The preponderance of matter over antimatter in the early universe, the dynamics of the SNBs that produced the heavy elements necessary for life, and whether protons eventually decay — these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our universe, its current state, and its eventual fate. The DUNE is an international world-class experiment dedicated to addressing these questions.

Experiments carried out over the past half century have revealed that neutrinos are found in three states, or flavors, and can transform from one flavor into another. These results indicate that each neutrino flavor state is a mixture of three different nonzero mass states, and to date offer the most compelling evidence for physics beyond the standard model. In a single experiment, DUNE will enable a broad exploration of the three-flavor model of neutrino physics with unprecedented detail. Chief among its potential discoveries is that of matter-antimatter asymmetries (through the mechanism of charge-parity symmetry violation (CPV)) in neutrino flavor mixing — a step toward unraveling the mystery of matter generation in the early universe. Independently, determination of the unknown neutrino mass ordering and precise measurement of neutrino mixing parameters by DUNE may reveal new fundamental symmetries of nature.

Neutrinos emitted in the first few seconds of a core-collapse supernova carry with them the potential for great insight into the evolution of the universe. DUNE’s capability to collect and analyze this high-statistics neutrino signal from a supernova within the Milky Way would provide a rare opportunity to peer inside a newly formed neutron star and potentially witness the birth of a black hole.

Grand unified theories (GUTs), which attempt to describe the unification of the known forces, predict rates for proton decay that cover a range directly accessible with the next generation of large underground detectors such as the DUNE far detector. The experiment’s sensitivity to key proton decay channels will offer unique opportunities for the ground-breaking discovery of this phenomenon.

To achieve its goals, the international DUNE experiment, hosted by the U.S. Department of Energy’s Fermilab in Illinois, comprises three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermilab, (2) a massive FD situated $1.5\text{\,}\mathrm{km}$ underground at the SURF in South Dakota, and (3) a composite ND installed just downstream of the neutrino source. Figure  illustrates the layout of these components. The far detector, the subject of this TDR, will be a modular LArTPC with a fiducial (sensitive) mass of $40\text{\,}\mathrm{kt}$¹¹ 1 For comparison, this is nearly twice the mass of the Statue of Liberty and nearly four times that of the Eiffel Tower. ($40\text{\,}\mathrm{Gg}$) of LAr, a cryogenic liquid that must be kept at $88\text{\,}\,$K ($-185\text{\,}\mathrm{\SIUnitSymbolDegree}$C). This detector will be able to uniquely reconstruct neutrino interactions with image-like precision and unprecedented resolution [1].

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[ Configuration of the LBNF beam and the DUNE detectors]fig:lbnf Cartoon illustrating the configuration of the LBNF beamline at Fermilab, in Illinois, and the DUNE detectors in Illinois and South Dakota, separated by $1300\text{\,}\mathrm{k}\mathrm{m}$.

The LBNF project, also hosted by Fermilab, provides the beamline and the civil construction, called CF, for the DUNE experiment. The organization and management of LBNF is separate from that of the experiment; its design and construction are organized as a U.S. DOE/Fermilab project incorporating international partners.

The LBNF beamline at Fermilab will deliver the world’s most intense neutrino beam to the near and far detectors in an on-axis configuration. The upgrade to the Proton Improvement Plan II (PIP-II) [2], a leading-edge, superconducting, linear proton accelerator under construction at Fermilab, will deliver between $1.0$ and $1.2\text{\,}\mathrm{M}\mathrm{W}$ of proton beam power from the Fermilab Main Injector to LBNF, which will aim and focus the beam, whereupon the protons, in a wide energy band of $60\text{\,}\mathrm{GeV}120\text{\,}\mathrm{GeV}$, will collide with a high-power production target, creating a secondary beam from which the intense neutrino flux will emerge, traveling in the direction of the DUNE detectors (Figure ). A further planned upgrade of the accelerator complex could provide up to $2.4\text{\,}\mathrm{MW}$ of beam power by 2030, potentially extending the DUNE science reach. The upgrade will also increase the reliability of the Fermilab accelerator complex and provide the flexibility to produce customized beams tailored to specific scientific needs.

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[Neutrino beamline and DUNE near detector hall in Illinois ]fig:beamlineNeutrino beamline and DUNE near detector hall at Fermilab in Illinois

The intense, wide-band neutrino beam, the massive LArTPC detector at the far site, and the composite (i.e., multi-purpose) ND will provide a rich ancillary science program for the DUNE experiment, beyond its primary goals, including accelerator-based neutrino flavor-transition measurements with sensitivity to physics beyond the standard model, measurements of tau neutrino appearance, measurements of neutrino oscillation phenomena using atmospheric neutrinos, and a rich neutrino interaction physics program using the DUNE ND, including a wide range of measurements of neutrino cross sections, studies of nuclear effects, and searches for dark matter. Further advances in LArTPC technology during FD construction may open up possibilities to observe very low-energy phenomena such as solar neutrinos or even the diffuse supernova neutrino flux – measurements that require a sensitivity that is presently beyond our reach.

The DUNE collaboration is a global organization with more than $1000$ scientists and engineers from $31$ countries (Figure ). It represents the combination of several worldwide efforts that developed independent paths toward a next-generation long-baseline neutrino experiment over the last decade. DUNE was formed in April 2015, combining the strengths of the lbne project in the U.S. and the Long Baseline Neutrino Observatory (LBNO) project in Europe, adding many new international partners in the process. DUNE thus represents the convergence of a substantial fraction of the worldwide neutrino-physics community around the opportunity provided by the large investment planned by the U.S. DOE and Fermilab to support a significant expansion of the underground infrastructure at SURF in South Dakota and to create a megawatt neutrino-beam facility at Fermilab.

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[DUNE collaboration global map]fig:map2The international DUNE collaboration. Countries with DUNE membership are in light brown.

DUNE and LBNF have developed the strategy presented in this TDR to meet the requirements laid out in the report of the U.S. Particle Physics Project Prioritization Panel (P5) in 2014. The strategy also takes into account the recommendations of the European Strategy for Particle Physics (ESPP) adopted by the CERN Council in 2013, which classified the long-baseline neutrino program as one of the four scientific objectives requiring significant resources, sizable collaborations, and sustained commitment.

The P5 report [3] set the goal of determining leptonic CPV with a precision of three standard deviations ($3$$\,\sigma$) or greater (i.e., a precision of at least $0.03\text{\,}\%$ ), over more than $75\text{\,}\%$ of the range of possible values (0 through 2$\pi$) of the unknown CP-violating phase $\delta_{\rm CP}$. It is impossible to provide coverage of $100\text{\,}\%$ since CPV effects vanish as the value of $\delta_{\rm CP}$ approaches $0$ or $\pi$. Based partly on this goal, the report stated that “the minimum requirements to proceed are the identified capability to reach an exposure of $120\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{MW}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{MW}\text{${}\cdot{}$}\mathrm{year}}$$²² 2 $1\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{MW}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{MW}\text{${}\cdot{}$}\mathrm{year}}$$ is the amount of exposure a detector of target mass $1\text{\,}\mathrm{k}\mathrm{t}$ of LAr would get in one year using a $1\text{\,}\mathrm{M}\mathrm{W}$ proton beam to generate the neutrinos. Exposure increases linearly as each of the factors increases. by the 2035 time frame, the far detector situated underground with cavern space for expansion to at least $40\text{\,}\mathrm{kt}$ LAr fiducial volume, and $1.2\text{\,}\mathrm{M}\mathrm{W}$ beam power upgradable to multi-megawatt power. The experiment should have the demonstrated capability to search for supernova neutrino bursts (SNBs) and for proton decay, providing a significant improvement in discovery sensitivity over current searches for proton decay.”

Here we briefly address how the LBNF and DUNE project (LBNF/DUNE) strategy and designs will satisfiy each of these requirements and deliver a world-leading neutrino program. The following chapters and the other volumes of this TDR elaborate on these concepts, providing a full picture of this ambitious enterprise.

Reach at least $120\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{MW}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{MW}\text{${}\cdot{}$}\mathrm{year}}$$ exposure by the 2035 timeframe and $1.2\text{\,}\mathrm{MW}$ beam power: To reach the necessary precision on its measurements, DUNE will need to collect a few thousand neutrino interactions over a period of about ten years. The number of interactions is the product of (1) the intensity of the neutrino beam, (2) the probability that a neutrino will oscillate (approximately $0.02$), (3) the interaction cross section, and (4) the detector mass. Currently, the highest-power proton beam that a beam target can safely withstand is between $1$ and $2\text{\,}\mathrm{MW}$, which caps the achievable neutrino beam intensity. This points to a required a detector mass in the tens-of-kilotons range. The DUNE FD cryostats will hold $17.5\text{\,}\mathrm{kt}$ of LAr each, for a total of nearly $70\text{\,}\mathrm{k}\mathrm{t}$, of which at least $40\text{\,}\mathrm{kt}$ will be encompassed by the four detector modules as fiducial mass. Higher usable fractions of the total volume are under study.

