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Prospects for beyond the Standard Model physics searches at the Deep Underground Neutrino Experiment

DUNE Collaboration

A preprint version of the article is available at arXiv.

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. 78.1, 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.

Table 1 LArTPC ND properties used in some of the BSM physics analyses

Neutrino beam assumptions

The analyses described in Sects. 345, 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. 345, 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:

$$\begin{aligned} 1 - P(\nu _{\mu } \rightarrow \nu _s)&\approx 1 - \cos ^4\theta _{14}\cos ^2\theta _{34}\sin ^{2}2\theta _{24}\sin ^2{\varDelta }_{41} \nonumber \\&\quad - \sin ^2\theta _{34}\sin ^22\theta _{23}\sin ^2{\varDelta }_{31} \nonumber \\&\quad + \frac{1}{2}\sin \delta _{24}\sin \theta _{24}\sin 2\theta _{23}\sin {\varDelta }_{31}, \end{aligned}$$
(1)

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:

$$\begin{aligned} P(\nu _{\mu } \rightarrow \nu _{\mu })&\approx 1 - \sin ^22\theta _{23}\sin ^2{\varDelta }_{31} \nonumber \\&\quad + 2\sin ^22\theta _{23}\sin ^2\theta _{24}\sin ^2{\varDelta }_{31} \nonumber \\&\quad - \sin ^22\theta _{24}\sin ^2{\varDelta }_{41}. \end{aligned}$$
(2)

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

$$\begin{aligned} P(\overset{(-)}{\nu }_e \rightarrow \overset{(-)}{\nu }_e)&\approx 1 - \sin ^22\theta _{13}\sin ^2{\varDelta }_{31} \nonumber \\&\quad - \sin ^22\theta _{14}\sin ^2{\varDelta }_{41}. \end{aligned}$$
(3)

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.

Fig. 1
figure1

Regions of L/E probed by the DUNE detector compared to 3-flavor and \(3+1\)-flavor neutrino disappearance and appearance probabilities. The gray-shaded areas show the range of true neutrino energies probed by the ND and FD. The top axis shows true neutrino energy, increasing from right to left. The top plot shows the probabilities assuming mixing with one sterile neutrino with \({\varDelta }m^2_{\mathrm{41}}=0.05 \, {\text {eV}}^2\), corresponding to the slow oscillations regime. The middle plot assumes mixing with one sterile neutrino with \({\varDelta }m^2_{\mathrm{41}}=0.5 \, {\text {eV}}^2\), corresponding to the intermediate oscillations regime. The bottom plot includes mixing with one sterile neutrino with \({\varDelta }m^2_{\mathrm{41}}=50 \, {\text {eV}}^2\), corresponding to the rapid oscillations regime. As an example, the slow sterile oscillations cause visible distortions in the three-flavor \(\nu _\mu \)  survival probability (blue curve) for neutrino energies \(\sim 10 \, {\text {GeV}}\), well above the three-flavor oscillation minimum

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.

Table 2 List of systematic errors assumed in the sterile neutrino studies

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

$$\begin{aligned} R^c(E,E')\equiv \frac{1}{\sigma (E)\sqrt{2\pi }}e^{-\frac{(E-E')^2}{2(\sigma (E))^2}}, \end{aligned}$$
(4)

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.

Fig. 2
figure2

The top plot shows the DUNE sensitivities to \(\theta _{14}\) from the \(\nu _e\) CC samples at the ND and FD, along with a comparison with the combined reactor result from Daya Bay and Bugey-3. The bottom plot is adapted from Ref. [18] and displays sensitivities to \(\theta _{24}\) using the \(\nu _\mu \) CC and NC samples at both detectors, along with a comparison with previous and existing experiments. In both cases, regions to the right of the contours are excluded

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

$$\begin{aligned} \begin{aligned} |U_{\mu 4}|^2 =&\,\,\cos ^2\theta _{14}\sin ^2\theta _{24} \\ |U_{\tau 4}|^2=&\,\,\cos ^2\theta _{14}\cos ^2\theta _{24}\sin ^2\theta _{34}, \end{aligned} \end{aligned}$$
(5)

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.

