## Abstract

The Deep Underground Neutrino Experiment (DUNE) will be a powerful tool for a variety of physics topics. The high-intensity proton beams provide a large neutrino flux, sampled by a near detector system consisting of a combination of capable precision detectors, and by the massive far detector system located deep underground. This configuration sets up DUNE as a machine for discovery, as it enables opportunities not only to perform precision neutrino measurements that may uncover deviations from the present three-flavor mixing paradigm, but also to discover new particles and unveil new interactions and symmetries beyond those predicted in the Standard Model (SM). Of the many potential beyond the Standard Model (BSM) topics DUNE will probe, this paper presents a selection of studies quantifying DUNE’s sensitivities to sterile neutrino mixing, heavy neutral leptons, non-standard interactions, CPT symmetry violation, Lorentz invariance violation, neutrino trident production, dark matter from both beam induced and cosmogenic sources, baryon number violation, and other new physics topics that complement those at high-energy colliders and significantly extend the present reach.

## Introduction

The Deep Underground Neutrino Experiment (DUNE) is a next-generation, long-baseline (LBL) neutrino oscillation experiment, designed to be sensitive to \(\nu _\mu \) to \(\nu _e \) oscillation. The experiment consists of a high-power, broadband neutrino beam, a powerful precision near detector (ND) complex located at Fermi National Accelerator Laboratory, in Batavia, Illinois, USA, and a massive liquid argon time-projection chamber (LArTPC) far detector (FD) located at the 4850 ft level of Sanford Underground Research Facility (SURF), in Lead, South Dakota, USA. The baseline of 1285 km provides sensitivity, in a single experiment, to all parameters governing LBL neutrino oscillation. The deep underground location of the FD facilitates sensitivity to nucleon decay and other rare processes including low-energy neutrino detection enabling, for instance, observation of neutrinos from a core-collapse supernova.

Owing to the high-power proton beam facility, the ND consisting of precision detectors capable of off-axis data taking and the massive FD, DUNE provides enormous opportunities to probe phenomena beyond the SM traditionally difficult to reach in neutrino experiments. Of such vast, rich physics topics that profoundly expand those probed in the past neutrino experiments, this paper reports a selection of studies of DUNE’s sensitivity to a variety of BSM particles and effects, initially presented in the physics volume of the DUNE Technical Design Report (TDR) [1] recently made available. Some of these phenomena impact the LBL oscillation measurement, while others may be detected by DUNE using specific analyses.

Section 2 describes some of the common assumptions and tools used in these analyses. Section 3 discusses sensitivity to sterile neutrinos, Sect. 4 looks into the effect of non-unitary of the neutrino mixing matrix, Sect. 5 describes sensitivity to non-standard neutrino interactions, Sect. 6 discusses sensitivity to CPT and Lorentz violation, Sect. 7 describes the sensitivity to new physics by measuring neutrino trident production, Sect. 8 discusses various dark matter searches that could be performed by DUNE, Sect. 9 describes sensitivity to baryon number violation by one and two units, and Sect. 10 lists some other possible avenues for BSM physics searches.

These studies reveal that DUNE can probe a rich and diverse BSM phenomenology at the discovery level, as in the case of searches for dark matter created in the high-power proton beam interactions and from cosmogenic sources, or by significantly improving existing constraints, as in the cases of sterile neutrino mixing, non-standard neutrino interactions, CPT violation, new physics enhancing neutrino trident production, and nucleon decay.

## Analysis details

The BSM searches presented in this paper span a wide variety of physics topics and techniques. The analyses rely on neutrino beam data taken at the ND and/or FD, atmospheric or other astrophysical sources of neutrinos, or signal from the detector material itself, as in nucleon decay searches. This section summarizes some of the common assumptions and tools used in the analyses, with more details provided in the following sections.

### Detector assumptions

The DUNE FD will consist of four \(10 \, \text {kt}\) fiducial mass LArTPC modules with integrated photon detection systems (PD systems) [2,3,4]. In these analyses, we assume all four modules have identical responses. All of the analyses described will use data from the FD, except for the analyses presented in Sects. 7, 8.1, and 10.3, which use data exclusively from the ND.

