CONNIE and Atucha-II Collaborations

Short baseline reactor antineutrino experiments arise as an opportunity to look for beyond the standard model (BSM) particles, such as QCD axions [1, 2], and other dark matter candidates [3, 4, 5]. Among the extensions to the standard model, millicharged particles (mCP) have gained significant attention and are considered highly compelling BSM candidates [6, 7, 8]. The TEXONO collaboration employed a point-contact 500 g germanium detector with a low-energy threshold of 300 eV, positioned 28 m away from a 2.9 GW_th nuclear reactor, using 124.2/70.3 kg-days of reactor ON/OFF data, to set the most stringent direct laboratory exclusion limits below 1 MeV up to date [9].

Silicon detectors have pushed the energy thresholds to lower values, allowing for higher sensitivity in the dark-matter low-mass range. CONNIE [10, 11] was the first experiment to use silicon charge-coupled devices (CCD) at nuclear reactor to look for coherent elastic neutrino-nucleus scattering and impose competitive constraints on BSM physics [12]. Recently, CONNIE upgraded its detector by substituting the CCDs with a pair of Skipper-CCDs [13], increasing its sensitivity and low-energy reach [14]. At the same time, the Atucha-II experiment has deployed a Skipper-CCD sensor inside a nuclear power plant, situated just 12 m from the reactor core. The initial results demonstrate promising potential to explore both standard-model physics and exotic searches [15].

In a recent contribution, the SENSEI experiment has achieved the most stringent exclusion limit for mCPs in the 30 to 380 MeV mass range using Skipper-CCDs [16]. Based on this, additional promising scenarios for enhancing this search have been proposed using a kg-scale experiment with the same technology [17]. There is, however, a compelling reason to conduct such an experiment in the vicinity of a nuclear reactor, as its core represents the most potent source of gamma rays on Earth. Moreover, mCPs produced by Compton-like interactions from gamma rays enable the exploration of sub-MeV masses, making the reactor experiments the most competitive in this energy range.

Tracking mCPs passing through a stack of detectors has also been proposed as a highly sensitive strategy for observing these particles when produced in an accelerator [18]. However, this strategy is not competitive below 1 MeV where the fraction of the elementary charge, $\varepsilon$, have already been excluded well beneath to 10^-5  [9]. Observing tracks for even smaller values of $\varepsilon$ would require extremely large stacked detectors.

In this Letter, we present world-leading direct laboratory exclusion limits for mCPs below 1 MeV, covering six orders of magnitude in mCP mass. This work also represents a collaborative effort between the CONNIE and Atucha-II experiments—the first to use Skipper-CCD technology for this type of search in reactor experiments—achieving combined results that enhance the robustness of the analysis and yield a stronger limit.

A possible channel for the generation of mCPs ($\chi_{q}$) in the sub-GeV mass range is through a Compton-like process, in which a $\gamma$ photon scatters off an electron in the material of the reactor core (Uranium), the photon could then kinetically mix with a dark photon [19, 20]. As a result, a new dark fermion pair $\chi_{q}-\overline{\chi}_{q}$, coupled to the dark photon, can acquire a small electric charge $q=\varepsilon e$ proportional to the kinetic mixing parameter. In the case of a pure mCP, the dark photon is massless and the resulting particles has an electromagnetic charge $\varepsilon$ which is a real number with $|\varepsilon|<1$ and $e$ is the elementary charge.

Approximately half of the $\gamma$ flux in the reactor core arises from highly excited fission fragments, with the remainder originating from radioactive de-excitation of the daughter nuclei, inelastic neutron scattering, and capture of neutrons by core materials. The $\gamma$-ray spectrum characteristic of neutron-induced fission of uranium, determined for an FRJ-1 (Merlin) research reactor core, can be parameterized by

which holds for photon energies $E_{\gamma}$ above 0.2 MeV, where $K=0.581\times 10^{18}$ MeV^-1s^-1, and $P$ is the reactor thermal power in MW. This model has been applied by the TEXONO collaboration [9] and has also been employed in recent dark matter searches [2, 9, 21, 22, 23]. To the best of our knowledge, however, secondary $\gamma$-rays were not taken into account in previous calculations although they are also able to produce mCPs. In this work, we calculate the limits in both scenarios, reflecting the contributions to mCP production of only primary $\gamma$-rays, as well as including secondary $\gamma$-rays from transport and energy loss in the nuclear core. The secondary contribution was estimated from a simulation using GEANT4 [24, 25].

The differential production cross-section for mCP through the mentioned channel can be estimated by adapting the lepton-pair production process [9]. To do this, the $\chi_{q}-\overline{\chi}_{q}$ production vertex is parameterized by $\varepsilon$ and the lepton mass is replaced by the proposed mCP mass, $m_{\chi_{q}}$,

where $m_{e}$ is the mass of the electron, $\alpha$ is the fine structure constant, and $E_{\overline{\chi}_{q}}=E_{\gamma}-E_{\chi_{q}}$.