Fig. 3
figure3

Comparison of the DUNE sensitivity to \(\theta _{34}\) using the NC samples at the ND and FD with previous and existing experiments. Regions to the right of the contour are excluded

Fig. 4
figure4

DUNE sensitivities to \(\theta _{\mu e}\) from the appearance and disappearance samples at the ND and FD are shown on the top plot, along with a comparison with previous existing experiments and the sensitivity from the future SBN program. Regions to the right of the DUNE contours are excluded. The plot is adapted from Ref. [18]. In the bottom plot, the ellipse displays the DUNE discovery potential assuming \(\theta _{\mu e}\) and \({\varDelta }m_{41}^2\) set at the best-fit point determined by LSND [19] (represented by the star) for the best-case scenario referenced in the text

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

$$\begin{aligned} N = \left\lgroup \begin{array}{ccc} 1-\alpha _{ee} &{} 0 &{} 0 \\ \alpha _{\mu e} &{} 1-\alpha _{\mu \mu } &{} 0 \\ \alpha _{\tau e} &{} \alpha _{\tau \mu } &{} 1-\alpha _{\tau \tau } \end{array} \right\rgroup U , \end{aligned}$$
(6)

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.

Table 3 Expected \(90\%\) CL constraints on the non-unitarity parameters \(\alpha \) from DUNE

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) [54] plug-in to cross validate our results.

Fig. 5
figure5

The impact of non-unitarity on the DUNE CPV discovery potential. See the text for details

Fig. 6
figure6

Expected frequentist allowed regions at the \(1 \sigma \), \(90\%\) and \(2\sigma \) CL for DUNE. All new physics parameters are assumed to be zero so as to obtain the expected non-unitarity sensitivities. A value \(\theta _{23} = 0.235 \pi \approx 0.738\) rad is assumed. The solid lines correspond to the analysis of DUNE data alone, while the dashed lines include the present constraints on non-unitarity. The values of \(\theta _{23}\) are shown in radians

Conversely, the presence of non-unitarity may affect the determination of the Dirac charge parity (CP)-violating phase \(\delta _{CP}\) in LBL experiments [50, 52, 53]. Indeed, when allowing for unitarity deviations, the expected CP discovery potential for DUNE could be significantly reduced. However, the situation is alleviated when a combined analysis with the constraints on non-unitarity from other experiments is considered. This is illustrated in Fig. 5. In the left panel, the discovery potential for charge-parity symmetry violation (CPV) is computed when the non-unitarity parameters introduced in Eq. (6) are allowed in the fit. While for the Asimov data all \(\alpha _{ij}=0\), the non-unitary parameters are allowed to vary in the fit with \(1 \sigma \) priors of \(10^{-1}\), \(10^{-2}\) and \(10^{-3}\) for the dotted green, dashed blue and solid black lines respectively. For the dot-dashed red line no prior information on the non-unitarity parameters has been assumed. As can be observed, without additional priors on the non-unitarity parameters, the capabilities of DUNE to discover CPV from \(\delta _{CP}\) would be seriously compromised [52]. However, with priors of order \(10^{-2}\) matching the present constraints from other neutrino oscillation experiments [31, 52], the sensitivity expected in the three-flavor model is almost recovered. If the more stringent priors of order \(10^{-3}\) stemming from flavor and electroweak precision observables are added [46, 53], the standard sensitivity is obtained.

The right panel of Fig. 5 concentrates on the impact of the phase of the element \(\alpha _{\mu e}\) in the discovery potential of CPV from \(\delta _{CP}\), since this element has a very important impact in the \(\nu _e\) appearance channel. In this plot the modulus of \(\alpha _{ee}\), \(\alpha _{\mu \mu }\) and \(\alpha _{\mu e}\) have been fixed to \(10^{-1}\), \(10^{-2}\), \(10^{-3}\) and 0 for the dot-dashed red, dotted green, dashed blue and solid black lines respectively. All other non-unitarity parameters have been set to zero and the phase of \(\alpha _{\mu e}\) has been allowed to vary both in the fit and in the Asimov data, showing the most conservative curve obtained. As for the right panel, it can be seen that a strong deterioration of the CP discovery potential could be induced by the phase of \(\alpha _{\mu e}\) (see Ref. [52]). However, for unitarity deviations of order \(10^{-2}\), as required by present neutrino oscillation data constraints, the effect is not too significant in the range of \(\delta _{CP}\) for which a \(3 \sigma \) exclusion of CP conservation would be possible and it becomes negligible if the stronger \(10^{-3}\) constraints from flavor and electroweak precision data are taken into account.