Moreover, the DUNE concept builds on the notion that a highly-performant detector technology with excellent neutrino energy reconstruction and background rejection capabilities can optimize sensitivity and cost with an on-axis exposure to an intense, wide-band, conventional (magnetic horn-focused) beam. The current generation of long-baseline neutrino experiments have benefited from narrow-band beam characteristics associated with off-axis detector deployment, which offers a low background rate in both electron neutrino ($\nu_{e}$) appearance and muon neutrino ($\nu_{\mu}$) disappearance channels. However, this advantage comes at a cost of flux and spectral information relative to an on-axis detector configuration [1, 4].

Situated underground: Given the rate of cosmic rays at the surface ($165\text{\,}\mathrm{k}\mathrm{H}\mathrm{z}$) and the neutrino beam parameters, the ratio of neutrino events to cosmic rays would be less than one to a million and the discovery potential for DUNE’s oscillation physics goals would be vanishingly small. Roughly $1500\text{\,}\mathrm{m}$ underground at the SURF site, this ratio becomes slightly higher than 1, raising the discovery potential to a very achievable level. Supernova neutrinos have energies on the order of $100$ times lower than beam neutrinos, and despite the fact that they arrive in a few-second burst, would be nearly impossible to identify on the surface. A meaningful search for nucleon decay is not possible at the surface. All three of the experiment’s primary goals require significant overburden for the FD, which the SURF site provides.

Use of liquid argon (LAr): This requirement implies the use of the LArTPC technology, which enables finer resolution for kiloton-scale particle detectors than earlier technologies do. The enhanced resolution leads to greater efficiency in distinguishing signal events from background, which in turn leads to a reduction in the necessary size of the detector and potentially broadens the physics program. It is especially important for the long-baseline program with a wide-band neutrino beam. Additionally, the choice of LArTPC technology provides valuable complementarity to other existing and planned detectors pursuing many of the same goals. As an example, the sensitivity of DUNE to the $\nu_{e}$ component of supernova neutrino flux, prevalent in the neutronization phase of the explosion, provides distinct information relative to that provided by water or organic scintillator-based detectors in which electron antineutrino ($\bar{\nu}_{e}$) interactions dominate.

Sensitivity to CPV: The physics that DUNE will pursue demands measurements at the few-percent level. With just a FD, the neutrino fluxes would be known only to about $10\text{\,}\%$ and interaction rates to at best $20\text{\,}\%$. To adequately reduce these uncertainties, is necessary to measure the neutrinos at a near location, e.g., $500\text{\,}\mathrm{m}$ from the neutrino source and at a far location, e.g., $1300\text{\,}\mathrm{k}\mathrm{m}$ away, using the same target nucleus in both detectors, and to extract the physics measurements from differences between the two. The ND can be smaller than the FD, but it must be multi-functional since the differences in the measurements are not due solely to oscillations. The detector rate is the product of the neutrino flux, the detector response, and the interaction cross section, the first two of which will differ between the ND and FD due to other factors as well, e.g., event rate and geometry. The ND must be able to measure the factors that go into the detector rate separately.

The optimal FD distance (baseline) to determine the mass hierarchy (MH), observe CPV, and observe $\delta_{\rm CP}$ is between $1000$ and $2000\text{\,}\mathrm{k}\mathrm{m}$; at shorter baselines the optimal neutrino energy is lower, the second oscillation maximum is too low in energy to be visible, and charge parity (CP) sensitivity is reduced by ambiguities from the unknown mass ordering. At longer baselines CP sensitivity is harmed by matter effects that increase with baseline. The $1300\text{\,}\mathrm{k}\mathrm{m}$ baseline offered by locating the FD at SURF is optimized for the neutrino oscillation physics goals of the DUNE program.

The scientific basis for DUNE’s foundational experimental design choices has been examined and validated through extensive review, undertaken at all stages of DUNE development. Recent experimental and theoretical developments have only strengthened the scientific case for DUNE and its basic configuration. The technical underpinnings for these choices have also been strengthened over time through a worldwide program of R&D and engineering development, as described in a suite of LBNF/DUNE project documents including this TDR, as well as through independent experiments and development activities.

The DUNE FD will consist of four LArTPC detector modules, each with a LAr mass in the sensitive region of the cryostat (fiducial mass) of at least $10\text{\,}\mathrm{k}\mathrm{t}$, installed approximately $1.5\text{\,}\mathrm{k}\mathrm{m}$ underground. excellent tracking and calorimetry performance, making it an ideal choice. Each LArTPC fits inside a cryostat of internal dimensions $15.1\text{\,}\mathrm{m}$ (w) $\times$ $14.0\text{\,}\mathrm{m}$ (h) $\times$ $62.0\text{\,}\mathrm{m}$ (l) containing a total LAr mass of about $17.5\text{\,}\mathrm{kt}$. The design of the four identically sized modules is sufficiently flexible for staging construction and evolving the LArTPC technology.

DUNE is planning for and currently developing two LArTPC technologies: SP in which all the detector elements inside the cryostat are immersed in liquid; and DP, in which some components operate in a layer of gaseous argon above the liquid.

• •

  In the SP technology, ionization charges drift horizontally in the LAr under the influence of an electric field (E field) towards a vertical anode, where they are read out. This design requires very low-noise electronics to achieve readout with a good signal-to-noise (S/N) ratio because no signal amplification occurs inside the cryostat. This technology was pioneered in the icarus project, and after several decades of worldwide R&D, is now mature. It is the technology used for Fermilab’s currently operating MicroBooNE detector, as well as the SBND detector, which is under construction. Figure  shows the operating principle of an SP LArTPC.

• •

  The DP technology was pioneered at a large scale by the wa105 collaboration at CERN. It is less mature than the SP technology, and whereas it presents some challenges, it offers several advantages. Here, ionization charges drift vertically upward in LAr and are transferred into a layer of argon gas above the liquid. Devices called LEMs amplify the signal charges in the gas phase before they reach a horizontal anode. The gain achieved in the gas reduces the stringent requirements on the electronics noise and the overall design increases the possible drift length, which, in turn, requires a correspondingly higher voltage. Figure  shows the operating principle of a DP LArTPC.

In both technologies, the drift volumes are surrounded by a FC that defines the active detector volume and ensures uniformity of the E field within that volume.

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[The single-phase (SP) LArTPC operating principle]fig:LArTPC1ch1 The general operating principle of the SP LArTPC. Negatively charged ionization electrons from the neutrino interaction drift horizontally opposite to the E field in the LAr and are collected on the anode, which is made up of the U, V and X sense wires. The right-hand side represents the time projections in two dimensions as the event occurs. Light ($\gamma$) detectors (not shown) will provide the $t_{0}$ of the interaction.

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[The dual-phase (DP) LArTPC operating principle]fig:DPprinciplech1The general operating principle of the DP LArTPC. The ionization charges drift vertically upward in LAr and are transferred into a layer of argon gas above the liquid where they are amplified before collection on the anode. The light detectors (PMTs) sit under the cathode.

Argon is an excellent scintillator at a wavelength of $126.8\text{\,}\mathrm{nm}$ (UV), a property that both detector designs exploit. This fast scintillation light (photons), once shifted into the visible spectrum, is collected by photon detectors (PDs) in both designs. The light collection provides an initial start time ($t_{0}$) for every event recorded by the TPC, indicating when the ionization electrons begin to drift. Comparing the time at which the ionization signal reaches the anode relative to this start time allows reconstruction of the event topology in the drift coordinate (i.e., horizontal and transverse to the beam for SP and vertical for DP); the precision of the measured $t_{0}$, therefore, directly corresponds to the precision of the spatial reconstruction in this direction.

Two key factors affect the performance of the DUNE LArTPCs: LAr purity and noise on the readout electronics. First, the LAr purity must be quite high to minimize charge and light attenuation over the longest drift lengths in the detector module. The SP and DP designs have slightly different purity requirements (expressed in minimum electron lifetimes of $3\text{\,}\mathrm{m}\mathrm{s}$ versus $5\text{\,}\mathrm{m}\mathrm{s}$) due to the different maximum drift lengths. Second, the electronic readout of the LArTPC requires very low noise levels for the signal from the drifting electrons to be clearly discerned over the baseline of the electronics. This requires using low-noise cryogenic electronics, especially in the case of the SP design.

