WIMP–Electron Scattering Cross Section

• The paper establishes rigorous 90% CL upper limits on WIMP–electron scattering, with <6.4×10⁻³³ cm² for light and <3.4×10⁻³⁷ cm² for heavy mediator scenarios.
• It employs advanced low-energy detection methods, including dual PMT coincidence and MLP-based pulse shape discrimination, to effectively reduce noise and isolate single-hit events.
• Future upgrades at deeper sites and lower thresholds aim to refine sensitivity, enabling annual modulation searches to probe sub-GeV dark matter candidates.

The WIMP–electron scattering cross section quantifies the probability of interaction between a weakly interacting massive particle (WIMP) and an atomic electron, mediated by hypothetical vector bosons. This parameter is a focal point in direct dark matter detection experiments targeting sub-GeV WIMP mass ranges, where nuclear recoils become kinematically suppressed and electron recoils offer an alternative signature. Precise determination of the cross section, constraints on its magnitude, and understanding its dependence on the properties of the propagating mediator are essential for interpreting potential dark matter signals and for constraining theoretical models invoking WIMPs as the dark matter constituent.

1. Experimental Methods in WIMP–Electron Searches

The COSINE-100 experiment exemplifies current methodologies for probing WIMP–electron scattering. Situated in the YangYang underground laboratory with an overburden of approximately 700 m, the setup utilizes eight ultrapure NaI(Tl) crystals, totaling 106 kg. For low-energy analyses, a subset of five crystals (effective mass 61.3 kg) is selected to maximize signal-to-noise, owing to their superior light yield and reduced intrinsic noise. Each crystal is optically coupled via quartz light guides to two low-background photomultiplier tubes, and the entire assembly is immersed in a 2200-liter liquid scintillator, functioning as both an active veto and a gamma-ray background suppressor. Additional shielding comprises copper, lead, and plastic scintillator panels for cosmic muon rejection.

Detector electronic channels are split into dynode readout (optimized for high-energy) and anode readout (optimized for low-energy) signals. Triggering employs coincidence logic between the two PMTs on a crystal, or between the crystal and external veto systems, enabling a detection threshold as low as 0.7 keV, equivalent to the production of eight photoelectrons.

2. Theoretical Benchmarks: Mediator Scenarios

Analysis of the WIMP–electron scattering cross section requires specifying the nature of the mediator responsible for the interaction:

• Heavy Mediator Scenario:

This case assumes the mediator mass ($m_{DP}$) is much greater than $\alpha \cdot m_e$ (where $\alpha$ is the fine-structure constant and $m_e$ is the electron mass). The dark matter form factor simplifies, $F_\chi(q) \to 1$, indicative of a contact interaction. The corresponding cross section for a free electron with typical momentum transfer $q \sim 1/a_0$ (Bohr radius $a_0$) is:

$$\overline{\sigma}_e = \frac{16\pi a_0^2 \alpha^2 \alpha_\chi^2}{((m_{DP} \, m_e)^2 + \alpha^2)^2}$$

Sensitivity is maximized for $m_\chi \sim 0.4$ GeV under these assumptions.

• Light Mediator Scenario:

Here, the mediator mass is negligible compared to $\alpha \cdot m_e$, giving rise to a momentum-dependent form factor, $F_\chi(q) \to 1/(a_0 q)^2$, enhancing the scattering rate at low $q$. Sensitivity peaks at $m_\chi \sim 0.25$ GeV. The spectral shapes corresponding to these scenarios dictate the expected electron recoil spectra and consequently the inferred upper limits on $\overline{\sigma}_e$.

3. Data Analysis Framework

The COSINE-100 analysis is based on a 2.82-year exposure, amounting to 172.9 kg·yr. The procedure includes:

• Event Selection:

With the detector threshold at 0.7 keV, stringent control of photomultiplier-induced noise is crucial. Only “single-hit” events—defined as those with coincident signals in both PMTs of a single crystal and no other detectors within preset time windows—are selected, matching the expectation for WIMPs. A multilayer perceptron (MLP) deep learning classifier is employed, leveraging pulse shape discrimination (PSD) metrics (mean time, amplitude, and frequency domain features) to distinguish true scintillation from spurious events, attaining noise contamination levels below 1%.