Similarly, the presence of non-unitarity worsens degeneracies involving \(\theta _{23}\), making the determination of the octant or even its maximality challenging. This situation is shown in Fig. 6 where an input value of \(\theta _{23} = 42.3^\circ \) was assumed. As can be seen, the fit in presence of non-unitarity (solid lines) introduces degeneracies for the wrong octant and even for maximal mixing [31]. However, these degeneracies are resolved upon the inclusion of present priors on the non-unitarity parameters from other oscillation data (dashed lines) and a clean determination of the standard oscillation parameters following DUNE expectations is again recovered.

Fig. 7
figure7

Allowed regions of the non-standard oscillation parameters in which we see important degeneracies (top) and the complex non-diagonal ones (bottom). We conduct the analysis considering all the NSI parameters as non-negligible. The sensitivity regions are for 68% CL [red line (left)], 90% CL [green dashed line (middle)], and 95% CL [blue dotted line (right)]. Current bounds are taken from [78]

The sensitivity that DUNE would provide to the non-unitarity parameters is comparable to that from present oscillation experiments, while not competitive to that from flavor and electroweak precision observables, which are roughly an order of magnitude more stringent. On the other hand, the capability of DUNE to determine the standard oscillation parameters such as CPV from \(\delta _{CP}\) or the octant or maximality of \(\theta _{23}\) would be seriously compromised by unitarity deviations in the PMNS matrix. This negative impact is however significantly reduced when priors on the size of these deviations from other oscillation experiments are considered, and disappears altogether if the more stringent constraints from flavor and electroweak precision data are added instead.

Non-standard neutrino interactions

Non-standard neutrino interactions (NSI), affecting neutrino propagation through the Earth, can significantly modify the data to be collected by DUNE as long as the new physics parameters are large enough [55]. Leveraging its very long baseline and wide-band beam, DUNE is uniquely sensitive to these probes. NSI may impact the determination of current unknowns such as CPV [56, 57], mass hierarchy [58, 59] and octant of \(\theta _{23}\) [60]. If the DUNE data are consistent with the standard oscillation for three massive neutrinos, off-diagonal NC NSI effects of order 0.1 \(G_F\) can be ruled out at the 68 to 95% CL [61, 62]. We note that DUNE might improve current constraints on \(|\epsilon ^m_{e \tau }|\) and \(|\epsilon ^m_{e \mu }|\), the electron flavor-changing NSI intensity parameters (see Eq. 8), by a factor 2-5 [55, 63, 64]. New CC interactions can also lead to modifications in the production, at the beam source, and the detection of neutrinos. The findings on source and detector NSI studies at DUNE are presented in [65, 66], in which DUNE does not have sensitivity to discover or to improve bounds on source/detector NSI. In particular, the simultaneous impact on the measurement of \(\delta _{\mathrm{CP}}\) and \(\theta _{23}\) is investigated in detail. Depending on the assumptions, such as the use of the ND and whether NSI at production and detection are the same, the impact of source/detector NSI at DUNE may be relevant. We focus our attention on the propagation, based on the results from [65].

NC NSI can be understood as non-standard matter effects that are visible only in an FD at a sufficiently long baseline. They can be parameterized as new contributions to the matter potential in the Mikheyev–Smirnov–Wolfenstein effect (MSW) [67,68,69,70,71,72] matrix in the neutrino-propagation Hamiltonian:

$$\begin{aligned} H = U \left( \begin{array}{ccc} 0 &{} &{} \\ &{} {\varDelta }m_{21}^2/2E &{} \\ &{} &{} {\varDelta }m_{31}^2/2E \end{array} \right) U^\dag + {\tilde{V}}_{\mathrm{MSW}} , \end{aligned}$$
(7)

with

$$\begin{aligned} {\tilde{V}}_{\mathrm{MSW}} = \sqrt{2} G_F N_e \left( \begin{array}{ccc} 1 + \epsilon ^m_{ee} &{} \epsilon ^m_{e\mu } &{} \epsilon ^m_{e\tau } \\ \epsilon ^{m*}_{e\mu } &{} \epsilon ^m_{\mu \mu } &{} \epsilon ^m_{\mu \tau } \\ \epsilon ^{m*}_{e\tau } &{} \epsilon ^{m*}_{\mu \tau } &{} \epsilon ^m_{\tau \tau } \end{array} \right) \end{aligned}$$
(8)

Here, U is the standard PMNS leptonic mixing matrix, for which we use the standard parameterization found, e.g., in [73], and the \(\epsilon \)-parameters give the magnitude of the NSI relative to standard weak interactions. For new physics scales of a few hundred GeV, a value of \(|\epsilon |\) of the order 0.01 or less is expected [74,75,76]. The DUNE baseline provides an advantage in the detection of NSI relative to existing beam-based experiments with shorter baselines. Only atmospheric-neutrino experiments have longer baselines, but the sensitivity of these experiments to NSI is limited by systematic effects [77].