The DUNE collaboration is committed to deploying both technologies. The full DUNE FD requires four modules. In this TDR, we describe plans for the first three modules: two SP modules, one of which will be the first module installed, and one dpmod. The actual sequence of detector module installation will depend on results from the prototype detectors, described below, and on available resources. Plans for the fourth detector module, which may use a more advanced design, remain to be determined.

The plans for the SP and DP modules are described briefly in the following sections, more fully in Chapters 3 and 4, and finally in great detail in Volumes IV and V of this TDR.

The DUNE collaboration has constructed and operated two large prototype detectors, ProtoDUNE-SP, and pddp, at CERN. Each is approximately one-twentieth the size of the planned FD modules but uses components identical in size to those of the full-scale module. ProtoDUNE-SP has the same $3.5\text{\,}\mathrm{m}$ maximum drift length as the full SP module. ProtoDUNE-DP has a $6\text{\,}\mathrm{m}$ maximum drift length, half that planned for the DP module. Figure  shows the two cryostats, ProtoDUNE-SP in the foreground and ProtoDUNE-DP at an angle in the rear. Figure  shows one of the two drift volumes of ProtoDUNE-SP on the left and the single drift volume of ProtoDUNE-DP on the right.

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[ProtoDUNE cryostats at the CERN Neutrino Platform] fig:protodunes_northarea ProtoDUNE-SP and ProtoDUNE-DP cryostats in the CERN Neutrino Platform in CERN’s North Area.

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[Interior views of the ProtoDUNEs] fig:protodunes_interior Left: View of one of the two drift volumes in ProtoDUNE-SP; the APA is on the left, the CPA is on the right, and two of the four the FC surfaces bounding the drift volume are at the center and bottom of the image. Right: the single ProtoDUNE-DP drift volume (still incomplete when the image was taken), looking up; the CRPs (orange) are at the top. Three sides of the surrounding FC are shown, but the cathode is not visible.    

This massive prototyping program was undertaken with both engineering and scientific goals in mind, namely:

1. 1.

   production of components: stress-test the production and QA processes of detector components and mitigate the associated risks for the FD;

2. 2.

   validation of installation procedures: test the interfaces between the detector elements and mitigate the associated risks for the FD;

3. 3.

   operation of the detector with cosmic rays: validate the detector designs and performance; and

4. 4.

   collection of test beam data: measure the physics response of the detector.

Construction of the ProtoDUNE-SP detector was finished in July 2018 and filled with LAr the following month. It collected hadron beam and cosmic ray data during the fall of 2018 and continues to collect cosmic ray data. Construction of the ProtoDUNE-DP detector was complete in June of 2019, and the detector started operations in September 2019.

The data taken with ProtoDUNE-SP demonstrate the detector’s excellent performance and have already provided valuable information on the design, calibration, and simulation of the DUNE FD. In all, $99.7\text{\,}\%$ of the 15360 TPC electronics channels are responsive in the LAr. The equivalent noise charge (ENC) amounts to $\approx 550$ $e^{-}$ on the collection wires and $\approx 650$ $e^{-}$ on the induction wires, roughly half of the allowed maximum. An average S/N of 38 for the collection plane is measured using cosmic-ray muons, while for the two induction planes, the S/N is 14 (U) and 17 (V), easily exceeding the requirement of 4 for the DUNE FD.

When an interaction occurs, we convert the charge deposited along the track to the energy loss ($dE/dx$) using stopping cosmic ray muons. Calibration constants have been derived with this method, which are applied to the energy deposits measured for the beam particles – muons, pions, protons, and positrons. Figure  (left) shows the calibrated $dE/dx$ values as a function of the track residual range for protons in the beam, in good agreement with expectations.

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[Calibrated $dE/dx$ vs residual range and PD response in ProtoDUNE-SP] fig:pdtpcpd Left: Calibrated $dE/dx$ (energy loss over distance) versus residual range measured by a TPC for 1 GeV/c stopping protons. Right: Response in ProtoDUNE-SP of an ARAPUCA PD module in APA3 as a function of incident electron kinetic energy.

The ProtoDUNE-SP beam run provides a unique set of high-quality data for detector performance characterization, physics studies, and calibration, and will allow us to perform hadron-argon cross section measurements, which are relevant for future DUNE neutrino oscillation analyses. Data collected during the beam run will also be used to characterize the PD system response to light signals. Other useful data sets include beam data with triggers determined by the beam instrumentation; cosmic ray data from random triggers or from those in coincidence with the cosmic ray tagger (CRT) modules; and calibration data, with triggers enabling programmed light pulses. The response and gain for each of the 256 readout channels of the PD system have been determined from calibration data, and the initial analysis results indicate very good performance and stability for this system.

Figure  (right) shows the response of an ARAPUCA PD module (not corrected for geometry and detection efficiency) as a function of incident electron kinetic energy measured in ProtoDUNE-SP. This preliminary analysis demonstrates the achieved energy linearity for beam electrons contained in the detector. In addition to verifying the PD system response and calibration, ProtoDUNE-SP shows excellent correlation between TPC timing and the PD system timing. The latter will enable the further optimized physics reach of DUNE.

Although not the subject of this TDR, an understanding of DUNE’s capabilities would be impossible without some description of the ND’s crucial contribution to the experiment. The ND will serve as the experiment’s control, constraining systematic errors and measuring the initial unoscillated $\nu_{\mu}$ and $\nu_{e}$ energy spectra (and that of the corresponding antineutrinos). Comparing the measured neutrino energy spectra near the beam source, before any oscillation takes place, and again at the far site allows us to disentangle the different energy-dependent effects that modulate the beam spectrum and to reduce the systematic uncertainties to the level required for discovering CPV. Its other key role in this arena is to measure neutrino-argon interactions with high precision using both gaseous and liquid argon, which will further reduce the systematic uncertainties associated with modeling these interactions.

The ND will have a physics program of its own, as well, independent of the FD. This program will include measuring neutrino interactions to explore the two pillars of the standard model: electroweak physics and quantum chromodynamics. It will also explore physics beyond the standard model, searching for non-standard interactions, sterile neutrinos, dark photons, and other exotic particles.

The ND will be located $574\text{\,}\mathrm{m}$ downstream from the neutrino beam source and will include three primary detector components, illustrated in Figure :

• •

  a LArTPC called ArgonCube;

• •

  a high-pressure gaseous argon TPC (HPgTPC) surrounded by an ECAL in a $0.5\text{\,}\mathrm{T}$ magnetic field, together called the multi-purpose detector (MPD); and

• •

  an on-axis beam monitor called System for on-Axis Neutrino Detection (SAND).

These components serve important individual and overlapping functions in the mission of the ND. The first two can move off-axis relative to the beam, providing access to different neutrino energy spectra. The movement off-axis, called DUNE Precision Reaction-Independent Spectrum Measurement (DUNE-PRISM), provides a crucial extra degree of freedom for the ND measurements and is an integral part of the DUNE ND concept.

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[DUNE near detector (ND) components] fig:neardetectors DUNE ND. The axis of the beam is shown as it enters from the right. Neutrinos first encounter the LArTPC (right), the MPD (center), and then the on-axis beam monitor (left).

The ArgonCube detector contains the same target nucleus and shares some aspects of form and functionality with the FD. This similarity in target nucleus and, to some extent, technology, reduces sensitivity to nuclear effects and detector-driven systematic uncertainties in extracting the oscillation signal at the FD. ArgonCube is large enough to provide high statistics ($1\text{\times}{10}^{8}$ $\nu_{\mu}$ charged current events/year on-axis), and its volume is sufficiently large to provide good hadron containment. The tracking and energy resolution, combined with the LAr mass, will allow measurement of the neutrino beam using several techniques.

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[DUNE ND hall with component detectors] fig:NDHallconfigs DUNE ND hall shown with component detectors all in the on-axis configuration (left) and with the LArTPC and MPD in an off-axis configuration (right). The beam monitor (SAND) is shown in position on the beam axis in both figures. The beam is shown entering the hall at the bottom traveling from right to left.

A LArTPC energy acceptance falls off for muons with a measured momentum higher than $\sim\,$$0.7\text{\,}\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{c}$ because the muons will not be contained in the LArTPC volume. Since muon momentum is critical to determining the incoming neutrino’s energy, a magnetic spectrometer is needed downstream of the LArTPC to measure the momentum and charge of the muons. In the DUNE ND concept, the MPD will make these measurements. The HPgTPC provides a lower density medium with excellent tracking resolution for muons from the LArTPC.

