Search for Neutrino-Produced Long-Lived Particles Using the SBND Cosmic Ray Tagger Beam Telescope

(The SBND Collaboration)*

@page 1/12 starts_mid=0 ends_mid=1 (The SBND Collaboration)*

aff-1 Universidade Federal do ABC, Santo Andre, SP 09210-580, Brazil aff-2 Argonne National Laboratory, Lemont, IL 60439, USA aff-3 Universidade Federal de Alfenas, Pocos de Caldas, MG 37715-400, Brazil aff-4 Brookhaven National Laboratory, Upton, NY 11973, USA aff-5 Universität Bern, Bern CH-3012, Switzerland aff-6 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Madrid E-28040, Spain aff-7 Colorado State University, Fort Collins, CO 80523, USA aff-8 Centro de Tecnologia da Informação Renato Archer, Campinas, SP 13069-901, Brazil aff-9 Universidade Estadual de Campinas, Campinas, SP 13083-970, Brazil aff-10 University of Chicago, Chicago, IL 60637, USA aff-11 Columbia University, New York, NY 10027, USA aff-12 University of Edinburgh, Edinburgh EH9 3FD, United Kingdom aff-13 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA aff-14 University of Florida, Gainesville, FL 32611, USA aff-15 Georgia Institute of Technology, Atlanta, GA 30332, USA aff-16 Universidad de Granada, Granada E-18071, Spain aff-17 Hanyang University, 222 Wangsimni-ro, Wangsimni-ro, Seongdong-gu, Seoul, 04763, Korea aff-18 Mount Holyoke College, South Hadley, MA 01075, USA aff-19 Indian Institute of Science, Centre for High Energy Physics, Bangalore 560012, India aff-20 Illinois Institute of Technology, Chicago, IL 60616, USA aff-21 Imperial College London, London SW7 2AZ, United Kingdom aff-22 University of Kansas, Lawrence, KS 66045, USA aff-23 Los Alamos National Laboratory, Los Alamos, NM 87545, USA aff-24 Louisiana State University, Baton Rouge, LA 70803, USA aff-25 Lancaster University, Lancaster LA1 4YW, United Kingdom aff-26 University of Liverpool, Liverpool L69 7ZE, United Kingdom

Introduction

The Short-Baseline Near Detector (SBND) [1] is a 112 ton liquid argon time projection chamber (LArTPC) positioned 110 m downstream of the target along the Booster Neutrino Beam (BNB) [2] at Fermi National Accelerator Laboratory (Fermilab). As the near detector of the Short-Baseline Neutrino (SBN) program [3], SBND contributes to a definitive multi-detector search for sterile neutrino oscillations at the eV mass scale and other phenomena beyond the Standard Model (BSM). SBND in particular offers a rich BSM physics program, enabled by the intense neutrino flux of the BNB and the detector’s proximity to the neutrino source [4].

In BSM theories, it is common for one or more newly introduced particles to have sufficiently long lifetimes to travel macroscopic distances before decaying. Searches for such particles, and their subsequent decays into observable Standard Model (SM) final states, fall under the moniker of long-lived-particle (LLP) searches. Conventionally, these searches at accelerator neutrino experiments focus on LLPs produced through meson decays [5, 6, 7, 8, 9]. However, intense neutrino beams, such as the BNB, offer a complementary production environment: LLPs can be generated via neutrino–nucleus scattering in the surrounding material and subsequently decay into visible final states downstream. The analysis presented here therefore targets LLPs produced through neutrino interactions, rather than the conventional meson-decay channel.

This paper presents a search for LLPs using data from the SBND experiment. The analysis is performed using a standalone configuration of the SBND Cosmic Ray Tagger (CRT) system, referred to as the CRT Beam Telescope. Prior to the installation of the SBND cryostat, which houses the LArTPC, a subset of CRT modules was deployed in the detector hall and operated between 2017 and 2018, as shown in Figure 1. The detector collected data corresponding to $2.95 \times10^{20}$ protons on target (POT) from the BNB. The CRT Beam Telescope was originally intended for commissioning and performance studies, and not as a dedicated BSM detector. Despite this, its geometry, spatial/timing resolution, and exposure to the neutrino beam have been shown to provide effective background rejection enabling a search for displaced decays at macroscopic distances from a LLP’s production point.