The total differential flux of mCP is calculated by taking the convolution of the reactor $\gamma$-ray spectrum and the differential production cross-section as in Eq. 3. The integral is normalized by the total interaction cross-section, $\sigma_{\rm tot}$. Following the same argument as in Refs. [9, 26], restricting the integral between 1 and 5 MeV, $\sigma_{\rm tot}$ can be approximated by the Compton cross-section, since this mechanism dominates over other interaction processes. The flux then becomes,

where $D$ is the distance between the detector and the center of the reactor core, and there is a factor of 2 from the fact that mCPs are produced in pairs.

Millicharged particles can be described as charged particles traveling with a velocity $\beta=\frac{p}{E_{\chi_{q}}}$, and are expected to interact electromagnetically, leading to the production of ionization wherein free charge carriers are released for energy depositions above the band gap of silicon. A first description of this phenomenon can be found in Ref. [27]. This description is semiclassical in the sense that the particle is considered to be relativistic with a $p_{\mu}$ and a classical source of electromagnetic fields. The effective cross-section for the interaction is then given by

where information regarding the interaction between virtual photons emitted by the mCP and the material is encoded in the complex dielectric function $\epsilon(\omega,k)=\epsilon_{1}(\omega,k)+i\epsilon_{2}(\omega,k)$, $N_{e}$ is the electron number density of the material and $k$ is the momentum transfer to the material.

The Photo Absorption Ionization (PAI) model (also known as Fermi virtual photon or Weizsacker-Williams approximation) has been used to describe the energy loss per unit length for standard model particles, but it has also been employed in mCP searches by scaling the coupling with the electron charge to the mCP charge [28, 29]. A full derivation of the modeling of the cross-section can be found in Ref. [30], as well as a discussion on the physical meaning of each term. This differential cross-section can be expressed as

where $\sigma_{\gamma}$ is the photoabsorption cross-section and $\tan\Theta=\epsilon_{2}\beta^{2}/(1-\beta^{2}\epsilon_{1})$.

Figure 1 illustrates the energy dependence of the interaction cross-section for an mCP with 1 eV mass and $\varepsilon=10^{-6}$. The sizable enhancement observed in the low-energy region comes from the interaction of the particles with bulk plasmons. The tabulated complex index of refraction and photoabsorption data is not valid for energy deposits below $\sim 50$ eV as there is a crucial difference between optical absorption and the scattering of relativistic particles. Photons are always transversely polarized, whereas a charged particle can also interact with the material via longitudinal Coulomb modes which dominate the response function in this regime. Optical absorption data have then been identified as a poor proxy for a relativistic scattering of charged particles at low energies.

To precisely calculate the interaction cross-section for mCPs near the plasmon peak, in Ref. [31] the electron loss function Im$(-1/\epsilon(\omega,k))$ is calculated for different models of the dielectric function in the DarkELF package [32], producing reliable results when compared to electron energy loss spectroscopy data when $\beta\geq 0.01$.

Thus, we turn to the DarkELF (GPAW) model to calculate the expected rate of mCPs below 50 eV as PAI model underestimates the cross-section near the plasmon peak, while GPAW provides a more accurate description, as stated in Ref. [31]. This integration constitutes the main contribution to systematic uncertainty (see Supplemental Material [33] for details).

The differential rate of events due to $\chi_{q}$ interactions can then be calculated by integrating the flux obtained in Eq. 3 convolved with the interaction cross-section,

where $\rho$ is the atomic number density and ($E_{\rm min}$, $E_{\rm max}$) are the values of the mCP energy.

Fully depleted high-resistivity silicon CCDs are being used in various experiments dedicated to dark matter [34] and low-energy neutrino detection, which require low thresholds and excellent background control. Skipper-CCDs [13] are the new generation of this imaging technology, achieving single-electron sensitivity by using the non-destructive readout of the charge packets held in each pixel [35, 36, 18, 37]. This capability allows for an excellent signal-to-noise ratio with detection thresholds as low as 15 eV in above-ground experiments [38]. Both the CONNIE and Atucha-II experiments employ Skipper-CCD sensors of 675 $\mu$m thickness and 15 $\mu$m pixel size, designed by LBNL Microsystems Laboratory and manufactured by Teledyne-DALSA. They are read out using a Low-Threshold Acquisition (LTA) controller board [39].

The Coherent Neutrino-Nucleus Interaction Experiment (CONNIE) [10, 11, 12, 14] is operating in a ground-level laboratory outside the dome of the 3.95 GW_th Angra 2 nuclear reactor near Rio de Janeiro, Brazil, at a distance of about 30 m from the core. The experiment has been taking data with two Skipper-CCDs of 0.247 g mass each since July 2021, totaling an exposure of 18.4 g-days. The sensors achieved an ultra-low readout noise of 0.15 e^- by sampling 400 times each pixel charge, allowing to measure for the first time the energy spectrum near a reactor down to a threshold of 15 eV, and obtaining a background rate in reactor-OFF data of around 4 $\rm{kg^{-1}d^{-1}keV^{-1}}$ [14].