The ND will be located at a distance of \(574 \, \text {m}\) from the target. The ND concept consists of a modular LArTPC, a magnetized high-pressure gas argon TPC and a beam monitor. The combination of the first two detectors is planned to be movable to sample the off-axis neutrino spectrum to reduce flux uncertainties, a concept called DUNE-PRISM [1]. Since the ND configuration, however, was not yet finalized at the time these studies were performed, we adopted only the LArTPC component of the detector and its fiducial volume. In the analyses presented here, the LArTPC is assumed to be \({7} \, \text {m}\) wide, \({3} \, \text {m}\) high, and \({5} \, \text {m}\) long. The fiducial volume is assumed to include the detector volume up to 50 cm of each face of the detector. The ND properties are given in Table 1. The signal and background efficiencies vary with the physics model being studied. Detailed signal and background efficiencies for each physics topic are discussed along with each analysis.

### Neutrino beam assumptions

The analyses described in Sects. 3, 4, 5, and 6 are based on analysis of neutrino beam data at both the ND and FD. The DUNE neutrino beam is produced using protons from Fermilab’s Main Injector and a traditional horn-focusing system [5]. The polarity of the focusing magnets may be reversed to produce a neutrino- or antineutrino-dominated beam. This optimized beam configuration includes a three-horn focusing system with a 1 m long target embedded within the first horn and a decay pipe with \(194 \, \text {m}\) length and \(4 \, \text {m}\) diameter. The neutrino flux produced by this beamline is simulated at a distance of \(574 \, \text {m}\) downstream of the neutrino target for the ND and \(1285 \, \text {km}\) for the FD. Fluxes have been generated for both neutrino mode and antineutrino mode using G4LBNF [1, 6], a Geant4-based simulation [7,8,9].

Results based on beam neutrino data are given for a \(300~\text {kt} \, \cdot \, \text {MW} \cdot \, \text {year} \) exposure. With the current deployment plan [1], this exposure will be achieved in approximately 7 years once the beam is operational. For results not based on beam data, the exposure is given in units of \(\text {kt} \, \cdot \, \text {year}\) in each relevant section.

### Tools

In the analyses presented in Sects. 3, 4, 5, and 6, the simulation of the DUNE experimental setup was performed with the General Long-Baseline Experiment Simulator (GLoBES) software [10, 11]. Unless otherwise noted, the neutrino fluxes used in the BSM physics analysis are the same as those used in the DUNE LBL three-flavor analysis [1]. The configuration of the beam used in ND analyses is assumed to be a 120 GeV proton beam with 1.2 MW beam power at 56% uptime, providing \(1.1\times 10^{21}\) POT/year. Cross-section files describing neutral current (NC) and charged current (CC) interactions with argon are generated using Generates Events for Neutrino Interaction Experiments (GENIE) [12, 13] version 2.8.4. The true-to-reconstructed smearing matrices and the selection efficiency as a function of energy for various signal and background modes are generated using nominal DUNE MC simulation. A \(40 \, \text {kt}\) fiducial mass is assumed for the FD, exposed to a \(120 \, \text {GeV}\), \(1.2 \, \text {MW}\) beam. The \(\nu _{e}\) and \({{\bar{\nu }}}_{e}\) appearance signal modes have independent normalization uncertainties of \(2\%\) each, while \(\nu _{\mu }\) and \({\bar{\nu }}_{\mu }\) disappearance signal modes have independent normalization uncertainties of \(5\%\). The background normalization uncertainties range from 5 to \(20\%\) and include correlations among various sources of background. More details can be found in Ref. [1].

The neutrino trident search presented in Sect. 7 and the baryon number violation analyses presented in Sect. 9 use samples of simulated and reconstructed signal and background events, produced using standard DUNE detection simulation and reconstruction software. Further details are given in those sections.

For analyses that use neither GLoBES nor the standard DUNE simulation and reconstruction software, such as the dark matter analyses described in Sect. 8 and several of the analyses described in Sect. 10, details are given in the relevant sections.

