sim 50–180\mathrm{MeV}/c^2$, significantly expanding the excluded parameter space over earlier work (other solid lines).

Figure 3

The curves are the expected spectra due to Migdal effect in June (red dash-dotted line), September (black solid line) and December (cyan dash line), where $m_{\chi }$ is equal to $1\mathrm{GeV}/c^2$, ${\sigma }_{\chi N}^{\mathrm{SI}}$ is equal to ${10}^{-36}{\mathrm{cm}}^2$. The energy resolution is taken into account, the standard deviation of which is $33.5+13.2\times E^{1/2}(\mathrm{eV})$, where $E$ is expressed in keV.

Figure 4

Upper limit at 90% C.L. on ${\sigma }_{\chi N}^{\mathrm{SI}}$ derived by AM analysis using CDEX-1B data about 4.2 years [19]. The energy threshold of the modulated analysis is 250 eVee, while the reach of the exclusion line (red solid line) is extended to $75\mathrm{MeV}/c^2$. The nuclear recoil only limits from the same data set is superimpsed [19]. Constraints [37] and allowed regions [22, 31, 38, 39, 40, 41] from AM analysis from other experiment are also shown.