The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

How to Read this Document

The LBNE science document is intended to inform a diverse readership about the goals and capabilities of the LBNE experiment. Your approach to reading this document will depend upon your purpose as well as your level of knowledge about high energy and neutrino physics.

The three chapters Chapter 1 Introduction and Executive Summary, Chapter 3 Project and Design and Chapter 9 Summary and Conclusion together provide a comprehensive overview of LBNE’s scientific objectives, its place in the landscape of neutrino physics experiments worldwide, the technologies it will incorporate and the capabilities it will possess. Much of the information in these chapters is accessible to the lay reader, but of course, the scientific concepts, goals and methods around which LBNE is designed are by their nature highly specialized, and the text in certain sections is correspondingly technical.

In Chapter 2 The Science of LBNE, the initial paragraphs in each section provide some introductory information, but in general this chapter assumes a working knowledge of high energy physics and, ideally, familiarity with neutrino physics.

The three chapters that delve into the areas corresponding to the scientific objectives of LBNE: Chapter 4 Neutrino Mixing, Mass Hierarchy and CP Violation, Chapter 5 Nucleon Decay Motivated by Grand Unified Theories and Chapter 6 Core-Collapse Supernova Neutrinos, assume a working knowledge of high energy physics and particle astrophysics. This is also true of Chapter 7 Precision Measurements with a High-Intensity Neutrino Beam and Chapter 8 Additional Far Detector Physics Opportunities, as well as the appendices.

Introduction and Executive Summary

Although neutrinos are the most abundant of known matter particles (fermions) in the Universe, their properties are the least well understood. The very existence of neutrino mass constitutes evidence of physics beyond the Standard Model. Understanding the nature of neutrinos has consequently become an essential goal for particle physics.

Observations of oscillations of neutrinos from one type (flavor) to another in numerous recent experiments have provided evidence for neutrino flavor mixing and for small, but nonzero, neutrino masses. The framework characterizing these observations is similar to that describing corresponding phenomena in the quark sector, but with a very different pattern of mixing angle values. As in the quark case, this framework involves a phase parameter, $\delta_{\rm CP}$, that changes sign under combined charge conjugation and parity (CP) reversal operations and thus would lead to CP symmetry-violating asymmetries between the pattern of oscillations for neutrinos and antineutrinos. While groundbreaking on its own, the observation of such asymmetries would also provide an experimental underpinning for the basic idea of leptogenesis Leptogenesis refers to the mechanisms that generated an asymmetry between leptons and antileptons in the early Universe, described in Section 2.2.1. as an explanation for the Baryon Asymmetry of the Universe (BAU).

Neutrino oscillation data so far tell us about differences in the squared masses of the neutrino mass states, and about the sign of the mass-squared difference between two of the states, but not about the difference of those with respect to the third, which may be heavier (normal ordering) or lighter (inverted ordering) than the other two. Resolving this neutrino mass hierarchy ambiguity, along with precise measurements of neutrino mixing angles, would have significant theoretical, cosmological and experimental implications. One important consequence of mass hierarchy determination, in particular, would be the impact on future experiments designed to determine whether — uniquely among the fundamental fermions — neutrinos are their own antiparticles, so-called Majorana particles. Though long suspected, this hypothesis that neutrinos are Majorana particles has yet to be either established or ruled out. Strong evidence for the inverted hierarchy would establish conditions required by the next generation of neutrinoless double-beta decay searches to settle this question even with a null result (no observation). Because the forward scattering of neutrinos in matter alters the oscillation pattern in a hierarchy-dependent way, the long baseline of LBNE — with the neutrinos traveling through the Earth’s mantle — enables a decisive determination of the hierarchy, independent of the value of $\delta_{\rm CP}$.

Additionally, the high-precision determination of oscillation parameters such as mixing angles and squared-mass differences will provide insight into the differences between the quark and lepton mixing patterns, which is necessary for deciphering the flavor structure of physics in the Standard Model. Taken together, the above suite of measurements will thoroughly test the standard three-neutrino flavor paradigm that guides our current understanding, and will provide greatly extended sensitivity to signatures for nonstandard neutrino interactions in matter.

The arena of non-accelerator physics using massive underground detectors such as the LBNE far detector is also ripe with discovery potential. The observation of nucleon decay would be a watershed event for the understanding of physics at high energy scales. Neutrinos from supernovae are expected to provide key insights into the physics of gravitational collapse, and may also reveal fundamental properties of the neutrino.

Among massive detectors designed for neutrino and nucleon decay physics, the LArTPC technology offers unmatched capabilities for position and energy resolution and for high-precision reconstruction of complex interaction topologies over a broad energy range. It also provides a compact, scalable approach for achieving the required sensitivity to the primary physics signatures to be explored by LBNE. As these capabilities are also important for non-accelerator neutrino physics, LBNE will complement the large, underground water Cherenkov and/or scintillator-based detectors that may be operating in parallel. LArTPC detectors are especially well-suited to proton decay modes such as the supersymmetry-favored $p\to K^{+}\overline{\nu}$ mode, uniquely providing detection efficiency and background rejection sufficient to enable a discovery with a single well-reconstructed event. With regard to supernova-neutrino detection, liquid argon detectors are primarily sensitive to the $\nu_{e}$ component of the flux, while $\overline{\nu}_{e}$ interactions dominate for water and scintillator-based detectors. Thus, LBNE will be sensitive to different features of the supernova-neutrino production process. Finally, the LArTPC technology opens up an avenue for precision studies of oscillation physics with atmospheric neutrinos, thereby augmenting the results of the beam-based measurements at the core of the experiment.

The highly capable near detector will measure the absolute flux and energy scales of all four neutrino species in the LBNE beam, as well as neutrino cross sections on argon, water, and other nuclear targets in the beam’s energy range. These measurements are needed to attain the ultimately desired precision of the oscillation parameter measurements. Additionally, the near detector will enable a broad range of precision neutrino-interaction measurements, thereby adding a compelling scientific program of its own.

LBNE is an extensively developed experiment whose execution will have substantial impact on the overall direction of high energy physics (HEP) in the U.S. The U.S. Department of Energy (DOE) has endorsed the science objectives of LBNE, envisioning the experiment as a phased program, and has given first stage (CD-1) approval with a budget of $867M toward the initial phase. The science scope of this and subsequent phases will depend on the level of investment by additional national and international partners.

This document outlines the LBNE physics program and how it may evolve in the context of long-term planning studies . The physics reach of this program is summarized under scenarios that are consistent with short-, medium- and long-term considerations. The general conclusions regarding the scientific capabilities of LBNE in a phased program are twofold:

A full-scope LBNE will provide an exciting broad-based physics program with exceptional capabilities for all of the identified core physics objectives, and many additional ones.

Section 1.2 provides the context for development of LBNE as a phased program that maintains flexibility for enhancements in each of its stages through the contributions of additional partners. The physics reach of LBNE at various stages is summarized in Section 1.3.