The LLPs considered in this analysis are produced via neutrino upscattering in the material, approximated as silicon, between the BNB target and the CRT Beam Telescope, outside the detector volume. They are modeled to propagate macroscopic distances before decaying into electron–positron pairs. As a result, the signal originates from displaced decays occurring within the volume between the two CRT panels, rather than from interactions within instrumented material. This distinguishes the present search from conventional neutrino interaction measurements, which target prompt, in-detector vertices. This search sets limits on the product of the LLP production cross section via neutrino upscattering and the LLP decay branching ratio, as a function of LLP lifetime. This parameter space has not previously been explored by other experiments.

To guide the signal modeling, this search is inspired by dark neutrino scenarios [10, 11], in which a SM neutrino upscatters into a heavier neutral fermion that subsequently decays into visible final states. Rather than focusing on one particular model realization, the results are presented in a framework that parametrizes the LLP production rate and decay lengths, allowing reinterpretation for models with similar phenomenology, for example when additional final states or dark neutrinos are added to the model that can modify the LLP lifetime substantially.

This paper is organized as follows. Section II describes the CRT Beam Telescope detector configuration and the beamline. Section III introduces the LLP model assumptions and the signal simulation. The background estimation is presented in Section IV. § 1.4 describes the reconstruction framework and its performance. The analysis strategy, event selection, and signal–background discrimination are presented in Section VI, and systematic uncertainties are discussed in Section VII. The results and their interpretation are given in Section VIII, and the conclusions are summarized in Section IX.

The CRT Beam Telescope and the BNB

Operating at the surface, SBND is instrumented with plastic scintillator panels forming the CRT [12] system, which tags and rejects cosmic backgrounds. A total of twenty-four CRT modules were installed in the SBND detector hall in 2017, prior to the installation of the cryostat.

The basic unit of the CRT is a polystyrene scintillator strip, in which charged particles produce scintillation photons. The light is collected by two wavelength-shifting fibers glued into grooves along the long edges of the strip and guided to its readout end, where each fiber is coupled to a Hamamatsu S12825-050P silicon photomultiplier (SiPM) [13]. The relative signal amplitudes of the SiPM pairs provide position information within the module. Each module is read out by a dedicated front-end board that biases, amplifies, and digitizes the SiPM signals and provides event timestamps with $\sim1$ ns precision; further details of the design are given in [12, 14].

Each CRT module consists of sixteen strips and measures approximately 272 cm in length, 96 cm in width, and 2 cm in thickness. The modules are grouped into two panels oriented perpendicular to the beam direction and separated by 9.26 m, forming the upstream and downstream panels of the SBND CRT Beam Telescope (Figure 1). Each panel contains both horizontally and vertically oriented modules; a coincidence is formed when overlapping horizontal and vertical modules register signals within a narrow time window ($\sim20$ ns), providing a two-dimensional hit position. With a timing resolution of $\sim1.5$ ns, the CRT enables precise temporal coincidence measurements between the upstream and downstream panels.

The upstream panel (approximately 23.5 m$^2$) consists of eighteen modules, while the downstream panel (approximately 7.8 m$^2$) consists of six modules. Both panels are centered with respect to each other along the beam direction. The CRT Beam Telescope uses a right-handed coordinate system where the $x$-axis is perpendicular to the neutrino beam direction, the $y$-axis is vertical, and the $z$-axis follows the beam direction.