## Sterile Neutrino Mixing

Experimental results in tension with the three-neutrino-flavor paradigm, which may be interpreted as mixing between the known active neutrinos and one or more sterile states, have led to a rich and diverse program of searches for oscillations into sterile neutrinos [14, 15]. DUNE is sensitive over a broad range of potential sterile neutrino mass splittings by looking for disappearance of CC and NC interactions over the long distance separating the ND and FD, as well as over the short baseline of the ND. With a longer baseline, a more intense beam, and a high-resolution large-mass FD, compared to previous experiments, DUNE provides a unique opportunity to improve significantly on the sensitivities of the existing probes, and greatly enhance the ability to map the extended parameter space if a sterile neutrino is discovered. In the sterile neutrino mixing studies presented here, we assume a minimal 3+1 oscillation scenario with three active neutrinos and one sterile neutrino, which includes a new independent neutrino mass-squared difference, \({\varDelta }m^2_{41}\), and for which the mixing matrix is extended with three new mixing angles, \(\theta _{14}\), \(\theta _{24}\), \(\theta _{34}\), and two additional phases \(\delta _{14}\) and \(\delta _{24}\).

Disappearance of the beam neutrino flux between the ND and FD results from the quadratic suppression of the sterile mixing angle measured in appearance experiments, \(\theta _{\mu e}\), with respect to its disappearance counterparts, \(\theta _{\mu \mu }\approx \theta _{24}\) for LBL experiments, and \(\theta _{ee}\approx \theta _{14}\) for reactor experiments. These disappearance effects have not yet been observed and are in tension with appearance results [14, 15] when global fits of all available data are carried out. The exposure of DUNE’s high-resolution FD to the high-intensity LBNF beam will also allow direct probes of non-standard electron (anti)neutrino appearance.

DUNE will look for active-to-sterile neutrino mixing using the reconstructed energy spectra of both NC and CC neutrino interactions in the FD, and their comparison to the extrapolated predictions from the ND measurement. Since NC cross sections and interaction topologies are the same for all three active neutrino flavors, the NC spectrum is insensitive to standard neutrino mixing. However, should there be oscillations into a fourth light neutrino, an energy-dependent depletion of the neutrino flux would be observed at the FD, as the sterile neutrino would not interact in the detector volume. Furthermore, if sterile neutrino mixing is driven by a large mass-square difference \({\varDelta }m^2_{{\mathrm{41}}} \, \sim 1\, {\text {eV}}^{2}\), the CC spectrum will be distorted at energies higher than the energy corresponding to the standard oscillation maximum. Therefore, CC disappearance is also a powerful probe of sterile neutrino mixing at long baselines.

We assume the mixing matrix augmented with one sterile state is parameterized by \(U=R_{34}S_{24}S_{14}R_{23}S_{13}R_{12}\) [16], where \(R_{ij}\) is the rotational matrix for the mixing angle \(\theta _{ij}\), and \(S_{ij}\) represents a complex rotation by the mixing angle \(\theta _{ij}\) and the *CP*-violating phase \(\delta _{ij}\). At long baselines the NC disappearance probability to first order for small mixing angles is then approximated by:

where \({\varDelta }_{ji} = \frac{{\varDelta }m^2_{ji}L}{4E}\). The relevant oscillation probability for \(\nu _\mu \) CC disappearance is the \(\nu _\mu \) survival probability, similarly approximated by:

Finally, the disappearance of \(\overset{(-)}{\nu }_e\) CC is described by:

Figure 1 shows how the standard three-flavor oscillation probability is distorted at neutrino energies above the standard oscillation peak when oscillations into sterile neutrinos are included.

The sterile neutrino effects have been implemented in GLoBES via the existing plug-in for sterile neutrinos and non-standard interactions [17]. As described above, the ND will play a very important role in the sensitivity to sterile neutrinos both directly, for rapid oscillations with \({\varDelta }m_{41}^2 > 1 \, {\text {eV}}^2\) where the sterile oscillation matches the ND baseline, and indirectly, at smaller values of \({\varDelta }m_{41}^2\) where the ND is crucial to reduce the systematic uncertainties affecting the FD to increase its sensitivity. To include these ND effects in these studies, the most recent GLoBES DUNE configuration files describing the FD were modified by adding a ND with correlated systematic errors with the FD. As a first approximation, the ND is assumed to be an identical scaled-down version of the TDR FD, with identical efficiencies, backgrounds and energy reconstruction. The systematic uncertainties originally defined in the GLoBES DUNE conceptual design report (CDR) configuration already took into account the effect of the ND constraint. Thus, since we are now explicitly simulating the ND, larger uncertainties have been adopted but partially correlated between the different channels in the ND and FD, so that their impact is reduced by the combination of both data sets. The full set of systematic uncertainties employed in the sterile neutrino studies is listed in Table 2.