2 Development of a World-Class Experiment

The concept of a high-intensity neutrino beam directed toward a distant, massive underground detector to simultaneously investigate the nature of the neutrino, proton decay and astrophysical sources of neutrinos has been under serious investigation since the late 1990s . Since that time both the science goals and concepts for implementation have been the subject of intense study and review by distinguished panels. These panels include the National Academies Neutrino Facilities Assessment Committee in 2003 , the National Science and Technology Council Committee on Science in 2004 , the National Academies EPP2010 panel in 2006 , the HEPAP/NSAC Neutrino Scientific Assessment Group in 2007 , the HEPAP Particle Physics Project Prioritization Panel (P5) in 2008 , the National Academies ad hoc Committee to Assess the Science Proposed for DUSEL in 2011 , and most recently the HEPAP Facilities Subpanel in 2013 . High-level studies performed in Europe and Asia have come to similar conclusions (e.g., ) about the merits and feasibility of such a program.

LBNE as described in this document has been developed by a collaboration formally established in 2009, which currently comprises over 475 collaborators from over 80 institutions in six countries. In January 2010 the DOE formally recognized the LBNE science objectives with approval of the mission need statement (CD-0) . This action established LBNE as a DOE project. Fermilab has recognized LBNE as a central component of its long-term future program.

The central role of LBNE within the U.S. particle physics program has been acknowledged in other documents prepared for the 2013 particle physics community planning exercise , including the Project X Physics Book and the reports from Intensity Frontier working groups on neutrino physics and baryon number violation .

2.2 Present Status of the LBNE Project

2.3 Global Partnerships

Global conditions are favorable for significant international partnerships in developing and building LBNE. As an example, the 2013 update of the European Strategy for Particle Physics document places long-baseline neutrino physics among the highest-priority large-scale activities for Europe, recognizing that it requires “significant resources, sizeable collaborations and sustained commitment.” It includes the primary recommendation of exploring “the possibility of major participation in leading long-baseline neutrino projects in the U.S. and Japan.” As of March 2014 the LBNE Collaboration includes institutions from the U.S., Brazil, India, Italy, Japan and the United Kingdom. Discussions with a number of potential international partners are underway — some already at an advanced stage. A summary of recent progress in these discussions can be found in the presentation of LBNE status to the U.S. Particle Physics Projects Prioritization Panel in November 2013 .

2.4 Context for Discussion of Physics Sensitivities

3 The LBNE Physics Program

This section summarizes LBNE’s potential for achieving its core physics objectives based on the current experimental landscape, scenarios for staging LBNE, and the technical capabilities of LBNE at each stage.

LBNE’s capability to achieve the physics objectives described in this document has been subject to extensive review over a number of years. In addition to the various reviews of the LBNE Project described in Section 1.2, reviews that focused strongly on LBNE’s science program include the DOE Office of Science Independent Review of Options for Underground Science in the spring of 2011 , the LBNE Science Capabilities Review (by an external panel commissioned by LBNE) in the fall of 2011, and the LBNE Reconfiguration Review in the summer of 2012.

Across the overwhelming majority of the parameter space for the mixing parameters that are not well known (mainly $\delta_{\rm CP}$ and $\sin^{2}{\theta_{23}}$), LBNE’s determination of the MH will be definitive, but even for unfavorable combinations of the parameter values, a statistically ambiguous outcome is highly unlikely.

CP Violation and the Measurement of $\delta_{\rm CP}$: The LBNE program has two somewhat distinct objectives with regard to CP symmetry violation in the $\nu_{\mu}\to\nu_{e}$ oscillation channel. First, LBNE aims to make a precise determination of the value of $\delta_{\rm CP}$ within the context of the standard three-flavor mixing scenario described by the PMNS matrix (discussed in Section 2.2). Second, and perhaps more significantly, LBNE aims to observe a signal for leptonic CP violation, independent of the underlying nature of neutrino oscillation phenomenology. Within the standard three-flavor mixing scenario, such a signal will be observable, provided $\delta_{\rm CP}$ is not too close to either of the values for which there is no CP violation (zero and $\pi$). Together, the pursuit of these two goals provides a thorough test of the standard three-flavor scenario.

3.2 Nucleon Decay Physics Motivated by Grand Unified Theories

3.3 Supernova-Neutrino Physics and Astrophysics

The neutrinos from a core-collapse supernova are emitted in a burst of a few tens of seconds duration, with about half in the first second. Energies are in the range of a few tens of MeV, and the luminosity is divided roughly equally between the three known neutrino flavors. Currently, experiments worldwide are sensitive primarily to electron antineutrinos ($\overline{\nu}_{e}$), with detection through the inverse-beta decay process on free protons This refers to neutrino interactions with the nucleus of a hydrogen atom in H2O in water detectors or in hydrocarbon chains in liquid scintillator detectors., which dominates the interaction rate in water and liquid-scintillator detectors. Liquid argon has a unique sensitivity to the electron-neutrino ($\nu_{e}$) component of the flux, via the absorption interaction on 40Ar as follows:

3.4 Precision Measurements with a High-Intensity Neutrino Source and High-Resolution Near Detector

The near neutrino detector will provide precision measurements of neutrino interactions, which in the medium to long term are essential for controlling the systematic uncertainties in the long-baseline oscillation physics program. The near detector, which will include argon targets, will measure the absolute flux and energy-dependent shape of all four neutrino species, $\nu_{\mu}$, $\overline{\nu}_{\mu}$, $\nu_{e}$ and $\overline{\nu}_{e}$ to accurately predict for each species the far/near flux ratio as a function of energy. It will also measure the four-momenta of secondary hadrons, such as charged and neutral mesons, produced in the neutral and charged current interactions that constitute the dominant backgrounds to the oscillation signals.

4 Summary

This chapter has touched only briefly on the most prominent portion of the full suite of physics opportunities enabled by LBNE. The following chapters cover these in detail, as well as topics that were omitted here in the interest of brevity and focus. In Chapter 9 progress toward LBNE physics milestones is addressed, based on one potential scenario for the operation of successive stages of LBNE detector and PIP-II implementations, and the broad role of LBNE is discussed in the context of such scenarios. The present chapter concludes with a summary of its key points.

The primary science goals of LBNE are drivers for the advancement of particle physics. The questions being addressed are of wide-ranging consequence: the origin of flavor and the generation structure of the fermions (i.e., the existence of three families of quark and lepton flavors), the physical mechanism that provides the CP violation needed to generate the Baryon Asymmetry of the Universe, and the high energy physics that would lead to the instability of matter. Achieving these goals requires a dedicated, ambitious and long-term program. No other proposed long-baseline neutrino oscillation program with the scientific scope and sensitivity of LBNE is as advanced in terms of engineering development and project planning. A phased program with a far detector of even modest size in the initial stage (e.g., 10 kt) will enable exciting physics in the intermediate term, including a definitive mass hierarchy determination and a measurement of the CP phase without ambiguities, while providing the fastest route toward achieving the full range of LBNE’s science objectives. Should LBNE find that the CP phase is not zero or $\pi$, it will have found strong indications ($>3\sigma$) of leptonic CP violation. Global interest is favorable for contributions from international partners to accelerate and enhance this program, including the LBNE first-phase scope.

Implementing the vision that has brought LBNE to this point will allow the U.S. to host this world-leading program, bringing together the world’s neutrino community to explore key questions at the forefront of particle physics and astrophysics. Moreover, the excitement generated by both the technical challenges of mounting LBNE and the potential physics payoffs are widely shared — among the generation of scientists who have been paving the way for these innovations, as well as the young scientists for whom LBNE will provide numerous research opportunities over the next two decades.