The hypothetical LLPs and other particles detectable by the CRT Beam Telescope are produced using the BNB. The BNB at Fermilab produces neutrinos by colliding protons with a kinetic energy of 8 GeV into a beryllium target [2]. Secondary mesons produced in the collisions, primarily pions and kaons, are focused (or de-focused) by the electromagnetic horn depending on their charge polarity. When positive mesons are focused with the horn, before entering and decaying in a 45 m long pipe, this gives rise to a neutrino-enhanced beam, referred to as neutrino mode. A 4 m thick steel absorber is placed at the end of the decay region to stop most remaining particles, with the exception of neutrinos. In neutrino mode, the beam composition is approximately $\sim93.5\%$ $\nu_\mu$, $\sim6\%$ $\bar{\nu}_\mu$, $\sim0.45\%$ $\nu_e$, and $\sim0.05\%$ $\bar{\nu}_e$ [15], with neutrino energies peaking at approximately 800 MeV. The BNB runs 7 m below ground and parallel to the Earth’s surface. After the absorber, neutrinos produced in the beamline must travel an additional 60 m through the ground to reach the SBND detector building.

The beam is delivered in pulses of 1.6 $\mu$s duration with a rate of $\sim5$ Hz, and a typical intensity of $\sim5 \times10^{12}$ protons per pulse. The data used in this analysis were collected in neutrino mode.

LLP Signal Modeling and Simulation

As described in the previous section, the roughly ten-meter separation between the detector panels defines a decay volume. As such, the CRT Beam Telescope is naturally suited to search for LLPs that are produced upstream and decay in flight between the panels. We focus on a specific subclass of LLP searches: scenarios in which an SM neutrino upscatters in the material upstream of the detector into a BSM particle state. This exotic particle will then subsequently decay with a macroscopic decay length. This phenomenon is predicted in “dark neutrino” models and many associated scenarios [10, 11, 16, 17, 18]. A diagram demonstrating this two-step process is provided in Figure 2.

As a benchmark, we consider an LLP signal with the following parameters:

The parameter $U_{\mu N}$ denotes the coupling strength between the SM muon neutrino and the LLP, and $\varepsilon$ parametrizes the kinetic mixing of the dark mediator $Z'$. These parameter values define the signal kinematics and detector acceptance for this benchmark scenario. For this set of parameters, the inclusive cross section for an SM neutrino to upscatter into the LLP $N$ in the surrounding material, including both coherent scattering off nuclei and incoherent elastic scattering off nucleons, is approximately $2 \times10^{-38}$ cm$^2$, provided $E_\nu\gtrsim1$ GeV — the energy range that dominates LLP production which is boosted enough to be detected in our detector. With these coupling strengths, the LLP decay length $c\tau$ is calculated to be 3.1 m, after which the LLP decays off-shell into the $e^{+}e^{-}\nu$ final state.

In this work we focus on fixed values of $m_N$ and $m_{Z'}$, while allowing the inclusive upscattering cross section $\sigma(\nu A \to NX)$, where $A$ and $X$ are the target nucleus before and after scattering, and the LLP decay length to vary as free parameters. Because we focus on decays of the LLP into electron-positron pairs and our detector is insensitive to neutrinos, we are only sensitive to the product of the production cross section and the branching ratio for $N \to e^{+}e^{-}+E_{\mathrm{miss}}$, $\sigma(\nu A \to NX) \times\operatorname{Br}(N \to e^{+}e^{-}+E_{\mathrm{miss}})$.

This approach allows reinterpretation for BSM scenarios sharing similar production and decay phenomenology. This includes scenarios with multiple dark neutrinos, such as those in which a heavier state $N_5$ decays as $N_5 \to N_4 e^{+}e^{-}$, provided that $N_4$ is sufficiently light that the visible decay kinematics and detector acceptance remain similar to those of the benchmark considered here. Dedicated DarkNews studies indicate that, for $m_N \lesssim600$ MeV, the neutrino-energy dependence of the upscattering cross section is only weakly affected by the choice of $m_N$ once above the production threshold, supporting the applicability of these limits over this mass range. The final results are presented as exclusion limits in the plane of LLP decay length versus effective production rate.

Simulation Details

The LLP production is performed using the DarkNews package [19], which focuses on specific model-based scenarios in the BSM parameter space. In what follows, to ensure a more generic analysis, we allow the LLP decay length and its production cross section to vary independently. We find that as long as the LLP mass is small relative to the BNB neutrino energy ($\mathcal{O}(100)$ MeV) and the BSM mediator $Z^\prime$ is relatively heavy ($\gtrsim$ GeV), this generic approach applies broadly.