In this analysis, we use GLoBES with the MonteCUBES C library, a plugin that replaces the deterministic GLoBES minimizer by a Markov Chain Monte Carlo (MCMC) method that is able to handle higher dimensional parameter spaces. In the simulations we use the configuration for the DUNE TDR [1]. Each point scanned by the MCMC is stored and a frequentist \(\chi ^2\) analysis is performed with the results. The analysis assumes an exposure of \(300~\text {kt} \, \cdot \, \text {MW} \cdot \, \text {year} \).

In an analysis with all the NSI parameters free to vary, we obtain the sensitivity regions in Fig. 7. We omit the superscript m that appears in Eq. (8). The credible regions are shown for different confidence levels. We note, however, that constraints on \(\epsilon _{\tau \tau }-\epsilon _{\mu \mu }\) coming from global fit analysis [55, 64, 78, 79] can remove the left and right solutions of \(\epsilon _{\tau \tau }-\epsilon _{\mu \mu }\) in Fig. 7.

In order to constrain the standard oscillation parameters when NSI are present, we use the fit for three-neutrino mixing from [78] and implement prior constraints to restrict the region sampled by the MCMC. The sampling of the parameter space is explained in [62] and the priors that we use can be found in Table 4.

Table 4 Oscillation parameters and priors implemented in MCMC for calculation of Fig. 7

The effects of NSI on the measurements of the standard oscillation parameters at DUNE are explicit in Fig. 8, where we superpose the allowed regions with non-negligible NSI and the standard-only credible regions at 90% CL. In the blue filled areas we assume only standard oscillation. In the regions delimited by the red, black dashed, and green dotted lines we constrain standard oscillation parameters allowing NSI to vary freely.

An important degeneracy appears in the measurement of the mixing angle \(\theta _{23}\). Notice that this degeneracy appears because of the constraints obtained for \(\epsilon _{\tau \tau }-\epsilon _{\mu \mu }\) shown in Fig. 7. We also see that the sensitivity of the CP phase is strongly affected.

Fig. 8
figure8

Projections of the standard oscillation parameters with nonzero NSI. The sensitivity regions are for 68, 90, and 95% CL. The allowed regions considering negligible NSI (standard oscillation (SO) at 90% CL) are superposed to the SO + NSI

The effects of matter density variation and its average along the beam path from Fermilab to SURF were studied considering the standard neutrino oscillation framework with three flavors [80, 81]. In order to obtain the results of Figs. 7 and 8, we use a high-precision calculation for the baseline of \(1285 \, \text {km}\) and the average density of \(2.848 \, {\text {g/cm}}^{3}\) [80].

The DUNE collaboration has been using the so-called PREM [82, 83] density profile to consider matter density variation. With this assumption, the neutrino beam crosses a few constant density layers. However, a more detailed density map is available for the USA with more than 50 layers and \(0.25 \times 0.25\) degree cells of latitude and longitude: The Shen–Ritzwoller or S.R. profile [80, 84]. Comparing the S.R. with the PREM profiles, Ref. [81] shows that in the standard oscillation paradigm, DUNE is not highly sensitive to the density profile and that the only oscillation parameter with its measurement slightly impacted by the average density true value is \(\delta _{\mathrm{CP}}\) . NSI, however, may be sensitive to the profile, particularly considering the phase \(\phi _{e\tau }\) [85], where \(\epsilon _{e\tau }=|\epsilon _{e\tau }|e^{i\phi _{e\tau }}\), to which DUNE will have a high sensitivity [55, 61,62,63,64], as we also see in Fig. 7.

In order to compare the results of our analysis predictions for DUNE with the constraints from other experiments, we use the results from [55]. There are differences in the nominal parameter values used for calculating the \(\chi ^2\) function and other assumptions. This is the reason why the regions in Fig. 9 do not have the same central values, but this comparison gives a good view of how DUNE can substantially improve the bounds on, for example, \(\varepsilon _{\tau \tau }-\varepsilon _{\mu \mu }\), \({\varDelta }m^2_{31}\), and the non-diagonal NSI parameters.