The Science of LBNE

LBNE has been designed to address a wide range of scientific topics using well-characterized, high-intensity, accelerator-based neutrino beams, a long baseline for neutrino oscillations, and a very large, deep-underground detector with excellent particle identification capabilities over a large range of energies. While maximizing the reach for a core set of scientific objectives, its design — described in Chapter 3 — accommodates the flexibility to extend the scope of measurements as additional resources become available.

The scientific objectives of LBNE have been categorized into primary, secondary, and additional secondary objectives according to priorities developed and agreed upon by the LBNE community and accepted as part of the CD-0 (Mission Need) approval by the U.S. Department of Energy .

Primary objectives of LBNE, in priority order, are the following measurements:

precision measurements of the parameters that govern $\nu_{\mu}\rightarrow\nu_{e}$ oscillations; this includes precision measurement of the third mixing angle $\theta_{13}$, measurement of the charge-parity (CP) violating phase $\delta_{\rm CP}$, and determination of the neutrino mass ordering (the sign of $\Delta m^{2}_{31}=m_{3}^{2}-m_{1}^{2}$), the so-called mass hierarchy

precision measurements of the mixing angle $\theta_{23}$, including the determination of the octant in which this angle lies, and the value of the mass difference, |$\Delta m^{2}_{32}$|, in $\nu_{\mu}\rightarrow\nu_{e,\mu}$ oscillations

search for proton decay, yielding significant improvement in the current limits on the partial lifetime of the proton ($\tau$/BR) in one or more important candidate decay modes, e.g., $p\rightarrow K^{+}\overline{\nu}$

detection and measurement of the neutrino flux from a core-collapse supernova within our galaxy, should one occur during the lifetime of LBNE

In a phased approach to LBNE, the goal of the first phase is to maximize the effectiveness of the facility to achieve the first two objectives, above. The mass hierarchy determination and the precision determination of $\theta_{23}$ will most likely be complete in the first phase of LBNE; while the precision determination of CP violation will require the full-scope LBNE, an initial measurement of the CP phase parameter $\delta_{\rm CP}$ will be performed in earlier phases.

Secondary objectives, which may also be enabled by the facility designed to achieve the primary objectives, include:

other accelerator-based, neutrino oscillation measurements; these could include further sensitivity to Beyond Standard Model (BSM) physics such as nonstandard interactions

measurements of neutrino oscillation phenomena using atmospheric neutrinos

measurement of other astrophysical phenomena using medium-energy neutrinos

Additional secondary objectives, the achievement of which may require upgrades to the facility that is designed to achieve the primary physics objectives (e.g., deployment of additional detector mass or alternate detector technologies), include:

detection and measurement of the diffuse supernova-neutrino flux

measurements of neutrino oscillation phenomena and of solar physics using solar neutrinos

measurements of astrophysical and geophysical neutrinos of low energy

In addition, a rich set of science objectives enabled by a sophisticated near neutrino detector have been identified. A primary and a secondary objective, respectively, are:

measurements necessary to achieve the primary physics research objectives listed above

studies of neutrino interactions that may be enabled either by the facility designed to achieve the primary objectives or by future upgrades to the facility and detectors; these include precision studies of the weak interaction, studies of nuclear and nucleon structure, and searches for new physics

2 Neutrino Three-Flavor Mixing, CP Violation and the Mass Hierarchy

The Standard Model of particle physics (Figure 2.1) presents a remarkably accurate description of the elementary particles and their interactions. However, its limitations beg deeper questions about Nature. The unexplained patterns of quarks, leptons, flavors and generations imply that a more fundamental underlying theory must exist. LBNE plans to pursue a detailed study of neutrino mixing, resolve the neutrino mass ordering, and search for CP violation in the lepton sector by studying the oscillation patterns of high-intensity $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ beams measured over a long baseline.

Neutrino oscillation arises from mixing between the flavor and mass eigenstates of neutrinos, corresponding to the weak and gravitational interactions, respectively. This three-flavor-mixing scenario can be described by a rotation between the weak-interaction eigenstate basis $(\nu_{e},\,\nu_{\mu},\,\nu_{\tau})$ and the basis of states of definite mass $(\nu_{1},\,\nu_{2},\,\nu_{3})$. In direct correspondence with mixing in the quark sector, the transformations between basis states is expressed in the form of a complex unitary matrix, known as the PMNS matrix :

The PMNS matrix in full generality depends on just three mixing angles and a CP-violating phase. The mixing angles and phase are designated as $(\theta_{12},\,\theta_{23},\,\theta_{13})$ and $\delta_{\rm CP}$. This matrix can be parameterized as the product of three two-flavor mixing matrices as follows, where $c_{\alpha\beta}=\cos\theta_{\alpha\beta}$ and $s_{\alpha\beta}=\sin\theta_{\alpha\beta}$:

The parameters of the PMNS matrix determine the probability amplitudes of the neutrino oscillation phenomena that arise from mixing.

The entire complement of neutrino experiments to date has measured five of the mixing parameters: the three angles $\theta_{12}$, $\theta_{23}$ and (recently) $\theta_{13}$, and the two mass differences $\Delta m^{2}_{21}$ and $\Delta m^{2}_{32}$. The sign of $\Delta m^{2}_{21}$ is known, but not that of $\Delta m^{2}_{32}$, which is the crux of the mass hierarchy ambiguity. The values of $\theta_{12}$ and $\theta_{23}$ are large, while $\theta_{13}$ is smaller . The value of $\delta_{\rm CP}$ is unknown. The real values of the entries of the PMNS mixing matrix, which contains information on the strength of flavor-changing weak decays in the lepton sector, can be expressed in approximate form as

The three-flavor-mixing scenario for neutrinos is now well established. However, the mixing parameters are not known to the same precision as are those in the corresponding quark sector, and several important quantities, including the value of $\delta_{\rm CP}$ and the sign of the large mass splitting, are still undetermined. In addition, several recent anomalous experimental results count among their possible interpretations phenomena that do not fit this model .

The relationships between the values of the parameters in the neutrino and quark sectors suggest that mixing in the two sectors is qualitatively different. Illustrating this difference, the value of the entries of the CKM quark-mixing matrix (analogous to the PMNS matrix for neutrinos, and thus indicative of the strength of flavor-changing weak decays in the quark sector) can be expressed in approximate form as

and compared to the entries of the PMNS matrix given in Equation 2.6. As discussed in , the question of why the quark mixing angles are smaller than the lepton mixing angles is an important part of the “flavor problem.”

Clearly much work remains in order to complete the standard three-flavor mixing picture, particularly with regard to $\theta_{23}$ (is it less than, greater than, or equal to $45^{\circ}$?), mass hierarchy (normal or inverted?) and $\delta_{\rm CP}$. Additionally, there is great value in obtaining a set of measurements for multiple parameters from a single experiment, so that correlations and systematic uncertainties can be handled properly. Such an experiment would also be well positioned to extensively test the standard picture of three-flavor mixing. LBNE is designed to be this experiment.