DarkNews generates events using a set of neutrino fluxes by flavor provided as a one-dimensional distribution in neutrino energy. Owing to the large transverse extent of the CRT Beam Telescope and the collimated nature of the beam, the neutrino flux varies significantly across the detector surface. This well-known off-axis effect [15] is accounted for by generating multiple off-axis neutrino flux distributions from a full flux simulation [2], adapted to the detector location along the beamline and provided as inputs to DarkNews for event generation.

Signal samples with different LLP decay lengths are generated by applying event-by-event weights to the benchmark model with an unboosted decay length $c\tau= 3.1$ m. For each decay length considered, the scaling factor used to reweight each simulated event is calculated as:

where $\gamma= E_N/m_N$, $\beta= \sqrt{1 - 1/\gamma^2}$, $l$ is the tested decay length in the rest frame, $l^\prime$ is the tested decay length in the lab frame, and $l_{\mathrm{benchmark}}$ is the decay length in the rest frame in the benchmark model. The decay lengths are chosen to span the region of parameter space in which a decay can occur within the geometric acceptance of the CRT Beam Telescope. Six signal samples are generated, with decay lengths of 0.31, 1, 3.1, 10, 50, and 100 m.

Background Characterization

The dominant backgrounds for this analysis come from neutrino interactions in the soil and building material surrounding the detector, and from cosmogenic activity. Neutrinos interacting around the CRT panels can produce secondary particles that then interact with the CRT, mimicking an LLP signature. We simulate neutrino interactions on surrounding materials of the SBND detector hall using the GENIE neutrino event generator (v3.00.06p G1810a0211a) [20, 21]. A total of approximately $2.78 \times10^{21}$ POT equivalent neutrino interactions, corresponding to 9 times the total beam telescope dataset statistics, were simulated to model the expected background. These simulated interactions are used to estimate neutrino-induced backgrounds relevant for this analysis.

The propagation of simulated particles, as well as the energy deposition in the scintillators, are simulated using the GEANT4 particle propagation toolkit (version v4.10.6.p01d) [22] with the QGSP_BERT_HP physics list [23]. The deposited energy simulated by GEANT4 is then passed to a custom CRT Beam Telescope detector simulation within sbndcode v09.59.00 [24] to model the charge response and timing. Once the charge signal exceeds a predefined threshold and satisfies the coincidence requirement between vertical and horizontal modules (as described in Section II), a trigger is simulated and events with the corresponding waveform amplitude and timing information are recorded, thus mimicking real data acquisition. This particle transport and detector simulation is also applied identically to our simulated signal events.

The second dominant background arises from cosmogenic activity. Rather than relying on simulation, this background is estimated directly from data using an independent sample. The CRT data acquisition window is 1 s in duration, which is much larger than the 1.6 $\mu$s BNB spill window. Since LLP decays are expected to occur either approximately in temporal coincidence, or after the BNB spill, a 1.6 $\mu$s time window immediately preceding the neutrino beam spill is selected as a background-only region, as it is free from both neutrino-induced interactions and potential LLP signals. CRT activity measured in this pre-spill window is used to estimate both the cosmogenic background and the accidental cosmogenic veto rate for signal events, the latter of which is found to be negligible and has a minimal impact on the signal efficiency. The cosmogenic background is statistically subtracted from all distributions presented in this paper. This approach provides a fully data-driven determination of the cosmic-ray background, avoiding any dependence on external simulations.

Event Reconstruction

This section describes how data and simulated events are reconstructed for use in the downstream analysis.

A CRT hit is formed by combining signals from two strips of different orientation (vertical and horizontal), and is characterized by its time of arrival and signal amplitude, from which timing, position, and deposited energy are subsequently derived. The position within each strip is determined by weighting according to the charge ratio measured by the two SiPMs. The overlapping geometry of the vertical and horizontal modules can produce combinatorial ambiguities when forming hit candidates. didates from multiple coincident strip signals. Several horizontal–vertical module combinations may therefore be reconstructed, where only one corresponds to the true particle crossing. This effect is intrinsic to the detector geometry and increases with strip multiplicity. Identifying the correct combination is challenging, and an incorrect pair may be selected; such misreconstructed candidates are referred to as “fake hits.” The selection of a fake hit in place of the true one, however, has little impact on the downstream analysis, which is largely insensitive to the specific pairing chosen.