The LArTPC and MPD can be moved sideways up to $33\text{\,}\mathrm{m}$ to take data in positions off the beam axis (DUNE-PRISM). As the detectors move off-axis, the incident neutrino flux spectrum changes, with the mean energy dropping and the spectrum becoming more monochromatic. The DUNE concept is based on reconstructing the energy-dependent neutrino spectrum and comparing measurements at the far and near sites. The ability to take measurements at the near site in off-axis locations will allow us to disentangle otherwise degenerate effects due to systematic biases of the energy reconstruction.

The final component of the DUNE ND suite is the beam monitor that remains on-axis at all times and serves as a dedicated neutrino spectrum monitor. It can also provide an excellent on-axis neutrino flux determination that can be used as an important point of comparison and a systematic crosscheck for the flux as determined by ArgonCube.

Chapter 5 of this TDR volume presents a more complete introduction to the ND and further details of the system can be found in the appendices. The DUNE collaboration is now in the process of finalizing studies for the ND Conceptual Design Report.

Neutrino oscillations imply nonzero neutrino masses and flavor-mixing in the leptonic charged current (CC) interactions. The nonzero neutrino mass is among the most important discoveries in fundamental particle physics of the twenty-first century. Understanding the mechanism behind nonzero neutrino masses is among the unresolved mysteries that drive particle physics today; they remain one of the few unambiguous facts that point to the existence of new particles and interactions, beyond those that make up the remarkable standard model of particle physics.

Almost all neutrino data can be understood within the three-flavor paradigm with massive neutrinos, the simplest extension of the standard model capable of reconciling theory with observations. It consists of introducing distinct, nonzero, masses for at least two neutrinos, while maintaining the remainder of the standard model. Hence, neutrinos interact only via the standard model CC and neutral current (NC) weak interactions. The neutrino mass eigenstates – defined as $\nu_{1},\nu_{2},\nu_{3}$ with masses, $m_{1},m_{2},m_{3}$, respectively – are distinct from the neutrino CC interaction eigenstates, also referred to as the flavor eigenstates – $\nu_{e}$, $\nu_{\mu}$, $\nu_{\tau}$, labeled according to the respective charged-lepton $e,\mu,\tau$ to which they couple in the CC weak interaction. The flavor eigenstates can be expressed as linear combinations of the mass eigenstates: the coefficients of the respective linear combinations define a unitary $3\times 3$ mixing matrix, the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, as follows:

$$\left(\begin{array}[]{c}\nu_{e}\\ \nu_{\mu}\\ \nu_{\tau}\end{array}\right)=\left(\begin{array}[]{ccc}U_{e1}&U_{e2}&U_{e3}\\ U_{\mu 1}&U_{\mu 2}&U_{\mu 3}\\ U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\end{array}\right)\left(\begin{array}[]{c}\nu_{1}\\ \nu_{2}\\ \nu_{3}\end{array}\right).$$

(2.1)

Nonzero values for at least some of the off-diagonal elements, coupled with nonzero differences in the masses of $\nu_{1}$, $\nu_{2}$ and $\nu_{3}$, lead to the phenomenon of neutrino oscillations, in which a neutrino – produced in a flavor eigenstate – acquires an oscillating probability of interacting as a different flavor (with an oscillation frequency proportional to the differences of the squares of the neutrino masses, $\Delta m^{2}_{ij}\equiv m_{i}^{2}-m_{j}^{2}$).

The PMNS matrix is the leptonic-equivalent of the Cabibbo-Kobayashi-Maskawa matrix (CKM matrix) that describes the CC interactions of quark mass eigenstates. If the neutrinos are Dirac fermions, the PMNS matrix, like the CKM matrix, can be unambiguously parameterized with three mixing angles and one complex phase.¹¹ 1 Additional nontrivial phases are present if neutrinos are Majorana fermions, but these do not affect oscillations at an observable level. By convention [10], the mixing angles are denoted $\theta_{12}$, $\theta_{13}$, and $\theta_{23}$, defined as

	$\displaystyle\sin^{2}\theta_{12}$	$\displaystyle\equiv$	$\displaystyle\frac{|U_{e2}|^{2}}{1-|U_{e3}|^{2}},$		(2.2)
	$\displaystyle\sin^{2}\theta_{23}$	$\displaystyle\equiv$	$\displaystyle\frac{|U_{\mu 3}|^{2}}{1-|U_{e3}|^{2}},$		(2.3)
	$\displaystyle\sin^{2}\theta_{13}$	$\displaystyle\equiv$	$\displaystyle|U_{e3}|^{2},$		(2.4)

and one phase $\delta_{\rm CP}$, which in the conventions of [10], is given by

$$\delta_{\rm CP}\equiv-{\rm arg}(U_{e3}).$$

(2.5)

For values of $\delta_{\rm CP}\neq 0,\pi$, and assuming none of the $U_{\alpha i}$ vanish ($\alpha=e,\mu,\tau$, $i=1,2,3$), the neutrino mixing matrix is complex and CP-invariance is violated in the lepton sector. This, in turn, manifests itself as different oscillation probabilities, in vacuum, for neutrinos and antineutrinos: $P(\nu_{\alpha}\to\nu_{\beta})\neq P(\bar{\nu}_{\alpha}\to\bar{\nu}_{\beta})$, $\alpha,\beta=e,\mu,\tau$, $\alpha\neq\beta$.

The central aim of the worldwide program of neutrino experiments past, present and planned, is to explore the phenomenology of neutrino oscillations in the context of the three-flavor paradigm, and, critically, to challenge its validity with measurements at progressively finer levels of precision. The world’s neutrino data significantly constrain all of the oscillation parameters in the three-flavor paradigm, but with precision that varies considerably from one parameter to the next.

Critical questions remain open. The neutrino mass ordering – whether $\nu_{3}$ is the heaviest (“normal” ordering) or the lightest (“inverted” ordering) – is unknown. Current data prefer the normal ordering, but the inverted one still provides a decent fit to the data. The angle $\theta_{23}$ is known to be close to the maximal-mixing value of $\pi/4$, but assuming it is not exactly so, the octant (whether $\sin^{2}\theta_{23}<0.5$ [$\theta_{23}<\pi/4$] or $\sin^{2}\theta_{23}>0.5$ [$\theta_{23}>\pi/4$]) is also unknown. The value of $\delta_{\rm CP}$ is only poorly constrained. While positive values of $\sin\delta_{\rm CP}$ are disfavored, all $\delta_{\rm CP}$ values between $\pi$ and $2\pi$, including the CP-conserving values $\delta_{\rm CP}=0,\pi$, are consistent with the world’s neutrino data.²² 2 It should be noted that recent results from the T2K experiment [11] show only marginal consistency with CP-conserving values of $\delta_{\rm CP}$. That the best fit to the world’s data favors large CPV is intriguing, providing further impetus for experimental input to resolve this particular question. It is central to the DUNE mission that all of the questions posed here can be addressed by neutrino oscillation experiments.

Conventional horn-focused beams, where either $\nu_{\mu}$ or $\bar{\nu}_{\mu}$ is the dominant species (depending on horn current polarity), provide access to these questions for experiments at long baselines as in the case of DUNE and the LBNF. By virtue of the near-maximal value of $\theta_{23}$, oscillations are mainly in the mode $\nu_{\mu}\rightarrow\nu_{\tau}$. For realizable baselines, this channel is best studied by measuring the $\nu_{\mu}$ disappearance probability as a function of neutrino energy rather than through direct observation of $\nu_{\tau}$ appearance. This is because oscillation maxima occur at energies below the threshold for $\tau$-lepton production in $\nu_{\tau}$ CC interactions in the detector. On the other hand, the sub-dominant $\nu_{\mu}\rightarrow\nu_{e}$ channel is amenable to detailed study through the energy dependence of the $\nu_{e}$ and $\bar{\nu}_{e}$ appearance probabilities, which is directly sensitive (in a rather complex way) to multiple PMNS matrix parameters, as described below.