In the particular parameterization of the PMNS matrix shown in Equation 2.2, the middle factor, labeled ‘II’, describes the mixing between the $\nu_{1}$ and $\nu_{3}$ mass states, and depends on the CP-violating phase $\delta_{\rm CP}$. In the three-flavor model, leptonic CP violation in an oscillation mode occurs due to the interference of contributions from terms in this factor — some of which contain $\delta_{\rm CP}$ (i.e., involve the $\nu_{1}$-$\nu_{3}$ mixing directly) and some of which do not. The presence of nonzero CP-odd terms, e.g., Equation 2.15, (which requires $\delta_{\rm CP}\neq 0$ or $\pi$) in the interference patterns would result in an asymmetry in neutrino versus antineutrino oscillations. The magnitude of the CP-violating terms in the oscillation depends most directly on the size of the Jarlskog Invariant , a function that was introduced to provide a measure of CP violation independent of mixing-matrix parameterization. In terms of the three mixing angles and the (as yet unmeasured) CP-violating phase, the Jarlskog Invariant is:

The relatively large values of the mixing angles in the lepton sector imply that leptonic CP-violation effects may be quite large — depending on the value of the phase $\delta_{\rm CP}$, which is currently unknown. Experimentally, it is unconstrained at the 2$\sigma$ level by the global fit . Many theoretical models, examples of which include , provide predictions for $\delta_{\rm CP}$, but these predictions range over all possible values so do not yet provide any guidance.

Given the current best-fit values of the mixing angles and assuming normal hierarchy,

This is in sharp contrast to the very small mixing in the quark sector, which leads to a very small value of the corresponding quark-sector Jarlskog Invariant ,

despite the large value of $\delta^{\rm CKM}_{CP}\approx 70^{\circ}$.

To date, all observed CP-violating effects have occurred in experiments involving systems of quarks, in particular strange and $b$-mesons . Furthermore, in spite of several decades of experimental searches for other sources of CP violation, all of these effects are explained by the CKM quark-mixing paradigm, and all are functions of the quark-sector CP phase parameter, $\delta_{\rm CP}^{\rm CKM}$. In cosmology, successful synthesis of the light elements after the Big Bang (Big Bang Nucleosynthesis) requires that there be an imbalance in the number of baryons and antibaryons to one part in a billion when the Universe is a few minutes old . CP violation in the quark sector has not, however, been able to explain the observed Baryon Asymmetry of the Universe (BAU), due to the small value of $J_{CP}^{CKM}$.

The heavy Majorana right-handed neutrino states that could give rise to leptogenesis in the very early Universe are also a natural consequence of the GUT-based seesaw mechanism — the simplest and most natural explanation of the observed super-light neutrino mass scales. The seesaw mechanism is a theoretical attempt to reconcile the very small masses of neutrinos to the much larger masses of the other elementary particles in the Standard Model. The seesaw mechanism achieves this unification by assuming an unknown new physics scale that connects the observed low-energy neutrino masses with a higher mass scale that involves very heavy sterile neutrino states. The seesaw mechanism as generator of neutrino mass is in addition to the Higgs mechanism that is now known to be responsible for the generation of the quark, charged lepton, and vector boson masses.

The no-equilibrium leptogenesis ingredient is expected in a hot Big Bang scenario, but the Majorana nature of the heavy neutrinos and needed CP violation can only be indirectly inferred from light neutrino experiments by finding lepton number violation (validating their Majorana nature via neutrinoless double-beta decay) and observing CP violation in ordinary neutrino oscillations.

The goal of establishing an experimental basis for assessing this possibility should rank very high on the list of programmatic priorities within particle physics, and can be effectively addressed by LBNE.

2.2 Observation of CP-Violating Effects in Neutrino Oscillation Experiments

Whereas the Standard Model allows for violation of charge-parity (CP) symmetries in weak interactions, CP transformations followed by time-reversal transformations (CPT) are invariant. Under CPT invariance, the probabilities of neutrino oscillation and antineutrino oscillation are equivalent, i.e., $P(\nu_{l}\rightarrow\nu_{l})=P(\overline{\nu}_{l}\rightarrow\overline{\nu}_{l})$ where $l=e,\,\mu,\,\tau$. Measurements of $\nu_{l}\rightarrow\nu_{l}$ oscillations in which the flavor of the neutrino before and after oscillations remains the same are referred to as disappearance or survival measurements. CPT invariance in neutrino oscillations was recently tested by measurements of $\nu_{\mu}\rightarrow\nu_{\mu}$ and $\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{\mu}$ oscillations ; no evidence for CPT violation was found. Therefore, asymmetries in neutrino versus antineutrino oscillations arising from CP violation effects can only be accessed in appearance experiments, defined as oscillations of $\nu_{l}\rightarrow\nu_{l^{\prime}}$, in which the flavor of the neutrino after oscillations has changed. Because of the intrinsic challenges of producing and detecting $\nu_{\tau}$’s, the oscillation modes $\nu_{\mu,e}\rightarrow\nu_{e,\mu}$ provide the most promising experimental signatures of leptonic CP violation.

For $\nu_{\mu,e}\rightarrow\nu_{e,\mu}$ oscillations that occur as the neutrinos propagate through matter, as in terrestrial long-baseline experiments, the coherent forward scattering of $\nu_{e}$’s on electrons in matter modifies the energy and path-length dependence of the vacuum oscillation probability in a way that depends on the magnitude and sign of $\Delta m^{2}_{32}$. This is the Mikheyev-Smirnov-Wolfenstein (MSW) effect that has already been observed in solar-neutrino oscillation (disappearance) experiments . The oscillation probability of $\nu_{\mu,e}\rightarrow\nu_{e,\mu}$ through matter, in a constant density approximation, keeping terms up to second order in $\alpha\equiv|\Delta m_{21}^{2}|/|\Delta m_{31}^{2}|$ and $\sin^{2}\theta_{13}$, is :

In the above, the CP phase $\delta_{\rm CP}$ appears (via $J_{cp}$) in the expressions for $P_{\sin\delta}$ (the CP-odd term) which switches sign in going from $\nu_{\mu}\to\nu_{e}$ to the $\overline{\nu}_{\mu}\to\overline{\nu}_{e}$ channel, and $P_{\cos\delta}$ (the CP-conserving term) which does not. The matter effect also introduces a neutrino-antineutrino asymmetry, the origin of which is simply the presence of electrons and absence of positrons in the Earth.

Recall that in Equation 2.2, the CP phase appears in the PMNS matrix through the mixing of the $\nu_{1}$ and $\nu_{3}$ mass states. The physical characteristics of an appearance experiment are therefore determined by the baseline and neutrino energy at which the mixing between the $\nu_{1}$ and $\nu_{3}$ states is maximal, as follows:

where $n=1,2,3...$ denotes the oscillation nodes at which the appearance probability is maximal.

The dependences on $E_{\nu}$ of the oscillation probability for the LBNE baseline of $L=$1,300 km are plotted on the right in Figures 2.3 and 2.4. The colored curves demonstrate the variation in the $\nu_{e}$ appearance probability as a function of $E_{\nu}$, for three different values of $\delta_{\rm CP}$.