The resulting distribution for the downstream panel is shown in Figure 4, comparing data to the simulated neutrino background broken down by particle type. Beam-induced muons from neutrino interactions in the surrounding soil are the dominant background and exhibit the characteristic minimum-ionizing behavior, while protons deposit considerably more energy. The CRT provides sufficient separation between minimum-ionizing particles and protons for the purposes of this analysis.

After the position is reconstructed, corrections for both charge and timing are applied to account for detector effects. The reconstructed CRT hit positions in the $x$–$y$ plane for the upstream panel are shown in Figure 3, where a clear beam profile is visible. We note that the distribution of hits in the downstream panel is more spatially uniform due to the angular spread of charged particles produced by neutrinos interacting with the surrounding soil and concrete, and the fact that the downstream panel detects particles from interactions that are on average farther away from the panel than those interacting with the upstream panel. Moreover, as illustrated in Figure 3, the center of the beamline is located approximately 100 cm above the top of the CRT Beam Telescope detector setup. This results in an off-axis configuration where the detector observes neutrinos from approximately $0.5^\circ$ to $2.5^\circ$ relative to the beam direction as measured from the target. Such detector position relative to the neutrino beam determines the geometric acceptance for LLP searches. The deposited energy is then evaluated from the calibrated hit amplitudes, with calibration applied to account for detector effects and ensure consistency between data and simulation. Calibration uses crossing tracks, corrected for incident angle, to recalibrate the energy loss per unit length from simulation to data. The resulting distribution for the downstream panel is shown in Figure 4, comparing data to the simulated neutrino background broken down by particle type.

Reconstruction performance has been validated using a sample of cosmic muons, which provide well-understood minimum-ionizing tracks traversing both CRT panels, and are used to verify the timing and position reconstruction.

Event Selection and Background Discrimination

The signal, illustrated in Figure 5, consists of an LLP produced via neutrino upscattering in material upstream of the detector, which subsequently decays into an $e^+e^-$ pair. We require no activity in the upstream panel, which serves as a veto against neutrino-induced background. This requirement has minimal impact on signal efficiency — signal LLPs are defined as those decaying between the two panels, whose decay products do not traverse the upstream panel — while significantly reducing neutrino-induced background. We refer to this requirement as the Upstream Veto cut.

Monte Carlo simulation of our benchmark signal shows that 89% of events consist of a single hit in the downstream panel, 8% of two hits, and 3% of more than two hits. This indicates that in most cases only one of the outgoing leptons intersects the downstream CRT, reflecting the interplay between the decay kinematics and the detector geometry. For a 400 MeV LLP, the distribution of the $e^{+}e^{-}$ opening angle peaks at $33^\circ$. This relatively large opening angle, combined with the $\sim100$ cm vertical offset between the beam axis and the center of the CRT panels (Figure 3), results in most events having only one decay product intercepting the downstream panel. While single-hit events comprise the majority of the signal events, they are largely overwhelmed by the beam-induced muon background, which, as can be seen in Figure 4, dominates all energy depositions when no constraints are applied. Requiring two hits substantially suppresses this background, and as such defines the second cut used in this analysis (Two-Hit Requirement). The remaining 3.0% of events arise from additional $e^{+}$ interactions in the CRT that produce extra hits, and are excluded from this analysis.

Finally, motivated by comparing the hit separation distance distributions for simulated signal and background, which reveals a large excess below 22 cm arising from neutrino interactions occurring inside the CRT itself and producing activity in adjacent CRT strips, we apply a Minimum Separation cut, requiring a distance greater than 22 cm between the two selected hits.

These three cuts — Upstream Veto, Two-Hits requirement, and Minimum Separation — form the minimal selection criteria to remove the most obvious neutrino-induced backgrounds. Since the cosmogenic background is measured directly from data and is statistically subtracted, the remaining dominant background is neutrino interaction events, which the analysis focuses on rejecting. According to our benchmark model simulation, the minimal selection cuts reject approximately 99.86% of the simulated background sample, leaving 767 background events and 16 signal events for $2.95 \times10^{20}$ POT.