Specifically, the oscillation probability of $\nu_{\mu}$ $\rightarrow$ $\nu_{e}$ through matter in a constant density approximation is, to first order [12]:

	$\displaystyle P(\nu_{\mu}\rightarrow\nu_{e})$	$\displaystyle\simeq$	$\displaystyle\sin^{2}\theta_{23}\sin^{2}2\theta_{13}\frac{\sin^{2}(\Delta_{31}-aL)}{(\Delta_{31}-aL)^{2}}\Delta_{31}^{2}$		(2.6)
			$\displaystyle+\sin 2\theta_{23}\sin 2\theta_{13}\sin 2\theta_{12}\frac{\sin(\Delta_{31}-aL)}{(\Delta_{31}-aL)}\Delta_{31}\frac{\sin(aL)}{(aL)}\Delta_{21}\cos(\Delta_{31}+\delta_{\rm CP})$
			$\displaystyle+\cos^{2}\theta_{23}\sin^{2}2\theta_{12}\frac{\sin^{2}(aL)}{(aL)^{2}}\Delta_{21}^{2},$

where $\Delta_{ij}=\Delta m^{2}_{ij}L/4E_{\nu}$, $a=G_{F}N_{e}/\sqrt{2}$, $G_{F}$ is the Fermi constant, $N_{e}$ is the number density of electrons in the Earth, $L$ is the baseline in km, and $E_{\nu}$ is the neutrino energy in GeV. In the equation above, both $\delta_{\rm CP}$ and $a$ switch signs in going from the $\nu_{\mu}\to\nu_{e}$ to the $\bar{\nu}_{\mu}\to\bar{\nu}_{e}$ channel; i.e., a neutrino-antineutrino asymmetry is introduced both by CPV ($\delta_{\rm CP}$) and the matter effect ($a$). As is evident from Equation 2.6, the matter effect introduces a sensitivity to the sign of $\Delta_{31}$, which specifies the neutrino mass ordering. The origin of the matter effect asymmetry is simply the presence of electrons and absence of positrons in the Earth. In the few-GeV energy range, the asymmetry from the matter effect increases with baseline as the neutrinos pass through more matter; therefore an experiment with a longer baseline will be more sensitive to the neutrino mass ordering. For baselines longer than $\sim$$1200\text{\,}\mathrm{km}$, the degeneracy between the asymmetries from matter and CPV effects can be resolved [13].

The electron neutrino appearance probability, $P(\nu_{\mu}\rightarrow\nu_{e})$, is plotted in Figure  at a baseline of $1300\text{\,}\mathrm{km}$ as a function of neutrino energy for several values of $\delta_{\rm CP}$. As this figure illustrates, the value of $\delta_{\rm CP}$ affects both the amplitude and phase of the oscillation. The difference in probability amplitude for different values of $\delta_{\rm CP}$ is larger at higher oscillation nodes, which correspond to energies less than 1.5 GeV. Therefore, a broadband experiment, capable of measuring not only the rate of $\nu_{e}$ appearance but of mapping out the spectrum of observed oscillations down to energies of at least 500 MeV, is desirable.

{dunefigure}

[Appearance probabilities for $\nu_{e}$ and $\bar{\nu}_{e}$ at $1300\text{\,}\mathrm{km}$]fig:oscprobThe appearance probability at a baseline of $1300\text{\,}\mathrm{km}$, as a function of neutrino energy, for $\delta_{\rm CP}$ = $-\pi/2$ (blue), 0 (red), and $\pi/2$ (green), for neutrinos (left) and antineutrinos (right), for normal ordering. The black line indicates the oscillation probability if $\theta_{13}$ were equal to zero. Note that the DUNE FD will be built at a baseline of $1300\text{\,}\mathrm{km}$.

DUNE is designed to address the questions articulated above, to over-constrain the three-flavor paradigm, and to reveal what may potentially lie beyond. Even if consistency is found, the precision measurements obtained by DUNE will have profound implications. As just one example, the discovery of CPV in neutrino oscillations would provide strong circumstantial evidence for the leptogenesis mechanism as the origin of the baryon asymmetry of the universe.

Going further, the patterns defined by the fermion masses and mixing parameters have been the subject of intense theoretical activity for the last several decades. Grand unified theories posit that quarks and leptons are different manifestations of the same fundamental entities, and thus their masses and mixing parameters are related. Different models make different predictions but, in order to compare different possibilities, it is important that lepton mixing parameters be known as precisely as quark mixing parameters. To enable equal-footing comparisons between quark and lepton mixing it is required that the mixing angles be determined at the few percent level while $\delta_{\rm CP}$ should be measured at the 10% level or better. Measurements with precision at these levels are expected from DUNE for the mixing angles $\theta_{23}$ and $\theta_{13}$, and the CP phase $\delta_{\rm CP}$. These measurements will thus open a new era of flavor physics, with the potential to offer insight on deep questions on which the SM is essentially silent.

Are protons stable? Few questions within elementary particle physics can be posed as simply and at the same time have implications as immediate. The apparent stability of protons suggests that baryon number is conserved in nature, although no known symmetry requires it to be so. Indeed, baryon number conservation is implicit in the formulation of the SM Lagrangian, and thus observation of baryon-number violating (BNV) processes such as nucleon decay or neutron-antineutron oscillation would be evidence for physics beyond the SM. On the other hand, continued non-observation of BNV processes will demand an answer to what new symmetry is at play that forbids them.

Especially compelling is that the observation of BNV processes could be the harbinger for grand unified theories, in which strong, weak and electromagnetic forces are unified. Numerous GUT models have been proposed, each with distinct features. Yet, BNV processes are expected on general grounds, and it is a feature of many models that nucleon decay channels can proceed at experimentally accessible rates. This is illustrated for several key nucleon decay channels relevant for DUNE in Figure , along with existing experimental limits.

{dunefigure}

[Summary of nucleon decay experimental limits and model predictions]fig:theoryexplimitsummarySummary of nucleon decay experimental lifetime limits from past or currently running experiments for several modes, and the model predictions for the lifetimes in the two modes $p\rightarrow e^{+}\pi^{0}$ and $p\rightarrow K^{+}\overline{\nu}$. The limits shown are 90% confidence level (CL) lower limits on the partial lifetimes, $\tau/B$, where $\tau$ is the total mean life and $B$ is the branching fraction. Updated from [14].

Given the scale of energy deposition in the few hundred $\mathrm{MeV}$ to few $\mathrm{GeV}$ range, a detector optimized for neutrino oscillation physics at long baselines is naturally well suited for sensitive searches for nucleon decay and neutron-antineutron oscillations. Thanks to the excellent imaging, calorimetric and particle identification capabilities of the LArTPC, backgrounds can in principle be reduced below the single-event level for key nucleon decay channels at exposures where other detector technologies are no longer background-free. On the other hand, a challenge presented by an argon-based detector is the impact of final-state interactions (FSI) on nucleon decay event reconstruction, which is expected to be more severe than for detectors based on water or liquid scintillator, for example. On balance, however, should nucleon decays occur at rates not far beyond current best limits, a handful of candidate events could be observed by DUNE in a given decay mode. For the case of zero observed candidates, DUNE has the potential to set partial lifetime limits for favorable channels at the ${10}^{34}\text{\,}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}$ level, as indicated in Section 2.3.2.

The burst of neutrinos [15, 16] from the celebrated core-collapse supernova 1987A in the Large Magellanic Cloud, about $50\text{\,}\mathrm{k}\mathrm{i}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{s}$ (kpc) from Earth, heralded the era of extragalactic neutrino astronomy. The few dozen recorded $\bar{\nu}_{e}$ events have confirmed the basic physical picture of core collapse and yielded constraints on a wide range of new physics [17, 18].

Core-collapse supernovae within a few hundred kpc of Earth – within our own galaxy and nearby – are quite rare on a human timescale. They are expected once every few decades in the Milky Way (within about 20 kpc), and with a similar rate in Andromeda, about 700 kpc away. These core collapses should be common enough to have a reasonable chance of occurring during the few-decade long lifetime of a typical large-scale neutrino detector.

It is important that at least one module of the DUNE FD be online at all times to observe this unpredictable and spectacular event, if and when it occurs. The rarity of these events makes it all the more critical for the community to be prepared to capture every last bit of information from them.

The information in a SNB available in principle to be gathered by experimentalists is the flavor, energy and time structure of a several-tens-of-second-long, all-flavor, few-tens-of-MeV neutrino burst [19, 20]. Imprinted on the neutrino spectrum as a function of time is information about the progenitor, the collapse, the explosion, and the remnant, as well as information about neutrino parameters and potentially exotic new physics. Neutrino energies and flavor content of the burst can be measured only imperfectly, due to the intrinsic nature of the weak interactions of neutrinos with matter, as well as due to imperfect detection resolution in any real detector. For example, SNB energies are below CC threshold for $\nu_{\mu}$, $\nu_{\tau}$, $\bar{\nu}_{\mu}$, and $\bar{\nu}_{\tau}$ (collectively $\nu_{x}$), which represent two-thirds of the flux; so these flavors are accessible only via NC interactions, which tend to have low cross sections and indistinct detector signatures. These issues make a comprehensive unfolding of neutrino flavor, time and energy structure from the observed interactions a challenging problem.

The core-collapse neutrino signal starts with a short, sharp neutronization (or break-out) burst primarily composed of $\nu_{e}$. These neutrinos are messengers of the shock front breaking through the neutrinosphere (the surface of neutrino trapping): when this happens, iron is disintegrated, the neutrino scattering cross section drops, and the lepton number trapped just below the original neutrinosphere is suddenly released. This quick and intense burst is followed by an accretion phase lasting some hundreds of milliseconds, depending on the progenitor star mass, as matter falls onto the collapsed core and the shock is stalled at the distance of perhaps $\sim 200$ km. The gravitational binding energy of the accreting material is powering the neutrino luminosity during this stage. The later cooling phase over $\sim$10 seconds represents the main part of the signal, over which the proto-neutron star sheds its trapped energy.