The variation in the $\nu_{\mu}\rightarrow\nu_{e}$ oscillation probabilities with the value of $\delta_{\rm CP}$ indicates that it is experimentally possible to measure the value of $\delta_{\rm CP}$ at a fixed baseline using only the observed shape of the $\nu_{\mu}\rightarrow\nu_{e}$ or the $\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{e}$ appearance signal measured over an energy range that encompasses at least one full oscillation interval. A measurement of the value of $\delta_{\rm CP}\neq 0\ {\rm or}\ \pi$, assuming that neutrino mixing follows the three-flavor model, would imply CP violation. The CP asymmetry, $\mathcal{A}_{CP}$, is defined as

In the three-flavor model the asymmetry can be approximated to leading order in $\Delta m_{21}^{2}$ as :

Regardless of the value obtained for $\delta_{\rm CP}$, it is clear that the explicit observation of an asymmetry between $P(\nu_{l}\rightarrow\nu_{l^{\prime}})$ and $P(\overline{\nu}_{l}\rightarrow\overline{\nu}_{l^{\prime}})$ is sought to directly demonstrate the leptonic CP violation effect that a value of $\delta_{\rm CP}$ different from zero or $\pi$ implies. For long-baseline experiments such as LBNE, where the neutrino beam propagates through the Earth’s mantle, the leptonic CP-violation effects must be disentangled from the matter effects.

2.3 Probing the Neutrino Mass Hierarchy via the Matter Effect

The asymmetry induced by matter effects as neutrinos pass through the Earth arises from the change in sign of the factors proportional to $\Delta m^{2}_{31}$ (namely $A$, $\Delta$ and $\alpha$; Equations 2.12 to 2.16) in going from the normal to the inverted neutrino mass hierarchy. This sign change provides a means for determining the currently unknown mass hierarchy. The oscillation probabilities given in these approximate equations for $\nu_{\mu}\rightarrow\nu_{e}$ as a function of baseline in kilometers and energy in GeV are calculated numerically with an exact formalism and shown in the oscillograms of Figure 2.3 and 2.4 for $\delta_{\rm CP}=0$, for normal and inverted hierarchies, respectively. The oscillograms include the matter effect, assuming an Earth density and electron fraction described by . These values are taken as a constant average over paths through regions of the Earth with continuous density change. Any baseline long enough to pass through a discontinuity is split into three or more segments each of constant average density and electron fraction. The solid black curves in the oscillograms indicate the location of the first and second oscillation maxima as given by Equation 2.18, assuming oscillations in a vacuum; matter effects will change the neutrino energy values at which the mixing between the $\nu_{1}$ and $\nu_{3}$ mass states is maximal.

The dependence of the matter effect on the mass hierarchy is illustrated in the oscillograms plotted on the left hand side of Figures 2.3 and 2.4, and can be characterized as follows:

For normal hierarchy, $P(\nu_{\mu}\rightarrow\nu_{e})$ is enhanced and $P(\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{e})$ is suppressed. The effect increases with baseline at a fixed $L/E$.

For inverted hierarchy, $P(\nu_{\mu}\rightarrow\nu_{e})$ is suppressed and $P(\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{e})$ is enhanced. The effect increases with baseline at a fixed $L/E$.

The matter effect has the largest impact on the probability amplitude at the first oscillation maximum.

The matter effect introduces a phase shift in the oscillation pattern, shifting it to a lower energy for a given baseline when the hierarchy changes from normal to inverted. The shift is approximately $-100$ MeV.

2.4 Disentangling CP-Violating and Matter Effects

In Figure 2.5, the asymmetries induced by matter and maximal CP violation (at $\delta_{\rm CP}=\pm\pi/2$) are shown separately as 2D oscillograms in baseline and neutrino energy. The matter effect induces an asymmetry in $P(\nu_{l}\rightarrow\nu_{l^{\prime}})$ and $P(\overline{\nu}_{l}\rightarrow\overline{\nu}_{l^{\prime}})$ that adds to the CP asymmetry. At longer baselines ($>1000\,$km), the matter asymmetry in the energy region of the first oscillation node is driven primarily by the change in the $\nu_{e}$ appearance amplitude. At shorter baselines ($\mathcal{O}(100\,\rm{km})$) the asymmetry is driven by the phase shift. The dependence of the asymmetry on baseline and energy, where the oscillation probabilities peak and the appearance signals are largest, can be approximated as follows:

The phenomenology of $\nu_{\mu}\rightarrow\nu_{e}$ oscillations described in Section 2.2.2 implies that the experimental sensitivity to CP violation and the mass hierarchy from measurements of the total asymmetry between $P(\nu_{l}\rightarrow\nu_{l^{\prime}})$ and $P(\overline{\nu}_{l}\rightarrow\overline{\nu}_{l^{\prime}})$ requires the disambiguation of the asymmetry induced by the matter effect and that induced by CP violation. This is particularly true for experiments designed to access mixing between the $\nu_{1}$ and $\nu_{3}$ mass states using neutrino beams of $\mathcal{O}(1\,\rm{GeV})$. Such beams require baselines of at least several hundred kilometers, at which the matter asymmetries are significant. The currently known values of the oscillation parameters permit calculation of the magnitude of the matter asymmetry within an uncertainty of $<10\%$; only the sign of the asymmetry, which depends on the sign of $\Delta m^{2}_{31}$, is unknown. Since the magnitude of the matter asymmetry is known, baselines at which the size of the matter asymmetry exceeds that of the maximal possible CP asymmetry are required in order to separate the two effects.

Figure 2.6 illustrates the ambiguities that can arise from the interference of the matter and CP asymmetries. The plots show the total asymmetry as a function of $\delta_{\rm CP}$ at four baseline values (clockwise from top left): 290 km, 810 km, 2,300 km and 1,300 km. The curves in black and red illustrate the asymmetries at the first and second oscillation nodes, respectively. The solid lines represent normal hierarchy, and the dashed lines represent inverted hierarchy. The plots demonstrate that experimental measurements of the asymmetry (Equation 2.19) at the first oscillation node could yield ambiguous results for short baselines if the hierarchy is unknown. This occurs in regions of the ($L,E,\delta_{\rm CP}$) phase space where the matter and CP asymmetries cancel partially or totally. For example, the green lines in Figure 2.6 indicate the asymmetry at the first node for maximal CP violation ($\delta_{\rm CP}=\pi/2$) with an inverted hierarchy. At a baseline of 290 km, the measured asymmetry at $\delta_{\rm CP}=\pi/2$ (inverted hierarchy) is degenerate with that at $\delta_{\rm CP}\sim 0$ (normal hierarchy) at the first node. Measurements of the asymmetry at different $L/E$ or at different baselines can break the degeneracies (Equation 2.22). At very long baselines, for which the matter asymmetry exceeds the maximal CP asymmetry at the first oscillation node, there are no degeneracies and the mass hierarchy and CP asymmetries can be resolved within the same experiment. For the current best-fit values of the oscillation parameters, the matter asymmetry exceeds the maximal possible CP asymmetry at baselines of $\geq$ 1,200 km.

2.5 Optimization of the Oscillation Baseline for CPV and Mass Hierarchy

2.6 Physics from Precision Measurements of Neutrino Mixing

Precision measurements of the neutrino mixing parameters in long-baseline oscillations not only reveal the neutrino mixing patterns in greater detail, but also serve as probes of new physics that manifests as perturbations in the oscillation patterns driven by three-flavor mixing.