While the background rejection is high, the purity of our sample is still only 2%, necessitating further background discrimination. This is achieved through a multivariate discrimination method using a Boosted Decision Tree (BDT).

The BDT is trained on position, timing, and deposited energy information from the CRT, using the Toolkit for Multivariate Data Analysis (TMVA) package [25]. A separate BDT is trained for each LLP decay length considered in the analysis, using 50% of the available signal and background statistics, with the remaining 50% reserved for statistical inference and final result extraction. The following variables are used as input to the BDT:

• The distance between the two hits.

• The horizontal distance between the two hits.

• The timing difference between the two hits.

• The mean deposited energy of the two hits.

Figure 6 shows the distributions of these variables for a signal LLP with a mass of 400 MeV and a decay length of 3.1 m, as well as for the simulated neutrino background, after applying the minimal selections. Good agreement is observed between the background prediction and data for all variables, in both shape and normalization. Although no individual variable exhibits strong discriminating power on its own, the BDT exploits correlations among the input variables to capture higher-dimensional information, achieving the required separation. The resulting score distribution is then used directly in the final statistical analysis, detailed in Section VIII.

Systematic Uncertainties

Systematic uncertainties are evaluated for the simulated background prediction by comparing variations to the central value (CV) simulation sample. We consider the impact of neutrino flux simulation, neutrino interaction modeling, and detector modeling.

To assess the uncertainties on the neutrino flux prediction, the flux simulation from the MiniBooNE Collaboration is utilized [2, 26], updated to the SBND CRT Beam Telescope location. For neutrino cross section modeling uncertainties, we use the event reweighting framework provided by GENIE [27]. For both cross section and flux systematics, we generate many MC replicas, called “universes,” where parameters in the models are varied within their uncertainties. Each universe represents a different reweighting. The simultaneous reweighting of all model parameters allows the correct treatment of correlations among them. We create $N$ such universes that can be combined to construct a covariance matrix:

where $b$ is a shorthand notation for the BDT score distribution, $i$ and $j$ are bin numbers, $b_i^{\mathrm{CV}}$ is the predicted count in the CV BDT score bin $i$, and $b_i^n$ is the predicted count in the universe $n$ BDT score bin $i$. This method produces two covariance matrices, one for the neutrino flux and one for the neutrino interaction systematic. In the case of the flux, an additional 2% uncertainty is added to account for POT counting uncertainty [2]. These matrices are then passed to the statistical analysis framework, described in Section VIII.

As detector model systematics are dominated by single detector parameters and are not possible to estimate through reweighting, a different procedure is used for this set of systematics uncertainties. The parameters used to simulate the CRT charge and timing response are derived from data and their uncertainties propagate to uncertainties in the detector modeling.

To assess this source of systematic uncertainty, BDT score variations are generated by independently shifting each parameter by $\pm1\sigma$, assuming no correlations, and running a new simulation that outputs BDT score distributions from new background sample variations generated with the new parameters. These distributions are then used as input to the statistical analysis framework, described in Section VIII.

The impact of flux and detector modeling systematic uncertainties on the signal are assessed in a dedicated limit-extraction study by assigning the signal the same fractional uncertainties as the background. As these uncertainties were found to have a negligible effect on the extracted limit, they are not included in the reported result.

The flux, neutrino interaction, and detector systematic uncertainties on the background, integrated over all BDT score bins, are summarized in Table I, along with the contribution from each individual source.

Source of Uncertainty	Relative Uncertainty [%]
Detector Modeling	16
Neutrino Interaction	16
Neutrino Flux	7
Sample Statistics	5
Total	25

Results and Discussion

The BDT score distributions for three representative LLP decay lengths after all selection criteria are shown in Figure 7. The red curves illustrate the signal+background hypothesis, where the expected LLP signal is normalized to the 99% Confidence Level ($CL$) excluded yield and added to the background. The signal hypothesis predicts an enhancement of $\sim171$–$217$ events (depending on decay length) relative to the 763.2 expected background events, which would manifest as a visible upturn in the rightmost bins of the distribution. The binning is chosen to balance statistical precision and discrimination of shape differences between signal and background, while avoiding bins with very low expected event counts. Alternative binning schemes were tested and found to yield consistent limits within statistical uncertainties.

