Long-baseline neutrino oscillation physics potential of the DUNE experiment

DUNE Collaboration


The sensitivity of the Deep Underground Neutrino Experiment (DUNE) to neutrino oscillation is determined, based on a full simulation, reconstruction, and event selection of the far detector and a full simulation and parameterized analysis of the near detector. Detailed uncertainties due to the flux prediction, neutrino interaction model, and detector effects are included. DUNE will resolve the neutrino mass ordering to a precision of 5\(\sigma \), for all \(\delta _{\mathrm{CP}}\) values, after 2 years of running with the nominal detector design and beam configuration. It has the potential to observe charge-parity violation in the neutrino sector to a precision of 3\(\sigma \) (5\(\sigma \)) after an exposure of 5 (10) years, for 50% of all \(\delta _{\mathrm{CP}}\) values. It will also make precise measurements of other parameters governing long-baseline neutrino oscillation, and after an exposure of 15 years will achieve a similar sensitivity to \(\sin ^{2} 2\theta _{13}\) to current reactor experiments.

A preprint version of the article is available at ArXiv.


The Deep Underground Neutrino Experiment (DUNE) is a next-generation, long-baseline neutrino oscillation experiment which will carry out a detailed study of neutrino mixing utilizing high-intensity \(\nu _\mu \) and \({\bar{\nu }}_\mu \) beams measured over a long baseline. \(\hbox {DUNE}\) is designed to make significant contributions to the completion of the standard three-flavor picture by measuring all the parameters governing \(\nu _1\)\(\nu _3\) and \(\nu _2\)\(\nu _3\) mixing in a single experiment. Its main scientific goals are the definitive determination of the neutrino mass ordering, the definitive observation of \(\hbox {charge-parity symmetry violation (CPV)}\) for more than 50% of possible true values of the charge-parity violating phase, \(\delta _{\mathrm{CP}}\), and precise measurement of oscillation parameters, particularly \(\delta _{\mathrm{CP}}\), \(\sin ^22\theta _{13}\), and the octant of \(\theta _{23}\). These measurements will help guide theory in understanding if there are new symmetries in the neutrino sector and whether there is a relationship between the generational structure of quarks and leptons [1]. Observation of \(\hbox {CPV}\) in neutrinos would be an important step in understanding the origin of the baryon asymmetry of the universe [2, 3].

The \(\hbox {DUNE}\) experiment will observe neutrinos from a high-power neutrino beam peaked at \(\sim \)2.5 GeV but with a broad range of neutrino energies, a \(\hbox {near detector (ND)}\) located at Fermi National Accelerator Laboratory, in Batavia, Illinois, USA, and a large \(\hbox {liquid argon time-projection}\) \(\hbox {chamber (LArTPC) far detector (FD)}\) located at the 4850 ft level of Sanford Underground Research Facility (SURF), in Lead, South Dakota, USA, 1285 km from the neutrino production point. The neutrino beam provided by \(\hbox {Long-Baseline Neutrino Facility (LBNF)}\) [4] is produced using protons from Fermilab’s Main Injector, which are guided onto a graphite target, and a traditional horn-focusing system to select and focus particles produced in the target [5]. The polarity of the focusing magnets can be reversed to produce a beam dominated by either muon neutrinos or muon antineutrinos. A highly capable \(\hbox {ND}\) will constrain many systematic uncertainties for the oscillation analysis. The 40-kt (fiducial) \(\hbox {FD}\) is composed of four 10 kt (fiducial) LArTPC modules [6,7,8]. The deep underground location of the \(\hbox {FD}\) reduces cosmogenic and atmospheric sources of background, which also provides sensitivity to nucleon decay and low-energy neutrino detection, for example, the possible observation of neutrinos from a core-collapse supernova [5].

The entire complement of neutrino oscillation experiments to date has measured five of the neutrino mixing parameters [9,10,11]: the three mixing angles \(\theta _{12}\), \(\theta _{23}\), and \(\theta _{13}\), and the two squared-mass differences \(\varDelta m^{2}_{21}\) and \(|\varDelta m^{2}_{31}|\), where \(\varDelta m^2_{ij} = m^2_{i} - m^{2}_{j}\) is the difference between the squares of the neutrino mass states in eV\(^{2}\). The neutrino mass ordering (i.e., the sign of \(\varDelta m^{2}_{31}\)) is unknown, though recent results show a weak preference for the normal ordering [12,13,14]. The value of \(\delta _{\mathrm{CP}}\) is not well known, though neutrino oscillation data are beginning to provide some information on its value [12, 15].