The determination of whether there is maximal mixing between $\nu_{\mu}$ and $\nu_{\tau}$ — or a measurement of the deviation from maximal — is of great interest theoretically . Models of quark-lepton universality propose that the quark and lepton mixing matrices (Equations 2.7 and 2.6, respectively) are given by

where $T$ is determined by Majorana physics and $\epsilon_{\rm Cabbibo}$ refers to small terms driven by the Cabbibo weak mixing angle ($\theta_{C}=\theta_{12}^{\rm CKM}$). In such models $\theta_{23}\sim\pi/4+\Delta\theta$, where $\Delta\theta$ is of order the Cabbibo angle, $\theta_{C}$, and $\theta_{13}\sim\theta_{C}/\sqrt{2}$. It is therefore important to determine experimentally both the value of $\sin^{2}\theta_{23}$ and the octant of $\theta_{23}$ if $\theta_{23}\neq 45^{\circ}$.

Direct unitarity tests, in which the individual components of the PMNS matrix are measured separately, are challenging due to limited experimentally available oscillation channels . Application of the “proof by contradiction” principle offers another way to perform the unitarity tests. In these tests, the mixing angles are extracted from the data by assuming unitarity in the standard three-flavor framework. If measurements of the same mixing angle by two different processes are inconsistent, then the standard three-flavor framework is insufficient and new physics beyond this framework is required. Observation of unitarity violation will constrain the phase space of possible new physics. In particular, the precision measurement of $\sin^{2}2\theta_{13}$ provides the most promising unitarity test for the PMNS matrix. It is important to note that several theoretical models of new physics, such as the existence of sterile neutrinos or nonstandard interactions, could lead to apparent deviations of the $\sin^{2}2\theta_{13}$ value measured in $\nu_{e}$ appearance experiments from that measured in reactor ($\overline{\nu}_{e}$ disappearance) experiments.

Precision measurements of $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ survival over long baselines could reveal nonstandard physics driven by new interactions in matter. Examples of some of these effects and the experimental signatures in long-baseline oscillations are discussed in Chapter 4.

In addition, experiments with long enough baselines and sufficient neutrino flux at $E_{\nu}>3$ GeV, coupled with high-resolution tracking detectors, as in the LBNE design, can also probe $\nu_{\mu}\rightarrow\nu_{\tau}$ appearance with higher precision than is currently possible using $\nu_{\tau}$ charged-current interactions. The combination of $\nu_{\mu}\rightarrow\nu_{\mu}$, $\nu_{\mu}\rightarrow\nu_{e}$, and $\nu_{\mu}\rightarrow\nu_{\tau}$ can ultimately over-constrain the three-flavor model of neutrino oscillations both in neutrino and antineutrino modes.

2.7 Oscillation Physics with Atmospheric Neutrinos

Atmospheric neutrinos are unique among sources used to study oscillations; the flux contains neutrinos and antineutrinos of all flavors, matter effects play a significant role, both $\Delta m^{2}$ values contribute to the oscillation patterns, and the oscillation phenomenology occurs over several orders of magnitude in both energy (Figure 2.8) and path length. These characteristics make atmospheric neutrinos ideal for the study of oscillations and provide a laboratory suitable to search for exotic phenomena for which the dependence of the flavor-transition and survival probabilities on energy and path length can be defined. The probabilities of atmospheric $\nu_{\mu}\rightarrow\nu_{e}$ and $\overline{\nu}_{\mu}\rightarrow\overline{\nu}_{e}$ oscillations for normal and inverted hierarchies are shown as a function of zenith angle in Figure 2.9.

Even with dedicated long-baseline experiments exploring the large mass splitting ($\Delta m^{2}_{32}$) for nearly a decade, atmospheric data continue to contribute substantially to our understanding of the neutrino sector. Broadly speaking:

The data demonstrate complementarity with beam results via two- and three-flavor fits and the measurement of a $\nu_{\tau}$ appearance signal consistent with expectations.

The data serve to increase measurement precision through global fits, given that the sensitivity of atmospheric neutrinos to the mass hierarchy is largely independent of $\delta_{\rm CP}$ and the octant of $\theta_{23}$.

New physics searches with atmospheric neutrinos have placed limits on CPT violation, nonstandard interactions, mass-varying neutrinos and Lorentz-invariance violation.

Atmospheric neutrinos can continue to play these roles in the LBNE era given LBNE’s deep-underground far detector. In particular, complementarity will be vital in a future where, worldwide, the number of high-precision, long-baseline beam/detector facilities is small. The physics potential of a large underground liquid argon detector for measuring atmospheric neutrinos is discussed in Section 4.6.

3 Nucleon Decay Physics Motivated by Grand Unified Theories

Although no evidence for proton decay has been detected, the lifetime limits from the current generation of experiments already constrain the construction of many contemporary GUT models. In some cases, these lifetime limits are approaching the upper limits allowed by GUT models. This situation points naturally toward continuing the search with new, larger detectors. These searches are motivated by a range of scientific issues:

Conservation laws arise from underlying symmetries in Nature . Conservation of baryon number is therefore unexplained since it corresponds to no known long-range force or symmetry.

Baryon number non-conservation has cosmological consequences, such as a role in inflation and the matter-antimatter asymmetry of the Universe.

Proton decay is predicted at some level by almost all GUTs.

Some GUTs can accommodate neutrinos with nonzero mass and characteristics consistent with experimental observations.

GUTs incorporate other previously unexplained features of the Standard Model such as the relationship between quark and lepton electric charges.

The unification scale is not accessible by any accelerator experiment; it can only be probed by virtual processes such as with proton decay.

GUTs usually predict the relative branching fractions of different nucleon decay modes. Testing these predictions would, however, require a sizeable sample of proton decay events.

The dominant proton decay mode of a GUT is often sufficient to roughly identify the likely characteristics of the GUT, such as gauge mediation or the involvement of supersymmetry.

3.2 Proton Decay Modes

From the body of literature, two decay modes (shown in Figure 2.10) emerge that dominate the LBNE experimental design. The more well-known of the two, the decay mode of $p\rightarrow e^{+}\pi^{0}$, arises from gauge mediation. It is often predicted to have the higher branching fraction and is also demonstrably the more straightforward experimental signature for a water Cherenkov detector. In this mode, the total mass of the proton is converted into the electromagnetic shower energy of the positron and two photons from $\pi^{0}$ decay, with a net momentum vector near zero.

The second key mode is $p\rightarrow K^{+}\overline{\nu}$. This mode is dominant in most supersymmetric GUTs, many of which also favor additional modes involving kaons in the final state. This decay mode with a charged kaon is uniquely interesting; since stopping kaons have a higher ionization density than other particles, a LArTPC could detect it with extremely high efficiency, as described in Chapter 5. In addition, many final states of $K^{+}$ decay would be fully reconstructable in a LArTPC.

There are many other allowed modes of proton or bound neutron into antilepton plus meson decay that conserve $B-L$ In these models, the quantum number $B-L$ is expected to be conserved even though $B$ and $L$ are not individually conserved., but none of these will influence the design of a next-generation experiment. The most stringent limits, besides those on $p\rightarrow e^{+}\pi^{0}$, include the lifetime limits on $p\rightarrow\mu^{+}\pi^{0}$ and $p\rightarrow e^{+}\eta$, both of which are greater than $4\text{\times}{10}^{33}$ years . Any experiment that will do well for $p\rightarrow e^{+}\pi^{0}$ will also do well for these decay modes. The decays $p\rightarrow\overline{\nu}\pi^{+}$ or $n\rightarrow\overline{\nu}\pi^{0}$ may have large theoretically predicted branching fractions, but they are experimentally difficult due to the sizeable backgrounds from atmospheric-neutrino interactions. The decay $p\rightarrow\mu^{+}K^{0}$ can be detected relatively efficiently by either water Cherenkov or LArTPC detectors.