A small upward fluctuation is observed in the high-BDT-score region (BDT $> -0.2$), where LLP decays would preferentially accumulate. A goodness-of-fit test yields $p$-values of 0.65, 0.86, and 0.71 for decay lengths of 1 m, 3.1 m, and 10 m, confirming consistency with the background-only hypothesis. No statistically significant excess is observed, and the absence of such an excess allows us to set exclusion limits.

The statistical interpretation of the results follows a modified frequentist ($CL_s$) approach [28, 29, 30], implemented using the pyhf [31, 32] framework. At each LLP decay length, the pyhf package uses the BDT score distribution and scales the signal to set an upper limit on LLP production.

The test statistic is defined using the log-likelihood ratio (LLR), which compares the signal-plus-background (S+B) hypothesis to the background-only (B) hypothesis. The $p$-values $CL_{S+B}$ and $CL_B$ are derived by integrating the LLR distribution under each hypothesis. A signal is excluded at 90% when

Systematic uncertainties on the background prediction are incorporated as nuisance parameters with Gaussian constraints. pyhf takes as input the deformations of the central-value spectrum and uses them to build template variations that parameterize the effect of each systematic uncertainty in the likelihood. For detector modeling, the variations described in Section VII are directly incorporated into pyhf.

For neutrino flux and neutrino interaction model systematics, bin-to-bin correlations are instead encoded in the covariance matrix defined in Eq. (3). Since pyhf only takes deformations of the spectrum, a principal component analysis (PCA) method [33, 34] is applied, which decomposes the covariance matrix into a set of orthogonal eigenmodes. After PCA decomposition, only the most significant principal components, with eigenvalues larger than 0.5% of the leading eigen-value, are retained as nuisance parameters in pyhf. These components are then passed to pyhf as shape variations of the CV spectrum.

The signal model used to determine exclusion limits assumes a specific neutrino upscattering cross section for LLP production and a specific branching ratio for the LLP decay into $e^+e^-$ with missing energy. The upper limit on the signal therefore constrains an effective cross section, derived from the product $\sigma(\nu A \to NX) \times\operatorname{Br}(N \to e^+e^- + E_{\mathrm{miss}})$.

The observed and median expected 90% $CL$ limits on the signal strength are shown versus LLP decay length in Figure 8. We see that the SBND CRT Beam Telescope enables exclusions for LLPs with $\mathcal{O}(\mathrm{m})$ decay lengths — this can be achieved in dark neutrino scenarios, especially ones with additional features such as other BSM states and/or interactions [11]. The resulting exclusions reach effective cross sections of order $\sim5 \times10^{-39}\ \mathrm{cm}^2$ at their strongest. To illustrate the interpretation of these limits in specific dark-neutrino scenarios [10, 35], Figure 8 also shows representative model trajectories obtained by varying the kinetic-mixing parameter $\varepsilon$, for which the upscattering cross section scales as $\varepsilon^2$ while the dark neutrino lifetime scales approximately as $\varepsilon^{-2}$. The trajectories assume a dark-neutrino mass of 400 MeV, a dark gauge boson mass of 1.25 GeV, and a fixed mixing $|U_{\mu4}|^2 = 4 \times10^{-6}$ between the SM muon neutrino and the dark neutrino. The minimal 3 + 1 scenario lies below the sensitivity of this search for this benchmark, while a representative 3 + 2 scenario, in which the dark neutrino of mass $m_5$ decays into a lighter dark neutrino of mass $m_4$ through a coupling of the same strength, extends into the region probed by this analysis for a relative mass splitting $\Delta\equiv(m_5 - m_4)/m_4 \simeq20\%$.