Finally, for oscillations observed at the ND, the uncertainty on the production point of the neutrinos can play an important role. We have included an additional \(20\%\) energy smearing, which produces a similar effect given the *L*/*E* dependence of oscillations. We implemented this smearing in the ND through multiplication of the migration matrices provided with the GLoBES files by an additional matrix with the \(20\%\) energy smearing obtained by integrating the Gaussian

with \(\sigma (E)=0.2 E\) in reconstructed energy \(E'\), where *E* is the true neutrino energy from simulation.

By default, GLoBES treats all systematic uncertainties included in the fit as normalization shifts. However, depending on the value of \({\varDelta }m^2_{41}\), sterile mixing will induce shape distortions in the measured energy spectrum beyond simple normalization shifts. As a consequence, shape uncertainties are very relevant for sterile neutrino searches, particularly in regions of parameter space where the ND, with virtually infinite statistics, has a dominant contribution. The correct inclusion of systematic uncertainties affecting the shape of the energy spectrum in the two-detector fit GLoBES framework used for this analysis posed technical and computational challenges beyond the scope of the study. Therefore, for each limit plot, we present two limits bracketing the expected DUNE sensitivity limit, namely: the black limit line, a best-case scenario, where only normalization shifts are considered in a ND + FD fit, where the ND statistics and shape have the strongest impact; and the grey limit line, corresponding to a worst-case scenario where only the FD is considered in the fit, together with a rate constraint from the ND.

Studying the sensitivity to \(\theta _{14}\), the dominant channels are those regarding \(\nu _e\) disappearance. Therefore, only the \(\nu _e\) CC sample is analyzed and the channels for NC and \(\nu _{\mu }\) CC disappearance are not taken into account, as they do not influence greatly the sensitivity and they slow down the simulations. The sensitivity at the 90% confidence level (CL), taking into account the systematic uncertainties mentioned above, is shown in Fig. 2, along with a comparison to current constraints.

For the \(\theta _{24}\) mixing angle, we analyze the \(\nu _{\mu }\) CC disappearance and the NC samples, which are the main contributors to the sensitivity. The results are shown in Fig. 2, along with comparisons with present constraints.

In the case of the \(\theta _{34}\) mixing angle, we look for disappearance in the NC sample, the only contributor to this sensitivity. The results are shown in Fig. 3. Further, a comparison with previous experiments sensitive to \(\nu _\mu \), \(\nu _\tau \) mixing with large mass-squared splitting is possible by considering an effective mixing angle \(\theta _{\mu \tau }\), such that \(\sin ^2{2\theta _{\mu \tau }}\equiv 4|U_{\tau 4}|^2|U_{\mu 4}|^2=\cos ^4\theta _{14}\sin ^22\theta _{24}\sin ^2\theta _{34}\), and assuming conservatively that \(\cos ^4\theta _{14}=1\), and \(\sin ^22\theta _{24}=1\). This comparison with previous experiments is also shown in Fig. 3. The sensitivity to \(\theta _{34}\) is largely independent of \({\varDelta }m^2_{41}\), since the term with \(\sin ^2\theta _{34}\) in Eq. (1), the expression describing \({P(\nu _{\mu }\rightarrow \nu _s)}\), depends solely on the \({\varDelta }m^2_{31}\) mass splitting.