The flavor content and spectra of the neutrinos emitted from the neutrinosphere change throughout these phases, and the supernova’s evolution can be followed with the neutrino signal. Some fairly generic features of these emitted neutrino fluxes are illustrated in Figure .

{dunefigure}

[Expected time-dependent neutrino burst characteristics for a core-collapse supernova]paramsExpected time-dependent signal for a specific flux model for an electron-capture supernova [21] at 10 kpc. No oscillations are assumed; the effect of neutrino flavor transitions under different mass ordering assumptions can be dramatic and is described in Volume II Chapter 7. Note that $\nu_{x}$ refers to $\nu_{\mu}$, $\nu_{\tau}$, $\bar{\nu}_{\mu}$, and $\bar{\nu}_{\tau}$ collectively. The top plot shows the luminosity as a function of time ($\nu_{x}$ is the sum of all, the second plot shows average neutrino energy, and the third plot shows the $\alpha$ (pinching) parameter. The vertical dashed line at 0.02 seconds indicates the time of core bounce, and the vertical lines indicate different eras in the supernova evolution. The leftmost time interval indicates the infall period. The next interval, from core bounce to 50 ms, is the neutronization burst era, in which the flux is composed primarily of $\nu_{e}$. The next period, from 50 to 200 ms, is the accretion period. The final era, from 0.2 to 9 seconds, is the proto-neutron-star cooling period. The general features are qualitatively similar for most core-collapse supernovae.

In the world’s current supernova neutrino flavor sensitivity portfolio [22, 19], the sensitivity is primarily to electron antineutrino flavor, via inverse beta decay. There is only minor sensitivity to the $\nu_{e}$ component of the flux, which carries with it particularly interesting information content of the burst (e.g., neutronization burst neutrinos are created primarily as $\nu_{e}$). While there is some $\nu_{e}$ sensitivity in existing and other planned detectors via elastic scattering on electrons and via subdominant channels on nuclei, statistics are relatively small, and it can be difficult to disentangle the flavor content. It is in this respect that an experiment with an argon target such as DUNE will be especially valuable, since the dominant process in this case is $\nu_{e}$ CC scattering.

The capabilities that enable access to the physics program described in the previous sections open a myriad of opportunities to search for evidence of physics beyond the standard model. Below we list the identified opportunities that we have investigated. Projected sensitivities are shown later in this chapter for only a few of these opportunities; we refer the reader to Volume II, DUNE Physics, for a more complete demonstration of the potential impact of DUNE’s searches for bsm phenomena, which can justifiably be considered as prominent ancillary elements of the DUNE science program. At the same time, it is important to note that new physics may appear in ways that have not yet been considered: history has repeatedly shown that nature can reward new experimental approaches and sensitive detectors with the appearance of entirely unanticipated phenomena.

Opportunities in BSM physics that have been considered as elements of the DUNE science program include:

Search for active-sterile neutrino mixing: 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.

Searches for non-unitarity of the PMNS matrix: Deviation from unitarity of the $3\times 3$ PMNS matrix due to extra heavy neutrino states may be observable. Parameters characterizing the degree of non-unitarity can become sizable as the masses of the new states decrease.

Searches for nonstandard interactions (NSIs): NSIs 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. If the DUNE data are consistent with standard oscillations for three massive neutrinos, interaction effects of order 0.1 $G_{F}$ can be ruled out at DUNE.

Searches for violation of Lorentz symmetry or charge, parity, and time reversal symmetry (CPT): DUNE can improve the present limits on Lorentz and CPT violation in the neutrino sector by several orders of magnitude, contributing an important experimental test of these fundamental assumptions underlying quantum field theory.

Studies of neutrino trident production: Interactions of neutrinos with the Coulomb field of a nucleus can lead to final states with a lepton-pair accompanying the lepton from the neutrino interaction vertex. With a predicted annual rate of over 100 dimuon neutrino trident interactions at the ND, DUNE will be able to measure deviations from the SM rates and test the presence of new gauge symmetries.

Search for light-mass dark matter (LDM): The lack of evidence for weakly-interacting massive particle (WIMP) DM candidates from direct detection and LHC experiments has resulted in a reconsideration of the WIMP paradigm, and has revitalized the effort to search for LDM candidates of around a GeV or below in mass. High-flux neutrino beam experiments, such as DUNE, have been shown to provide coverage of DM +mediator parameter space that cannot be covered by either direct detection or collider experiments. DM particles can be detected in the ND through NC-like interactions either with electrons or nucleons in the detector material and enable DUNE’s search for LDM to be competitive and complementary to other experiments.

Search for boosted dark matter (BDM): Using its large FD, DUNE will be able to search for BDM. In these models there are several DM particles with different masses and properties concerning their interactions with SM particles. DUNE will search for such particles as generally produced anywhere in the cosmos or specifically through annihilation in the core of the sun, allowing competitive results for both production scenarios

Search for heavy neutral leptons (HNLs): HNLs in the context of the $\nu$MSM model with masses less than 2 GeV can be produced in the beam-dump of the proton beam to generate the DUNE neutrino beam. The ND data can be used to search for HNL decays, and competitive results with other present and proposed facilities can be obtained.

Physics sensitivities are based on the optimized design of a $1.2\text{\,}\mathrm{M}\mathrm{W}$ neutrino beam and corresponding protons-on-target per year assumed to be $1.1\times 10^{21}$ POT. These numbers assume a combined uptime and efficiency of the Fermilab accelerator complex and the LBNF beamline of 56%.³³ 3 This projection, from which one year of LBNF beam operations (live time) can be expressed as $1.7\text{\times}{10}^{7}\text{\,}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}\mathrm{s}$, is based on extensive experience with intense neutrino beams at Fermilab, and in particular the numi beam line, which incorporates elements like those in the proposed LBNF beamline design and faces similar operating conditions.

For the neutrino oscillation physics program, it is assumed that equal exposures (time-integrated beam power times fiducial mass) are obtained with both horn current polarities, and therefore with the corresponding mix of primarily $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ data samples.

It is assumed that the DUNE FD will include some combination of the different $10\text{\,}\mathrm{k}\mathrm{t}$ fiducial volume implementations – SP or DP– of the LArTPC concept for which technical designs have been developed. For much of the science program it is expected that the capabilities of the two proposed FD module implementations will be comparable. As a result of the current state of reconstruction and analysis software development (see Section 2.2.3), the physics sensitivity studies reported in this TDR are based on the SP LArTPC implementation, documented in full in Volume IV.

It is also assumed that validation of the DUNE FD designs will come from data and operational experience acquired with the large-scale ProtoDUNE detectors staged at the CERN, including single-particle studies of data obtained in test-beam running.

The ND for DUNE has been under active development, and a CDR is in preparation. Correspondingly, the descriptions in this TDR are consistent with this level of development.

Where presented as a function of calendar year, sensitivities are calculated with the following assumed deployment plan, which is based on a technically limited schedule:

• •

  Start of beam run: Two FD module volumes for total fiducial mass of $20\text{\,}\mathrm{k}\mathrm{t}$, $1.2\text{\,}\mathrm{M}\mathrm{W}$ beam;

• •

  After one year: Add one FD module volume for total fiducial mass of $30\text{\,}\mathrm{k}\mathrm{t}$;

• •

  After three years: Add one FD module volume for total fiducial mass of $40\text{\,}\mathrm{kt}$; and

• •

  After six years: Upgrade to $2.4\text{\,}\mathrm{M}\mathrm{W}$ beam.

The development of algorithms and software infrastructure needed to carry out physics sensitivity studies has been an active effort within DUNE and the associated scientific community. Significant progress has been made: event reconstruction codes can be run on fully simulated neutrino interaction events in DUNE FD modules; the DUNE computing infrastructure allows high-statistics production runs; and end-user interfaces are functioning. Robust end-to-end analyses not previously possible have now been performed and are being reported in this document.

For some aspects – for example, beamline modeling and GeV-scale neutrino interaction simulations – well-developed and validated (with data) software packages have been available throughout much of DUNE’s design phase. For others, corresponding tools did not exist and needed to be either developed from scratch or adapted with substantial modifications from other experimental programs. Concurrent with these development efforts, interim descriptions such as parametric detector response modeling, necessarily simple but based on reasonable extrapolation from experience and dedicated studies, were employed to assess physics capabilities. Even for the case of the better-developed tools – again, neutrino interaction modeling is a good example – significant incremental improvements have been made as data from neutrino experiments and other sources have become available and as theoretical understandings have advanced.