The Atucha-II nuclear power plant is a 2.175 GW_th pressurized heavy water reactor that utilizes natural UO₂ as fuel, located in Buenos Aires province, Argentina. Since December 2021, a Skipper-CCD with 2.2 g mass is taking data inside the containment sphere, 12 m away from the nuclear core. The sensor is operated with a readout noise of 0.17 e^-, achieved by averaging 300 samples of the charge in each pixel, and a background rate in reactor-OFF data of around 30 $\rm{kg^{-1}d^{-1}keV^{-1}}$. The dataset used in this work corresponds to 82 g-days of unpublished data from the 2023 run.

In the interaction cross-section from Fig. 1, the plasmon peak located between 10 and 25 eV is easily identified as the most convenient region to look for mCPs. Above 25 eV, the cross-section decreases significantly until reaching 100 eV. At this point, the energy released in the detector is sufficient to ionize the silicon $p$ shell, increasing in 6 the number of electrons acting as targets. Based on this and before unblinding the data, a 200 eV energy interval starting at the lowest energy possible in each experiment was established (see Table 1). It is noteworthy that the CONNIE threshold of 15 eV enables the inclusion of most of the plasmon peak while extending the interval above 240 eV for Atucha II would result in a loss of sensitivity due to the decrease in the cross-section against a constant background rate.

Table 1 summarizes the results obtained from each experimental run. Upper limits at 90% C.L. on the numbers of events were computed using the frequentist approach, as outlined in Ref. [40]. Efficiency corrections were implemented by convolving the expected theoretical event count with the efficiency curves from Refs. [14, 15].

Figure 2 depicts the independent exclusion limits attained by each experiment. The results show an improvement by the CONNIE and Atucha-II experiments for two cases: primary plus secondary (solid lines), or only primary $\gamma$-ray production (dashed lines). Moreover, a combined analysis of the outcomes from both experiments is performed following Ref. [40], yielding a further improvement on the individual results (see Supplemental Material [33] for details). The upper limit was derived based on the attenuation of mCPs in the material between the reactor and the detector, accounting for Bremsstrahlung and ionization stopping power, as outlined in Ref. [41] The total combined error obtained through Monte Carlo propagation was 9.5%. A detailed description of each source and its contribution can also be found in the Supplemental Material [33].

The mCP search is particularly challenging because the number of observed events scales with $\varepsilon^{4}$. A factor $\varepsilon^{2}$ originates from the mCP production within the reactor core (Eq. Search for reactor-produced millicharged particles with Skipper-CCDs at the CONNIE and Atucha-II experiments), while another factor $\varepsilon^{2}$ results from the probability of interaction (Eq. 4). Therefore, achieving a 2.5-fold improvement in the limit around 100 keV (see Fig. 2) is equivalent to a 40-fold increase in experimental exposure. Such an enhancement is impractical with previous strategies, given that the best results to date was achieved with a half-kilogram detector and exposure times of hundreds of days [9]. On the other hand, mCP flux scales linearly with the thermal power of the reactor but inversely with the square of the distance. Achieving such an increase in flux would require reducing the distance by a factor of six, which is unfeasible in most reactor experimental scenarios.

The capability of observing interactions at the eV scale allows CONNIE to take advantage of the plasmon resonance [42]. This collective mode of electronic excitation in semiconductor materials significantly enhances the detection sensitivity for sub-MeV relativistic particles. Accessing recoil energies in the eV range results in a flatter cross-section dependence on mCP mass, compared to the TEXONO experiment, which operated above 300 eV, showing a logarithmic dependence on the inverse of the mCP mass through the equivalent photon approximation cross-section [9]. The Atucha-II experiment possesses a three times higher mCP flux and a four times higher reactor ON exposure compared to the CONNIE experiment. This is compensated by the fact that the CONNIE’s energy interval accounts for a 4.5 times larger probability of mCP interaction (see Fig. 1) than Atucha’s energy interval, as well as a background rate six times lower. Consequently, both experiments feature a similar signal-to-square-root-of-background ratio, which explains the closeness of the achieved exclusion limits.

We have demonstrated an alternative approach to improving limits using Skipper-CCD technology, which combines a 1.1 eV silicon band gap with sub-electron readout noise. This enables experiments with sensitivity at the eV scale to exploit the significant enhancement in the cross-section. We present for the first time a combined analysis of the collaborative effort between the two experiments, resulting in a very robust limit that strongly mitigates systematic errors eventually introduced by any of them. The combined result extends the experimental exclusion limits further towards 700 keV in mCP mass, as well as down towards $\varepsilon\sim 1\times 10^{-6}$ for the lowest mCP masses of 1 eV, thus becoming the best direct laboratory constraint on mCP coupling. Futhermore, both experiments are currently conducting this search with only around 1 g of sensor, and have plans for substantial increases in sensor mass [15, 14]. The scaling of mass to reach the kilogram range has already been developed [17, 18], and the potential physics impact of such an experiment has also been evaluated [43, 44].