Another quantitative comparison of our results for \(\theta _{24}\) and \(\theta _{34}\) with existing constraints can be made for projected upper limits on the sterile mixing angles assuming no evidence for sterile oscillations is found, and picking the value of \({\varDelta }m^2_{41} = 0.5 \, {\text {eV}}^2\) corresponding to the simpler counting experiment regime. For the \(3+1\) model, upper limits of \(\theta _{24}\, < \, 1.8^{\circ } \, (15.1^{\circ })\) and \(\theta _{34}\, < \, 15.0^{\circ } \, (25.5^{\circ })\) are obtained at the 90% CL from the presented best(worst)-case scenario DUNE sensitivities. If expressed in terms of the relevant matrix elements

these limits become \(|U_{\mu 4}|^{2} \, < \,0.001\) (0.068) and \(|U_{\tau 4}|^{2} \, < \,0.067\) (0.186) at the 90% CL, where we conservatively assume \(\cos ^2\theta _{14} \,=\,1\) in both cases, and additionally \(\cos ^2\theta _{24} \,=\,1\) in the second case.

Finally, sensitivity to the \(\theta _{\mu e}\) effective mixing angle, defined as \(\sin ^2{2\theta _{\mu e}}\equiv 4|U_{e4}|^2|U_{\mu 4}|^2=\sin ^22\theta _{14}\sin ^2\theta _{24}\), is shown in Fig. 4, which also displays a comparison with the allowed regions from the Liquid Scintillator Neutrino Detector (LSND) and MiniBooNE, as well as with present constraints and projected constraints from the Fermilab Short-Baseline Neutrino (SBN) program.

As an illustration, Fig. 4 also shows DUNE’s discovery potential for a scenario with one sterile neutrino governed by the LSND best-fit parameters:

\(\left( {\varDelta }m_{41}^2= 1.2\;\text {eV}^2;\,\,\sin ^2{2\theta _{\mu e}}=0.003\right) \) [19]. A small 90% CL allowed region is obtained, which can be compared with the LSND allowed region in the same figure.

## Non-unitarity of the neutrino mixing matrix

A generic characteristic of most models explaining the neutrino mass pattern is the presence of heavy neutrino states, additional to the three light states of the SM of particle physics [20,21,22]. These types of models imply that the \(3 \times 3\) Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix is not unitary due to mixing with additional states. Besides the type-I seesaw mechanism [23,24,25,26], different low-scale seesaw models include right-handed neutrinos that are relatively not-so-heavy, with mass of 1–10 TeV [27], and perhaps detectable at collider experiments.

These additional heavy leptons would mix with the light neutrino states and, as a result, the complete unitary mixing matrix would be a squared \(n \times n\) matrix, with *n* the total number of neutrino states. Therefore, the usual \(3 \times 3\) PMNS matrix, which we dub *N* to stress its non-standard nature, will be non-unitary. One possible general way to parameterize these unitarity deviations in *N* is through a triangular matrix [28]^{Footnote 1}

with *U* representing the unitary PMNS matrix, and the \(\alpha _{ij}\) representing the non-unitary parameters.^{Footnote 2} In the limit where \(\alpha _{ij}=0\), *N* becomes the usual PMNS mixing matrix.

The triangular matrix in this equation accounts for the non-unitarity of the \(3 \times 3\) matrix for any number of extra neutrino species. This parameterization has been shown to be particularly well-suited for oscillation searches [28, 31] since, compared to other alternatives, it minimizes the departures of its unitary component *U* from the mixing angles that are directly measured in neutrino oscillation experiments when unitarity is assumed.

The phenomenological implications of a non-unitary leptonic mixing matrix have been extensively studied in flavor and electroweak precision observables as well as in the neutrino oscillation phenomenon [26, 28, 32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. For recent global fits to all flavor and electroweak precision data summarizing present bounds on non-unitarity see Refs. [46, 53].

Recent studies have shown that DUNE can constrain the non-unitarity parameters [31, 52]. The summary of the \(90 \%\) CL bounds on the different \(\alpha _{ij}\) elements profiled over all other parameters is given in Table 3.

These bounds are comparable with other constraints from present oscillation experiments, although they are not competitive with those obtained from flavor and electroweak precision data. For this analysis, and those presented below, we have used the GLoBES software [10, 11] with the DUNE TDR configuration presented in Ref. [1] and assumed a data exposure of \(300~\text {kt} \, \cdot \, \text {MW} \cdot \, \text {year} \). The standard (unitary) oscillation parameters have also been treated as in [1]. The unitarity deviations have been included both by an independent code (used to obtain the results shown in Ref. [52]) and via the Monte Carlo Utility Based Experiment Simulator (MonteCUBES) [