The oscillation probability of \(\nu _\mu \) \(\rightarrow \) \(\nu _e\) through matter in the standard three-flavor model and a constant density approximation is, to first order [16]:



$$\begin{aligned} a = \pm \frac{G_{\mathrm {F}}N_e}{\sqrt{2}} \approx \pm \frac{1}{3500~\mathrm {km}}\left( \frac{\rho }{3.0~\mathrm {g/cm}^{3}}\right) , \end{aligned}$$

\(G_{\mathrm {F}}\) is the Fermi constant, \(N_e\) is the number density of electrons in the Earth’s crust, \(\varDelta _{ij} = 1.267 \varDelta m^2_{ij} L/E_\nu \), L is the baseline in km, and \(E_\nu \) is the neutrino energy in GeV. Both \(\delta _{\mathrm{CP}}\) and a terms are positive for \(\nu _\mu \rightarrow \nu _e\) and negative for \(\bar{\nu }_\mu \rightarrow \bar{\nu }_e\) oscillations; i.e., a neutrino-antineutrino asymmetry is introduced both by \(\hbox {CPV}\) (\(\delta _{\mathrm{CP}}\)) and the matter effect (a). The origin of the matter effect asymmetry is simply the presence of electrons and absence of positrons in the Earth [17, 18]. The (anti-)electron neutrino appearance probability is shown in Fig. 1 at the \(\hbox {DUNE}\) baseline of \(1285\hbox { km}\) as a function of neutrino energy for several values of \(\delta _{\mathrm{CP}}\).

Fig. 1

The appearance probability at a baseline of \(1285\hbox { km}\), as a function of neutrino energy, for \(\delta _{\mathrm{CP}}\) = \(-\pi /2\) (blue), 0 (red), and \(\pi /2\) (green), for neutrinos (top) and antineutrinos (bottom), for normal ordering

\(\hbox {DUNE}\) has a number of features that give it unique physics reach, complementary to other existing and planned experiments [19,20,21]. Its broad-band beam makes it sensitive to the shape of the oscillation spectrum for a range of neutrino energies. \(\hbox {DUNE}\)’s relatively high energy neutrino beam enhances the size of the matter effect and will allow \(\hbox {DUNE}\) to measure \(\delta _{\mathrm{CP}}\) and the mass ordering simultaneously. The unique \(\hbox {LArTPC}\) detector technology will enhance the resolution on \(\hbox {DUNE}\)’s measurement of the value of \(\delta _{\mathrm{CP}}\), and along with the increased neutrino energy, gives \(\hbox {DUNE}\) a different set of systematic uncertainties to other experiments, making \(\hbox {DUNE}\) complementary with them.

This paper describes studies that quantify DUNE’s expected sensitivity to long-baseline neutrino oscillation, using the accelerator neutrino beam. Note that atmospheric neutrino samples would provide additional sensitivity to some of the same physics, but are not included in this work. The flux simulation and associated uncertainties are described in Sect. 2. Section 3 describes the neutrino interaction model and systematic variations. The near and far detector simulation, reconstruction, and event selections are described in Sects. 4 and 5, respectively, with a nominal set of event rate predictions given in Sect. 6. Detector uncertainties are described in Sect. 7. The methods used to extract oscillation sensitivities are described in Sect. 8. The primary sensitivity results are presented in Sect. 9. We present our conclusions in Sect. 10.

Neutrino beam flux and uncertainties

The expected neutrino flux is generated using G4LBNF [5, 22], a \(\hbox {Geant4}\)-based [23] simulation of the \(\hbox {LBNF}\) neutrino beam. The simulation uses a detailed description of the \(\hbox {LBNF}\) optimized beam design [5], which includes a target and horns designed to maximize sensitivity to \(\hbox {CPV}\) given the physical constraints on the beamline design.