A number of other possible modes exist, such as those that conserve $B+L$, that violate only baryon number, or that decay into only leptons. These possibilities are less well-motivated theoretically, as they do not appear in a wide range of models, and are therefore not considered here.

Figure 2.11 shows a comparison of experimental limits, dominated by recent results from Super–Kamiokande to the ranges of lifetimes predicted by an assortment of GUTs. At this time, the theory literature does not attempt to precisely predict lifetimes, concentrating instead on suggesting the dominant decay modes and relative branching ratios. The uncertainty in the lifetime predictions comes from details of the theory, such as masses and coupling constants of unknown heavy particles, as well as poorly known details of matrix elements for quarks within the nucleon.

It is apparent from Figure 2.11 that a continued search for proton decay is by no means assured of obtaining a positive result. With that caveat, an experiment with sensitivity to proton lifetimes between $10^{33}$ and $10^{35}$ years is searching in the right territory over virtually all GUTs; even if no proton decay is detected, stringent lifetime limits will provide strong constraints on such models. Minimal SU(5) was ruled out by the early work of IMB and Kamiokande and minimal SUSY SU(5) is considered to be ruled out by Super–Kamiokande. In most cases, another order of magnitude in improved limits will not rule out specific models but will constrain their allowed parameters; this could allow identification of models which must be fine-tuned in order to accommodate the data, and are thus less favored.

As Chapter 5 will show, the performance and scalability of the LArTPC technology opens up nucleon decay channels that are not as readily accessible in existing and proposed water Cherenkov detectors, providing LBNE with a unique and compelling opportunity for discovery.

4 Supernova-Neutrino Physics and Astrophysics

For over half a century, researchers have been grappling to understand the physics of the neutrino-driven core-collapse supernova. The interest in observing the core-collapse supernova explosion mechanism comes from the key role supernovae of this type have played in the history of the Universe. Without taking supernova feedback into account, for example, modern simulations of galaxy formation cannot reproduce the structure of our galactic disk. More poetically, the heavy elements that are the basis of life on Earth were synthesized inside stars and ejected by supernova explosions.

Neutrinos from a core-collapse supernova are emitted in a burst of a few tens of seconds duration, with about half emitted in the first second. They record the information about the physical processes in the center of the explosion during the first several seconds — as it is happening. Energies are in the few-tens-of-MeV range and luminosity is divided roughly equally between flavors. The basic model of core collapse was confirmed by the observation of neutrino events from SN1987A, a supernova in the Large Magellanic Cloud — outside the Milky Way — 50 kpc (kiloparsecs) away. Nineteen events were detected in two water Cherenkov detectors and additional events were reported in a scintillator detector . The neutrino signal from a core-collapse supernova in the Milky Way is expected to generate a high-statistics signal from which LBNE could extract a wealth of information .

The explosion mechanism is thought to have three distinct stages: the collapse of the iron core, with the formation of the shock and its breakout through the neutrinosphere; the accretion phase, in which the shock temporarily stalls at a radius of about 200 km while the material keeps raining in; and the cooling stage, in which the hot proto-neutron star loses its energy and trapped lepton number, while the re-energized shock expands to push out the rest of the star. Each of these three stages is predicted to have a distinct signature in the neutrino signal. Thus, it should be possible to directly observe, for example, how long the shock is stalled. More exotic features of the collapse may be observable in the neutrino flux as well, such as possible transitions to quark matter or to a black hole. (An observation in conjunction with a gravitational wave detection would be especially interesting; e.g. .)

Over the last two decades, neutrino flavor oscillations have been firmly established in solar neutrinos and a variety of terrestrial sources. The physics of the oscillations in the supernova environment promises to be much richer than in any of the cases measured to date, for a variety of reasons:

Neutrinos travel through the changing profile of the explosion with stochastic density fluctuations behind the expanding shock and, due to their coherent scattering off of each other, their flavor states are coupled.

The oscillation patterns come out very differently for the normal and inverted mass hierarchies.

The expanding shock and turbulence leave a unique imprint in the neutrino signal.

Additional information on oscillation parameters, free of supernova model-dependence, will be available if matter effects due to the Earth can be observed in detectors at different locations around the world .

The observation of this potentially copious source of neutrinos will also allow limits on coupling to axions, large extra dimensions, and other exotic physics (e.g., ).

The oscillations of neutrinos and antineutrinos from a core-collapse supernova manifest very differently. In the neutrino channel, the oscillation features are in general more pronounced, since the initial spectra of $\nu_{e}$ and $\nu_{\mu}$ ($\nu_{\tau}$) are always significantly different. It would be extremely valuable to detect both neutrino and antineutrino channels with high statistics.

Only about two dozen neutrinos were observed from SN1987A, which occurred in a nearby galaxy; in contrast, the currently proposed next-generation detectors would register thousands or tens of thousands of interactions from a core-collapse supernova in our galaxy. The type of observed interactions will depend on the detector technology: a water-Cherenkov detector is primarily sensitive to $\overline{\nu}_{e}$’s, whereas a LArTPC detector has excellent sensitivity to $\nu_{e}$’s. In each case, the high event rate implies that it should be possible to measure not only the time-integrated spectra, but also their second-by-second evolution. This is a key feature of the supernova-burst physics potential of the planned LBNE experiment.

Because the neutrinos emerge promptly after core collapse, in contrast to the electromagnetic radiation which must beat its way out of the stellar envelope, an observation could provide a prompt supernova alert , allowing astronomers to find the supernova in early light turn-on stages, which could yield information about the progenitor (in turn, important for understanding oscillations). Further, observations and measurements by multiple, geographically separated detectors during a core collapse — of which several are expected to be online over the next few decades — will enhance the potential science yield from such a rare and spectacular event .

Project and Design

In its 2008 report, the U.S. Particle Physics Project Prioritization Panel (P5) P5 is an advisory panel to the two main funding bodies for particle physics in the United States, the Department of Energy (DOE) and the National Science Foundation (NSF). recommended a world-class neutrino physics program as a core component of a U.S. particle physics program that revolves around three research frontiers as shown in Figure 3.1. Included in the report is the long-term vision of a large far detector at the site of the former Homestake Mine in Lead, SD, and a high-intensity, wide-band neutrino source at Fermilab. At the time, the proposed Deep Underground Science and Engineering Laboratory (DUSEL) was planned to occupy the site of the former mine; it is now the Sanford Underground Research Facility.

On January 8, 2010 the DOE approved the Mission Need statement A Mission Need statement initiates the process and provides initial funding toward developing the conceptual design of a DOE scientific project. for a new long-baseline neutrino experiment that would enable this world-class program and firmly establish the U.S. as the leader in neutrino science. The LBNE experiment is designed to meet this Mission Need.

