SENSEI: A Search for Diurnal Modulation in sub-GeV Dark Matter Scattering

TL;DR

This work investigates diurnal modulation signatures of sub-GeV dark matter arising from Earth shielding using SENSEI Skipper-CCD data taken at Fermilab. It develops both a model-independent daily modulation search and a model-dependent framework for DM–electron scattering via a dark-photon mediator, incorporating Earth traversal via DaMaSCUS and an isodetection-angle that varies with sidereal time. No evidence for daily modulation is found, and the study sets a 90% CL upper limit on the modulation amplitude $a_1$ of $6.8\ \mathrm{e^{-}}\ \mathrm{g}^{-1}\ \mathrm{day}^{-1}$, along with competitive constraints on DM–electron scattering for $m_\chi \lesssim 2$ MeV, improving previous direct-detection bounds by about an order of magnitude in the 1e− channel. The results demonstrate the viability of time-domain analyses to probe highly interactive sub-MeV DM and highlight the potential gains from larger exposures and continued methodological refinements, including robust treatment of non-Poisson backgrounds and comprehensive supplemental studies.

Abstract

Dark matter particles with sufficiently large interactions with ordinary matter can scatter in the Earth's atmosphere and crust before reaching an underground detector. This Earth-shielding effect can induce a directional dependence in the dark matter flux, leading to a sidereal daily modulation in the signal rate. We perform a search for such a modulation using data from the SENSEI experiment, targeting MeV-scale dark matter. We achieve an order-of-magnitude improvement in sensitivity over previous direct-detection bounds for dark-matter masses below 1 MeV, assuming the Standard Halo Model with a Maxwell--Boltzmann velocity distribution, and constrain the amplitude of a general daily modulation signal to be below 6.8 electrons per gram per day.

Figures (7)

• Figure 1: Results of the bootstrap test validating the assumption of a Poisson-distributed, time-independent background of our observed data. The gray band shows the 2$\sigma$ variance around a mean $p$-value calculated from fitting background-only Poisson based Monte Carlo datasets. The blue and yellow bands indicate the calculated variance of the $p$-value obtained from bootstrapping the observed data multiple times. No statistical deviation of the background from the Poisson assumption is observed. All horizontal bands are signal-to-noise ratio(SNR) independent. For the simulation bootstrap test the $p$-value is shown as a function of the SNR. For each value of SNR, the mean $p$-value from 500 simulated datasets was calculated, assuming a model-independent (Eq. \ref{['eq:mod_dep_sig']}; yellow) and model-dependent (Eq. \ref{['eq:mod_ind_signal']}; blue) signal. The solid lines indicate fits using time-ordered timestamps, while dashed lines indicate fits using bootstrap-resampled timestamps.
• Figure 2: Comparison of the fluctuation around the average of both the measured 1$\mathrm{\,e^{-}}$ rate ( black circles) with the rate predicted for a 1 MeV DM particle interacting with ordinary matter through a heavy dark-photon mediator with a cross section of $\sigma_e = 5\times10^{-32},\mathrm{cm}^2$ ( solid red line), which represents the current most stringent bound at this mass. The measured rate is taken from the lowest-noise CCD quadrant, with an average value of $135~e^{-}/\mathrm{gr}/\mathrm{day}$. The lower $x$-axis shows the first ten days of measurement, while the upper $x$-axis indicates the corresponding iso-detection angles. Vertical error bars denote the statistical uncertainty of each image, given by the square root of the counts in the image, while horizontal error bars indicate the estimated average rate over the associated $6$-hour exposure (note that the $6$-hour exposures were not taken sequentially).
• Figure 3: 90% C.L. upper-limits on the DM electron scattering cross-section for a light ( left) and heavy ( right) dark-photon mediator, calculated with DaMaSCUS and QCDark. Solid purple line and shaded region correspond to the constraints applied directly to the model referenced in Eq. \ref{['eq:mod_dep_sig']}, while the dashed line indicates the 90% C.L. upper-limit obtained by recasting our constraint in Eq. \ref{['eq:a1limit']} on the model-independent modulation amplitude $a_1$ of Eq. \ref{['eq:mod_ind_signal']}; the latter was calculated by fitting the mass and $\bar{\sigma}_{e}$ that generates the same daily modulation amplitude $a_1$. The blue dashed curve shows the constraint from solar‐reflected halo DM, assuming a dark‐photon mediator Emken:2024noxAn:2021qdlaprile2025search. The orange solid curve indicates the canonical freeze-in benchmark target for the light-mediator model Essig:2011njEssig:2015cdaChu:2011beDvorkin:2019zdi and freeze-out region for the heavy mediator Boehm:2003hmEssig:2011njEssig:2015cdaEssig:2022dfaBoehm:2003hmLin:2011gjIzaguirre:2015yjaHochberg:2014draKuflik:2017iqsDAgnolo:2019zkfChu:2011beDvorkin:2019zdi. The solid gray line and shaded region denote the existing SENSEI limits senseisnolab2023sensei1epaper. The turquoise region show the DAMIC-M limit from aggarwal2025probing; we show the DAMIC-M daily modulation constraint from DAMIC-M:2023hgj in the Supplemental Materials, as it is based on QEDark without screening.
• Figure 4: Measured single-electron event spectrum from CCD 1, quadrant 2 (blue bins), together with the best-fit scaled-Poisson background model (orange curve, $\hat{c} = 1.90$, $\hat{\lambda} = 12.16$) and the corresponding standard Poisson distribution (green dashed curve, $\hat{\mu} = 12.16$). The comparison shows that the scaled-Poisson model captures the broader tail of the data more accurately than the Poisson model.
• Figure 5: Comparison of our main results obtained with the scaled-Poisson background model (blue) and the Poisson background model (purple; same as Fig. \ref{['fig:results_qcdark_main']}), shown for a light mediator (left) and a heavy mediator (right). The two curves agree within $10\%$, indicating that the analysis is not affected by our non-Poissonian background deviations.