Fig. 2

Neutrino fluxes at the \(\hbox {FD}\) for neutrino-enhanced, FHC, beam running (top) and antineutrino, RHC, beam running (bottom)

Neutrino fluxes for neutrino-enhanced, forward horn current (FHC), and antineutrino-enhanced, reverse horn current (RHC), configurations of \(\hbox {LBNF}\) are shown in Fig. 2. Uncertainties on the neutrino fluxes arise primarily from uncertainties in hadrons produced off the target and uncertainties in the design parameters of the beamline, such as horn currents and horn and target positioning (commonly called “focusing uncertainties”) [5]. Given current measurements of hadron production and \(\hbox {LBNF}\) estimates of alignment tolerances, flux uncertainties are approximately 8% at the first oscillation maximum and 12% at the second. These uncertainties are highly correlated across energy bins and neutrino flavors. The unoscillated fluxes at the \(\hbox {ND}\) and \(\hbox {FD}\) are similar, but not identical. The relationship is well understood, and flux uncertainties mostly cancel for the ratio of fluxes between the two detectors. Uncertainties on the ratio are dominated by focusing uncertainties and are \(\sim \) 1% or smaller except at the falling edge of the focusing peak (\(\sim \)4 GeV), where they rise to 2%. The rise is due to the presence of many particles which are not strongly focused by the horns in this energy region, which are particularly sensitive to focusing and alignment uncertainties. The near-to-far flux ratio and uncertainties on this ratio are shown in Fig. 3.

Fig. 3

Ratio of \(\hbox {ND}\) and \(\hbox {FD}\) fluxes show for the muon neutrino component of the \(\hbox {FHC}\) flux and the muon antineutrino component of the \(\hbox {RHC}\) flux (top) and uncertainties on the \(\hbox {FHC}\) muon neutrino ratio (bottom)

Beam-focusing and hadron-production uncertainties on the flux prediction are evaluated by reproducing the full beamline simulation many times with variations of the input model according to those uncertainties. The resultant uncertainty on the neutrino flux prediction is described through a covariance matrix, where each bin corresponds to an energy range of a particular beam mode and neutrino species, separated by flux at the \(\hbox {ND}\) and \(\hbox {FD}\). The output covariance matrix has \(208 \times 208\) bins, despite having only \(\sim \)30 input uncertainties. To reduce the number of parameters used in the fit, the covariance matrix is diagonalized, and each principal component is treated as an uncorrelated nuisance parameter. The 208 principal components are ordered by the magnitude of their corresponding eigenvalues, which is the variance along the principal component (eigenvector) direction, and only the first \(\sim \)30 are large enough that they need to be included. This was validated by including more flux parameters and checking that there was no significant change to the sensitivity for a small number of test cases. By the 10th principal component, the eigenvalue is 1% of the largest eigenvalue. As may be expected, the largest uncertainties correspond to the largest principal components as shown in Fig. 4. The largest principal component (component 0) matches the hadron production uncertainty on nucleon-nucleus interactions in a phase space region not covered by data. Components 3 and 7 correspond to the data-constrained uncertainty on proton interactions in the target producing pions and kaons, respectively. Components 5 and 11 correspond to two of the largest focusing uncertainties, the density of the target and the horn current, respectively. Other components not shown either do not fit a single uncertain parameter or may represent two or more degenerate systematics or ones that produce anti-correlations in neighboring energy bins.

Fig. 4

Select flux principal components are compared to specific underlying uncertainties from the hadron production and beam focusing models. Note that while these are shown as positive shifts, the absolute sign is arbitrary

Future hadron production measurements are expected to improve the quality of, and the resulting constraints on, these flux uncertainty estimates. Approximately 40% of the interactions that produce neutrinos in the \(\hbox {LBNF}\) beam simulation have no direct data constraints. Large uncertainties are assumed for these interactions. The largest unconstrained sources of uncertainty are proton quasielastic interactions and pion and kaon rescattering in beamline materials. The proposed EMPHATIC experiment [24] at Fermilab will be able to constrain quasielastic and low-energy interactions that dominate the lowest neutrino energy bins. The NA61 experiment at CERN has taken data that will constrain many higher energy interactions, and also plans to measure hadrons produced on a replica \(\hbox {LBNF}\) target, which would provide tight constraints on all interactions occurring in the target. A similar program at NA61 has reduced flux uncertainties for the T2K experiment from \(\sim \)10 to \(\sim \)5% [25]. Another proposed experiment, the \(\hbox {LBNF}\) spectrometer [26], would measure hadrons after both production and focusing in the horns to further constrain the hadron production uncertainties, and could also be used to experimentally assess the impact of shifted alignment parameters on the focused hadrons (rather than relying solely on simulation).