As a result of the rapid pace of development as well as practical considerations including human resource availability, different levels of rigor have been applied in the evaluation of physics capabilities for different elements of the program. The strategy adopted for this TDR has been to hold the primary elements of the program to the highest standard of rigor, involving direct analysis of fully simulated data, using actual event reconstruction codes and analysis tools that could be applied to real data from DUNE FD modules. For other elements of the program, sensitivities use realistic beam and physics simulations, but employ parametric detector response models in place of full reconstruction.

The implementation of this strategy comes with caveats and clarifications that are discussed in the corresponding chapters of Volume II. We mention some of these here.

• •

  In the case of the long-baseline oscillation physics program, this approach requires a combination of the full end-to-end analysis of simulated FD data with the concurrent analysis of simulated data from ND systems to capture in a realistic way the level of control over systematic errors. Given the current state of development of the DUNE ND design and corresponding analysis tools, it has been necessary to employ parametric detector response modeling for ND components.

• •

  In the case of the nucleon decay searches, reconstruction and analysis tools dedicated to addressing the particular challenges presented are not as well developed as in the case of the beam-based oscillation physics program. Effort is ongoing to improve the performance of these tools.

• •

  The SNB program relies on reconstruction of event signatures from LArTPC signals generated by low-energy (MeV-scale) particles (electrons and de-excitation gammas). Full simulation and reconstruction is used for some studies, such as for those demonstrating the supernova pointing capability of DUNE. For other studies, a modified strategy is employed in order to efficiently explore model space: reconstruction metrics (resolution smearing matrices, for example) are derived from analysis of fully simulated and reconstructed low-energy particles and events in the FD, and are applied to understanding the mean detector response over a range of signal predictions.

• •

  For scientific program elements where analysis of fully reconstructed simulated data has not yet been performed, the parametric response models used for the analyses presented here have been well characterized with dedicated studies and incorporation of results from other experiments. The demonstration of sensitivities for the long-baseline oscillation physics program (with full reconstruction) that are comparable to those previously obtained based on parametric response validates this approach.

The key strength of the DUNE design concept is its ability to robustly measure the oscillation patterns of $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ over a range of energies spanning the first and second oscillation maxima.

This is accomplished by a coordinated analysis of the reconstructed $\nu_{\mu}$, $\bar{\nu}_{\mu}$, $\nu_{e}$, and $\bar{\nu}_{e}$ energy spectra in near and far detectors, incorporating data collected with forward (neutrino-dominated) and reverse (antineutrino-dominated) horn current polarities.

The statistical power of DUNE relative to the current generation of long-baseline oscillation experiments is a result of many factors including (1) on-axis operations, (2) the LBNF beam power, (3) long-baseline and correspondingly high energy oscillation maxima and strong separation of normal and inverted neutrino mass ordering scenarios, (4) detector mass, and (5) event reconstruction and selection capabilities. Tables  and give the expected event yields for the appearance ($\nu_{e}$ and $\bar{\nu}_{e}$) and disappearance ($\nu_{\mu}$ and $\bar{\nu}_{\mu}$) channels, respectively, after seven years of operation. For these estimates, $\delta_{\rm CP}=0$ is assumed, and values for other parameters are taken from the nufit [23, 24] global fit to world neutrino data. (See also [25] and [26] for other recent global fits.) The DUNE $\nu_{e}$ and $\bar{\nu}_{e}$ event yields represent order-of-magnitude increases relative to those in the current NOvA [27] and T2K [28, 11] data samples, while the corresponding increases are even larger for the $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ channels thanks to DUNE’s on-axis exposure to the LBNF beam. Figures  and  show the corresponding distributions in reconstructed neutrino energy. {dunetable} [$\nu_{e}$ and $\bar{\nu}_{e}$ appearance yields] lrr tab:execsumm-apprates $\nu_{e}$ and $\bar{\nu}_{e}$ appearance yields: Integrated yield of selected $\nu_{e}$ CC-like events between 0.5 and 8.0 GeV assuming $3.5$-year (staged) exposures in the neutrino-beam and antineutrino-beam modes. The signal yields are shown for both normal mass ordering (NO) and inverted mass ordering (IO), and all the background yields assume normal mass ordering. All the yields assume $\delta_{\rm CP}=0$, and NuFIT 4.0 [23, 24] values for other parameters. Expected Events (3.5 years staged per mode)
\toprowrule $\nu$ mode $\bar{\nu}$ mode
\colhline$\nu_{e}$ signal NO (IO) 1092 (497) 76 (36)
$\bar{\nu}_{e}$ signal NO (IO) 18 (31) 224 (470)
\colhlineTotal signal NO (IO) 1110 (528) 300 (506)
\colhlineBeam $\nu_{e}+\bar{\nu}_{e}$ CC background 190 117
NC background 81 38
$\nu_{\tau}+\bar{\nu}_{\tau}$ CC background 32 20
$\nu_{\mu}+\bar{\nu}_{\mu}$ CC background 14 5
\colhlineTotal background 317 180

{dunetable}

[$\nu_{\mu}$ and $\bar{\nu}_{\mu}$ disappearance yields] lrr tab:execsumm-disrates $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ disappearance yields: Integrated yield of selected $\nu_{\mu}$ CC-like events between 0.5 and 8.0 GeV assuming a $3.5$-year (staged) exposure in the neutrino-beam mode and antineutrino-beam mode. The yields are shown for normal mass ordering and $\delta_{\rm CP}=0$. Expected Events (3.5 years staged)
\toprowrule$\nu$ mode
\colhline$\nu_{\mu}$ Signal 6200
\colhline$\bar{\nu}_{\mu}$ CC background 389
NC background 200
$\nu_{\tau}+\bar{\nu}_{\tau}$ CC background 46
$\nu_{e}+\bar{\nu}_{e}$ CC background 8
\toprowrule$\bar{\nu}$ mode
\colhline$\bar{\nu}_{\mu}$ signal 2303
\colhline$\nu_{\mu}$ CC background 1129
NC background 101
$\nu_{\tau}+\bar{\nu}_{\tau}$ CC background 27
$\nu_{e}+\bar{\nu}_{e}$ CC background 2

{dunefigure}

[$\nu_{e}$ and $\bar{\nu}_{e}$ appearance spectra]fig:appspectra $\nu_{e}$ and $\bar{\nu}_{e}$ appearance spectra: Reconstructed energy distribution of selected $\nu_{e}$ CC-like events assuming 3.5 years (staged) running in the neutrino-beam mode (left) and antineutrino-beam mode (right), for a total of seven years (staged) exposure. The plots assume normal mass ordering and include curves for $\delta_{\rm CP}=-\pi/2,0$, and $\pi/2$.

{dunefigure}

[$\nu_{\mu}$ and $\bar{\nu}_{\mu}$ disappearance spectra]fig:disspectra $\nu_{\mu}$ and $\bar{\nu}_{\mu}$ disappearance spectra: Reconstructed energy distribution of selected $\nu_{\mu}$ CC-like events assuming 3.5 years (staged) running in the neutrino-beam mode (left) and antineutrino-beam mode (right), for a total of seven years (staged) exposure. The plots assume normal mass ordering.

Experimental sensitivities were evaluated based on the methodologies described in the preceding section, including incorporation of ND simulations and uncertainties from all known sources of systematic error. Considerable attention and sophistication has been applied to the treatment of systematic errors and the crucial role of the ND, both of which are documented in Volume II, DUNE Physics.

A summary of representative sensitivity milestones for neutrino mass ordering and CPV discovery, as well as precision on $\delta_{\rm CP}$ and $\sin^{2}2\theta_{13}$ is given in Table . The ultimate level of precision that can be obtained on oscillation parameters highlights the point that DUNE will provide crucial input for flavor physics: Patterns required by particular symmetries underlying fermion masses and mixing angles may appear. The unitarity of the neutrino mixing matrix can be tested directly through comparisons of $\sin^{2}2\theta_{13}$ with the value obtained from reactor experiments. In conjunction with $\sin^{2}2\theta_{13}$ and other parameters, the precise value of $\delta_{\rm CP}$ can constrain models of leptogenesis that are leading candidates for explanation of the baryon asymmetry of the universe.