• Background Model:

Geant4-based simulations quantify the primary background constituents, notably internal $\beta$-emitters ($^3$H, $^{210}$Pb) and Compton-scattered $\gamma$-rays. The detector response at low energies is calibrated with $^{22}$Na (0.87 keV X-ray) and $^{40}$K (3.2 keV) sources, validating the response down to single-digit photoelectrons. The intrinsic energy resolution is modeled via a scaled Poisson kernel, which better represents the non-Gaussian nature of signals in this regime.

• Spectral Fitting:

Signal and background spectra are fit using a Bayesian likelihood approach, with a Poisson likelihood and Markov Chain Monte Carlo (MCMC) sampler. Nuisance parameters include the background component normalizations, governed by Gaussian priors encapsulating systematic and statistical uncertainties. The amplitude of the possible WIMP–electron contribution, $\overline{\sigma}_e$, is simultaneously varied. The fit window extends to 8 keV (100 photoelectrons).

4. Experimental Results and Derived Limits

No statistically significant WIMP–electron excesses were observed. The resulting 90% confidence level (CL) upper limits on the cross section are:

Mediator Scenario	$m_\chi$ [GeV]	$\overline{\sigma}_e$ [cm$^2$]
Light	0.25	$< 6.4 \times 10^{-33}$
Heavy	0.4	$< 3.4 \times 10^{-37}$

These limits explicitly account for detector effects (such as resolution and PMT non-linearity) and utilize relativistically computed electron ionization factors ($f_\text{ion}$) for both sodium and iodine atomic shells. The excluded cross section region, particularly for NaI(Tl) targets, is the most restrictive to date for this class of experiments. Notably, these constraints fully exclude previously proposed best-fit regions that interpreted DAMA/LIBRA’s annual modulation signal in terms of WIMP–electron scattering.

5. Comparison, Context, and Significance

The derived COSINE-100 limits are unique to NaI(Tl)-based searches. Although less stringent than those achieved by experiments using lower-threshold technologies such as PandaX-4T, XENONnT, SENSEI, or DAMIC-M, COSINE-100 scrutinizes a detector material identical to that of the DAMA/LIBRA experiment. This yields a critical independent test of interpretations invoking WIMP–electron interactions to explain modulation signals. The use of multiple detector technologies is essential in the broader program to establish or refute dark matter signals across varying detector media.

A plausible implication is that, within the WIMP–electron scattering paradigm and for the explored benchmark scenarios, a significant fraction of previously allowed parameter space is now constrained for NaI(Tl).

6. Prospects and Planned Upgrades

Several strategies are outlined for future improvement:

• Detector Upgrade (COSINE-100U):

COSINE-100U is under construction to operate at a site 300 m deeper (Yemilab) to further suppress cosmogenic backgrounds. Planned improvements include enhanced crystal encapsulation and cooling to –30 °C, increasing light yield by approximately 40%. This is projected to lower the detection threshold from eight to five photoelectrons, enhancing sensitivity to lower-mass WIMPs and reducing energy uncertainties in the keV and sub-keV regime.

• Annual Modulation Search at Lower Thresholds:

Extension of analysis to thresholds at, or near, single photoelectron equivalents is anticipated. Given that background modeling at single-photon levels becomes highly challenging, the focus will shift to searches for annual modulation—an effect insensitive to absolute rate modeling but highly dependent on long-term experimental stability.

These initiatives aim to extend experimental reach to the regime of sub-GeV and potentially MeV-scale WIMPs, and to interrogate unexplored parameter spaces.

7. Summary

Current best constraints on the WIMP–electron scattering cross section with a NaI(Tl) target have been established by COSINE-100, setting upper limits at a 90% CL of $6.4\times 10^{-33}$ cm$^2$ for a 0.25 GeV WIMP in the light mediator scenario, and $3.4\times 10^{-37}$ cm$^2$ for a 0.4 GeV WIMP with a heavy mediator. These results eliminate regions of parameter space implicated in interpretations of DAMA/LIBRA’s annual modulation in terms of WIMP–electron scattering. Continued improvements in threshold, mass, and background rejection are expected to further tighten these constraints and probe the electron interaction channel for light dark matter candidates.