Neutrino interaction model and uncertainties

A framework for considering the impact of neutrino interaction model uncertainties on the oscillation analysis has been developed. The default interaction model is implemented in v2.12.10 of the \(\hbox {GENIE}\) generator [27, 28]. Variations in the cross sections are implemented in various ways: using \(\hbox {GENIE}\) reweighting parameters (sometimes referred to as “\(\hbox {GENIE}\) knobs”); with ad hoc weights of events that are designed to parameterize uncertainties or cross-section corrections currently not implemented within \(\hbox {GENIE}\); or through discrete alternative model comparisons. The latter are achieved through alternative generators, alternative \(\hbox {GENIE}\) configurations, or custom weightings, which made extensive use of the NUISANCE package [29] in their development.

The interaction model components and uncertainties can be divided into seven groups: (1) initial state, (2) hard scattering and nuclear modifications to the quasielastic, or one-particle one-hole (1p1h) process, (3) multinucleon, or two-particle two-hole (2p2h), hard scattering processes, (4) hard scattering in pion production processes, (5) higher invariant mass (W) and \(\hbox {neutral current (NC)}\) processes, (6) \(\hbox {final-state interactions (FSI)}\), (7) neutrino flavor dependent differences. Uncertainties are intended to reflect current theoretical freedom, deficiencies in implementation, and/or current experimental knowledge.

The default nuclear model in \(\hbox {GENIE}\) describing the initial state of nucleons in the nucleus is the Bodek–Ritchie global Fermi gas model [30]. There are significant deficiencies that are known in global Fermi gas models: these include a lack of consistent incorporation of the high-momentum tails in the nucleon momentum distribution that result from correlations among nucleons; the lack of correlation between location within the nucleus and momentum of the nucleon; and an incorrect relationship between momentum and energy of the off-shell, bound nucleon within the nucleus. They have also been shown to agree poorly with neutrino-nucleus scattering data [31]. \(\hbox {GENIE}\) modifies the nucleon momentum distribution empirically to account for short-range correlation effects, which populates the high-momentum tail above the Fermi cutoff, but the other deficiencies persist. Alternative initial state models, such as spectral functions [32, 33], the mean field model of GiBUU [34], or continuum random phase approximation (CRPA) calculations [35] may provide better descriptions of the nuclear initial state [36], but are not considered further here.

The primary uncertainties considered in 1p1h interactions (\(\nu _{l}+n \rightarrow l^{-}+p\), \(\bar{\nu }_{l}+p \rightarrow l^{+}+n\)) are the axial form factor of the nucleon and the nuclear screening—from the so-called \(\hbox {random phase approximation (RPA)}\) calculations—of low momentum transfer reactions. The Valencia group’s [37, 38] description of \(\hbox {RPA}\) comes from summation of \(W^\pm \) self-energy terms. In practice, this modifies the 1p1h (quasielastic) cross section in a non-trivial way, with associated uncertainties presented in Ref. [39], which were evaluated as a function of \(Q^2\). Here we use T2K’s 2017/8 parameterization of the Valencia RPA effect [12]. The shape of the correction and error is parameterized with a third-order Bernstein polynomial up to \(Q^2=1.2\text { GeV}^2\) where the form transitions to a decaying exponential. The BeRPA (Bernstein RPA) function has three parameters controlling the behavior at increasing \(Q^2\) (A, B and D), a fourth parameter (E) that controls the high-\(Q^2\) tail, and a fifth (U), which changes the position at which the behaviour changes from polynomial to exponential. The BeRPA parameterization modifies the central value of the model prediction, as decribed in Table 3. BeRPA parameters E and U are not varied in the analysis described here, the parameters A and B have a prefit uncertainty of 20%, and D has a prefit unertainty of 15%. The axial form factor parameterization we use, a dipole, is known to be inadequate [40]. However, the convolution of BeRPA uncertainties with the limited axial form factor uncertainties do provide more freedom as a function of \(Q