Fig. 9
figure9

One-dimensional DUNE constraints compared with current constraints calculated in Ref. [55]. The left half of the figure shows constraints on the standard oscillation parameters, written in the bottom of each comparison. The five comparisons in the right half show constraints on non-standard interaction parameters

NSI can significantly impact the determination of current unknowns such as CPV and the octant of \(\theta _{23}\). Clean determination of the intrinsic CP phase at LBL experiments, such as DUNE, in the presence of NSI, is a formidable task [86]. A feasible strategy to disambiguate physics scenarios at DUNE using high-energy beams was suggested in [87]. The conclusion here is that, using a tunable beam, it is possible to disentangle scenarios with NSI. Constraints from other experiments can also solve the NSI induced degeneracy on \(\theta _{23}\).

CPT and Lorentz violation

Charge, parity, and time reversal symmetry (CPT) is a cornerstone of our model-building strategy. DUNE can improve the present limits on Lorentz and CPT violation by several orders of magnitude [88,89,90,91,92,93,94,95], contributing as a very important experiment to test these fundamental assumptions underlying quantum field theory.

CPT invariance is one of the predictions of major importance of local, relativistic quantum field theory. One of the predictions of CPT invariance is that particles and antiparticles have the same masses and, if unstable, the same lifetimes. To prove the CPT theorem one needs only three ingredients [88]: Lorentz invariance, hermiticity of the Hamiltonian, and locality.

Experimental bounds on CPT invariance can be derived using the neutral kaon system [96]:

$$\begin{aligned} \frac{|m(K^0) - m({\overline{K}}^0)|}{m_K} < 0.6 \times 10^{-18}. \end{aligned}$$
(9)

This result, however, should be interpreted very carefully for two reasons. First, we do not have a complete theory of CPT violation, and it is therefore arbitrary to take the kaon mass as a scale. Second, since kaons are bosons, the term entering the Lagrangian is the mass squared and not the mass itself. With this in mind, we can rewrite the previous bound as: \( |m^2(K^0) - m^2({\overline{K}}^0)| < 0.3~\text{ eV}^2 \, \). Modeling CPT violation as differences in the usual oscillation parameters between neutrinos and antineutrinos, we see here that neutrinos can test the predictions of the CPT theorem to an unprecedented extent and could, therefore, provide stronger limits than the ones regarded as the most stringent ones to date.Footnote 3

In the absence of a solid model of flavor, not to mention one of CPT violation, the spectrum of neutrinos and antineutrinos can differ both in the mass eigenstates themselves as well as in the flavor composition of each of these states. It is important to notice then that neutrino oscillation experiments can only test CPT in the mass differences and mixing angles. An overall shift between the neutrino and antineutrino spectra will be missed by oscillation experiments. Nevertheless, such a pattern can be bounded by cosmological data [97]. Unfortunately direct searches for neutrino mass (past, present, and future) involve only antineutrinos and hence cannot be used to draw any conclusion on CPT invariance on the absolute mass scale, either. Therefore, using neutrino oscillation data, we will compare the mass splittings and mixing angles of neutrinos with those of antineutrinos. Differences in the neutrino and antineutrino spectrum would imply the violation of the CPT theorem.

In Ref. [93] the authors derived the most up-to-date bounds on CPT invariance from the neutrino sector using the same data that was used in the global fit to neutrino oscillations in Ref. [98]. Of course, experiments that cannot distinguish between neutrinos and antineutrinos, such as atmospheric data from Super-Kamiokande [99], IceCube-DeepCore [100, 101] and ANTARES [102] were not included. The complete data set used, as well as the parameters to which they are sensitive, are (1) from solar neutrino data [103,104,105,106,107,108,109,110,111,112]: \(\theta _{12}\), \({\varDelta }m_{21}^2\), and \(\theta _{13}\); (2) from neutrino mode in LBL experiments K2K [113], MINOS [114, 115], T2K [116, 117], and NO\(\nu \)A [118, 119]: \(\theta _{23}\), \({\varDelta }m_{31}^2\), and \(\theta _{13}\); (3) from KamLAND reactor antineutrino data [120]: \({\overline{\theta }}_{12}\), \({\varDelta }{\overline{m}}_{21}^2\), and \({\overline{\theta }}_{13}\); (4) from short-baseline reactor antineutrino experiments Daya Bay [121], RENO [122], and Double Chooz [123]: \({\overline{\theta }}_{13}\) and \({\varDelta }{\overline{m}}_{31}^2\); and (5) from antineutrino mode in LBL experiments MINOS [114,