Several robustness checks were performed to assess the stability of the extracted limits. These include variations of the BDT score threshold, alternative binning configurations of the BDT distribution, and the exclusion of individual systematic uncertainty sources from the fit. In all cases, the resulting limits were found to be consistent within the expected statistical and systematic variations, demonstrating that the sensitivity is not dominated by a single analysis choice or systematic effect. As discussed above, the sensitivity is maximized for meter-scale decay lengths, reflecting the finite decay volume and geometric acceptance of the CRT Beam Telescope.

While these limits are weaker than those obtained in model-specific searches such as MicroBooNE [36], which probe both prompt and long-lived dark-neutrino decay regimes, the present search provides a complementary approach. As shown in Figure 8, this search focuses on LLPs produced via neutrino upscattering in surrounding material and decaying at macroscopic distances, providing coverage of meter-scale decay lengths (0.3–100 m) using displaced decay signatures.

Conclusions

In this work, we present a search for LLPs using data collected with the SBND CRT Beam Telescope exposed to the BNB at Fermilab. The analysis targets LLPs produced via neutrino upscattering in surrounding material and decaying at macroscopic distances into visible final states, using timing, spatial and calorimetric information from the CRT system operating in a standalone configuration.

Using a data set corresponding to $2.95 \times10^{20}$ POT, we set 90% CL upper limits on a generic class of LLPs produced via neutrino upscattering and decaying exclusively into an $e^{+}e^{-} + E_{\mathrm{miss}}$ final state. No statistically significant deviation from the background-only hypothesis is observed in the data. LLPs with laboratory decay lengths on the order of meters are excluded at the 90% $CL$ for effective production cross sections at the level of $10^{-37}$–$10^{-39}\ \mathrm{cm}^{2}$, depending on the assumed decay length in the range 0.3–100 m.

This analysis constitutes the first physics beyond the Standard Model search performed with SBND data, and uses the subset of CRT modules as a standalone detector for LLP searches. Although the resulting exclusions are limited by the geometric acceptance and the event information available in the CRT-only configuration, the close proximity of SBND to the BNB target enables meaningful sensitivity, demonstrating the feasibility of performing LLP searches with detector subsystems not originally designed for this purpose.

Building on the present analysis, future studies using data from the full SBND detector and combining information from the liquid argon TPC, CRT, and photon detection systems could extend these exclusions to a broader range of LLP decay lengths and topologies.

Acknowledgments

This document was prepared by the SBND Collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, Office of High Energy Physics HEP User Facility. Fermilab is managed by Fermi-Forward Discovery Group, LLC, acting under Contract No. 89243024CSC000002. The SBND Collaboration acknowledges the generous support of the following organizations: the U.S. Department of Energy, Office of Science, Office of High Energy Physics; the U.S. National Science Foundation; Los Alamos National Laboratory for LDRD funding, the Science and Technology Facilities Council (STFC), part of United Kingdom Research and Innovation (UKRI), the UKRI Future Leaders Fellowship (grant number MR/V022407/1), and The Royal Society; the Swiss National Science Foundation; the Spanish Ministerio de Ciencia, Innovación y Universidades (MI-CIU/ AEI/ 10.13039/ 501100011033) under grants No PRE2019-090468, CNS2022-136022, RYC2022-036471-I, PID2023-147949NB-C51 & C53 and Comunidad de Madrid (PEJ-2023-AI/COM-28399); the European Union’s Horizon 2020 research and innovation program under GA no 101004761 and the Marie Sklodowska-Curie grant agreements No 822185, 101081478, and 101003460; the São Paulo Research Foundation 1098 (FAPESP), the National Council of Scientific and Technological Development (CNPq) and Ministry of Science, Technology & Innovations-MCTI of Brazil; the Minas Gerais research foundation (FAPEMIG), grants APQ-00544-23 and APQ-01249-24; the Anusandhan National Research Foundation (ANRF, India) under the Ramanujan Fellowship (Grant No. RJF/2025/000203). An award of computer time was provided by the ASCR Leadership Computing Challenge (ALCC) program. This research used resources of the Argonne Leadership Computing Facility, which is a U.S. Department of Energy Office of Science User Facility operated under contract DE-AC02-06CH11357.

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