{dunetable}

[Projected DUNE oscillation physics milestones] lcc tab:milestones_execsumm-es Exposure in years, assuming true normal ordering and equal running in neutrino and antineutrino mode, required to reach selected physics milestones in the nominal analysis, using the NuFIT 4.0 [23, 24] best-fit values for the oscillation parameters. As discussed in Volume II, DUNE Physics, Chapter 5, there are significant variations in sensitivity with the value of $\sin^{2}\theta_{23}$, so the exact values quoted here (using $\sin^{2}\theta_{23}$ = 0.580) are strongly dependent on that choice. The staging scenario presented in Section 2.2.2 is assumed. Exposures are rounded to the nearest “staged” calendar year. For reference, 30, 100, 200, 336, 624, and $1104\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{MW}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{MW}\text{${}\cdot{}$}\mathrm{year}}$$ correspond to 1.2, 3.1, 5.2, 7, 10, and 15 staged years, respectively. Physics Milestone Exposure (staged years)
5$\sigma$ mass ordering 1
xxx($\delta_{\rm CP}$ = -$\pi/2$)
\colhline5$\sigma$ mass ordering 2
xxx(100% of $\delta_{\rm CP}$ values)
\colhline3$\sigma$ CPV 3
xxx($\delta_{\rm CP}$ = -$\pi/2$)
\colhline3$\sigma$ CPV 5
xxx(50% of $\delta_{\rm CP}$ values)
\colhline5$\sigma$ CPV 7
xxx($\delta_{\rm CP}$ = $-\pi/2$)
\colhline5$\sigma$ CPV 10
xxx(50% of $\delta_{\rm CP}$ values)
\colhline3$\sigma$ CPV 13
xxx(75% of $\delta_{\rm CP}$ values)
\colhline$\delta_{\rm CP}$ resolution of 10 degrees 8
xxx($\delta_{\rm CP}$ = 0)
\colhline$\delta_{\rm CP}$ resolution of 20 degrees 12
xxx($\delta_{\rm CP}$ = -$\pi/2$)
\colhline$\sin^{2}2\theta_{13}$ resolution of 0.004 15

The milestones presented in Table  form a coarse snapshot of the DUNE program in oscillation physics, demonstrating the prospects for important results throughout the lifetime of the experiment. More detail on the sensitivities for the individual program elements is presented in the sections below.

By virtue of its deep underground location and large fiducial mass, as well as its excellent event imaging, particle identification and calorimetric capabilities, the DUNE FD will be a powerful instrument to probe baryon-number violation. DUNE will be able to observe signatures of decays of protons and neutrons, as well as the phenomenon of neutron-antineutron mixing, at rates below the limits placed by the current generation of experiments.

Many nucleon decay modes are accessible to DUNE. As a benchmark, a particularly compelling discovery channel is the decay of a proton to a positive kaon and a neutrino, $p\rightarrow K^{+}\overline{\nu}$. In this channel, the kaon and its decay products can be imaged, identified, and tested for kinematic consistency with the full decay chain, together with precision sufficient to reject backgrounds due to atmospheric muon and neutrino interactions. Preliminary analysis of single-particle beam and cosmic ray tracks in the ProtoDUNE-SP LArTPC is already demonstrating the particle identification capability of DUNE, as illustrated in Figure . The signature of the kaon track and its observable decay particles is sufficiently rich that a credible claim of evidence for proton decay could be made on the basis of just one or two sufficiently well-imaged events, for the case where background sources are expected to contribute much less than one event.

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[Reconstructed $dE/dx$ of protons and muons in ProtoDUNE-SP]fig:pdsp_dedx_execsum Energy loss of protons (left) and muons (right) in 1-GeV running with the ProtoDUNE-SP LArTPC at CERN, as a function of residual range. The protons are beam particles identified from beamline instrumentation; the muons are reconstructed stopping cosmic rays collected concurrently. The red curves represent the mean of the corresponding expected signature. Note the difference in the vertical scale of the two plots. The kaon $dE/dx$ curve will lie between the two curves shown.    

Projecting from the current analysis of $p\rightarrow K^{+}\overline{\nu}$ in the DUNE FD, with a detection efficiency of $30$% as described in Volume II, DUNE Physics, Chapter 6, the expected 90% C.L. lower limit on lifetime divided by branching fraction is $1.3\text{\times}{10}^{34}\text{\,}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}$ for a $400\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{year}}$$ exposure, assuming no candidate events are observed. This is roughly twice the current limit of $5.9\text{\times}{10}^{33}\text{\,}\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}$ from Super–Kamiokande [29], based on an exposure of $260\text{\,}$\mathrm{}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{\_}\mathrm{a}\mathrm{s}\mathrm{=}{presentation}\mathrm{]}{\text{${}\cdot{}$}\mathrm{kt}\mathrm{year}}{\mathrm{kt}\text{${}\cdot{}$}\mathrm{year}}$$. Thus, should the rate for this decay be at the current Super–Kamiokande limit, five candidate events would be expected in DUNE within ten years of running with four FD modules. Ongoing work is aimed at improving the efficiency in this and other channels.

As has been demonstrated with SN1987a, the observation of neutrinos [15, 16] from a core-collapse supernova can reveal much about these phenomena that is not accessible in its electromagnetic signature. Correspondingly, there is a wide range of predictions from supernova models for even very basic characteristics of the SNBs. Typical models predict that a supernova explosion in the center of the Milky Way will result in several thousand detectable neutrino interactions in the DUNE FD occurring over an interval of up to a few tens of seconds. The neutrino energy spectrum peaks around $10\text{\,}\mathrm{MeV}$, with appreciable flux up to about $30\text{\,}\mathrm{MeV}$.

LAr based detectors are sensitive to the $\nu_{e}$ component of the flux, while water Cherenkov and organic scintillator detectors are most sensitive to the $\bar{\nu}_{e}$ component. Thus DUNE is uniquely positioned to study the neutronization burst, in which $\nu_{e}$’s are produced during the first few tens of milliseconds. More generally, measurements of the (flavor-dependent) neutrino flux and energy spectrum as a function of time over the entirety of the burst can be sensitive to astrophysical properties of the supernova and its progenitor, and distortions relative to nominal expectations can serve as signatures for phenomena such as shock wave and turbulence effects, or even black hole formation.

Below, we present the results of analyses of DUNE’s capabilities for two elements of the SNB program: (1) fits to the reconstructed neutrino energy spectrum and comparison to models in which none of the distortions listed above are present, and (2) neutrino flux direction determination for angular localization of the supernova position.

The unique combination of the high-intensity LBNF neutrino beam with DUNE’s ND and massive LArTPC FD modules at a $1300\text{\,}\mathrm{km}$ baseline enables a variety of probes of BSM physics, either novel or with unprecedented sensitivity.

As examples of the potential impact of DUNE, we present results from the analysis of simulated data sets for two BSM scenarios, one with a sterile neutrino species participating in oscillations, and the other with anomalous “neutrino trident” events. From the sterile neutrino analysis, the DUNE sensitivities to the effective mixing angle $\theta_{\mu e}$ (which depends on new mixing angles $\theta_{14}$ and $\theta_{24}$), from the appearance and disappearance samples at the ND and FD are shown in Figure .

Considering a neutrino trident analysis in ND data, existing constraints and projected sensitivity to parameters of a $Z^{\prime}$ boson resulting from the gauging of the difference between muon and tau lepton numbers, $L_{\mu}-L_{\tau}$, are presented in Figure . This plot indicates that DUNE can cover much of parameter space for which this model is able to explain the departure of the present observed muon $g-2$ central value from standard model expectations.

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[Sensitivity to effective mixing angle $\theta_{\mu e}$ from a DUNE sterile neutrino analysis] fig:th_me2 DUNE 90% C.L. sensitivities to $\theta_{\mu e}$ from the appearance and disappearance samples at the ND and FD is shown 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.

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[Projected sensitivity to BSM contributions to neutrino trident events] fig:LmuLtau2 Existing constraints and projected DUNE sensitivity in the $Z^{\prime}$ parameter spaced associated with gauging $L_{\mu}-L_{\tau}$. Shown in green is the region where the $(g-2)_{\mu}$ anomaly can be explained at the $2\sigma$ level. The parameter regions already excluded by existing constraints are shaded in gray and correspond to a cms search for $pp\to\mu^{+}\mu^{-}Z^{\prime}\to\mu^{+}\mu^{-}\mu^{+}\mu^{-}$ [34] (“LHC”), a BaBar search for $e^{+}e^{-}\to\mu^{+}\mu^{-}Z^{\prime}\to\mu^{+}\mu^{-}\mu^{+}\mu^{-}$ [35] (“BaBar”), a previous measurement of the trident cross section [36, 37] (“CCFR”), a measurement of the scattering rate of solar neutrinos on electrons [38, 39, 40] (“Borexino”), and bounds from Big Bang Nucleosynthesis [41, 42] (“BBN”). The DUNE sensitivity shown by the solid blue line assumes a measurement of the trident cross section with $40\%$ precision.