With the facilities provided by the LBNE Project and the unique features of the experiment — in particular the long baseline of 1,300 km, the wide-band beam and the high-resolution, underground far detector --- LBNE will conduct a broad scientific program addressing key physics questions concerning the nature of our Universe as described in Chapter 2. The focus of the long-baseline neutrino program will be the explicit demonstration of leptonic CP violation, if it exists, and the determination of the neutrino mass hierarchy.

The focus of the non-beam scientific program will be to search for proton decay, to enable detailed studies of atmospheric neutrinos, and to detect and measure the neutrino flux from a supernova, should one occur within our galaxy.

It is currently planned to implement LBNE as a phased program, with increased scientific capabilities at each phase. The initial phase of LBNE will achieve significant advances with respect to its primary scientific objectives as compared to current experiments. The goal for the initial phase of LBNE is:

A liquid argon time-projection chamber (LArTPC) detector of fiducial mass at least 10 kt located at the Sanford Underground Research Facility at a depth of 4,850 feet.

A high-precision near neutrino detector on the Fermilab site.

2 Near Site: Fermi National Accelerator Laboratory

Fermi National Accelerator Laboratory, originally named the National Accelerator Laboratory, was commissioned by the U.S. Atomic Energy Commission, under a bill signed by President Lyndon B. Johnson on November 21, 1967. On May 11, 1974, the laboratory was renamed in honor of 1938 Nobel Prize winner Enrico Fermi, one of the preeminent physicists of the atomic age.

Today, the DOE operates national laboratories throughout the United States, including Fermilab. The DOE awarded to Fermi Research Alliance (FRA) the management and operating contract for Fermilab, effective January 1, 2007. The FRA is a tax-exempt, limited liability company (LLC) organized and operated for charitable, scientific and educational purposes under Section 501(c)(3) of the Internal Revenue Code. The two members of FRA are the University of Chicago and the Universities Research Association (URA). FRA has earned extensions to the Fermilab contract through Dec. 31, 2015.

At Fermilab, a robust scientific program pushes forward on the three interrelated scientific frontiers specified by the P5 panel in 2008 and illustrated in Figure 3.1:

At the Energy Frontier, Fermilab scientists are significant contributors to the LHC and to the CMS experiment.

At the Intensity Frontier, Fermilab operates two neutrino beams that support a number of experiments. In the next few years several new neutrino and muon experiments will be coming online, of which LBNE will be the largest.

At the Cosmic Frontier, Fermilab runs and/or participates in several experiments, with instruments installed in North America, South America and Europe.

Upgrades to the Recycler The Recycler, a fixed 8-GeV kinetic energy storage ring located directly above the MI beamline, stores protons from the 8-GeV Booster during MI ramp up. and MI as part of the NO$\nu$A Project, as well as the Proton Improvement Plan (PIP) that is currently underway, comprise a set of improvements to the existing Linac, Booster and MI aimed at supporting 15-Hz beam operations from the Booster (Figure 3.4).

A conceptual plan for further upgrades to the Fermilab accelerator complex has been completed. Called the Proton Improvement Plan-II (PIP-II) , its goal is to increase the capabilities of the existing accelerator complex to support delivery of 1.2 MW of beam power to the LBNE production target at the initiation of operations, while simultaneously providing a platform for subsequent upgrades of the complex to multi-MW capability. The starting point of this plan is the Project X Reference Design Report .

3 Far Site: Sanford Underground Research Facility

In 2006, Barrick Gold Corporation donated the Homestake Gold Mine site, located in Lead, South Dakota (Figure 3.7) to the State of South Dakota, following over 125 years of mining. Mining operations created over 600 km of tunnels and shafts in the facility, extending from the surface to over 8,000 feet below ground. The mining levels are distributed $\sim$150 feet apart and are referenced by their depth below the facility entrance, e.g., the level 4,850 feet below ground is referred to as the 4850L. This former mine encompasses the deepest caverns in the western hemisphere, offering extensive drifts both vertically and laterally. A detailed vertical cross section of the 60 underground levels developed for mining is shown in Figure 3.8.

In 2004, the South Dakota state legislature created the South Dakota Science and Technology Authority (SDSTA) to foster scientific and technological investigations, experimentation and development in South Dakota. A six-member board of directors appointed by the governor of South Dakota directs the SDSTA. The SDSTA’s first task was to reopen the former Homestake site to the 4,850-foot level for scientific research. At this site, the SDSTA now operates and maintains the Sanford Underground Research Facility through a contract managed and overseen by a dedicated operations office at Lawrence Berkeley National Laboratory as a deep-underground research laboratory. The Sanford Underground Research Facility property comprises 186 acres on the surface and 7,700 acres underground. The surface campus includes approximately 253,000 gross square feet of existing structures. A surface schematic of the campus is shown in Figure 3.9.

The state legislature has since committed more than $40 million in state funds to the development of the Sanford Underground Research Facility, and the state has also obtained a$10 million Community Development Block Grant to help rehabilitate the site. In addition, a $70 million donation from philanthropist T. Denny Sanford has been used to reopen the site for science and to establish the Sanford Center for Science Education. The initial concepts for the facility were developed with the support of the U.S. National Science Foundation (NSF) as the primary site for the NSF’s Deep Underground Science and Engineering Laboratory (DUSEL). With the National Science Board’s decision to halt development of the NSF-supported underground laboratory, the DOE now supports the operation of the facility in addition to state and private funding. Both the NSF and the DOE support experiments at the site.

Access to the underground areas has been reestablished and the primary access rehabilitated and improved. The facility has been stabilized and the accumulated underground water has been pumped out below 5,680 ft. The area around the Davis cavern at the 4850L, named for the late Ray Davis, has been enlarged and adapted primarily for current and next-generation dark matter and neutrinoless double-beta decay experiments. This upgraded area of the 4850L is now called the Davis Campus. Additional science efforts are located throughout the facility, including an ultrapure detector development laboratory, geophysics and geological efforts, and a public outreach program. A 3D schematic highlighting the planned development of the 4850L is shown in Figure 3.10.

Another advantage of the 4850L Sanford Underground Research Facility site for LBNE is the low level of rock radioactivity that could contribute backgrounds to the supernova burst neutrino signal and other low-energy physics searches. It was found that the U/Th/K radioactivity for the underground bedrocks at Homestake is in general very low when compared to common construction materials such as concrete and shotcrete; some samples are in the sub-ppm levels. However, samples from rhyolite intrusions, a very small fraction of the total, show a relatively high content of U, Th, and K more typical of the levels found in other laboratories, in particular those in granitic formations. Regions of potential rhyolite intrusions have been identified and documented as shown in Figure 3.12. In some cases local shielding significantly mitigates the impact of the rhyolite intrusions. Table 3.1 presents some of the assay results, obtained by direct gamma counting for rock samples from the mine, including those collected close to the 4850L .

The Large Underground Xenon (LUX) experiment is now operating in the cavern first excavated for Davis in the 1960s. LUX is the most sensitive detector yet to search for dark matter . The Majorana Demonstrator experiment (MJD), also being installed in a newly excavated space adjacent to the original Davis cavern, will search for neutrinoless double-beta decay. Figure 3.13 shows four photographs of facilities and activities at the Sanford Underground Research Facility related to the LUX and MJD at the 4850L.

The LBNE far detector will benefit from the common infrastructure being developed to house large experiments underground. The layout of the different proposed experiments at the 4850L, including the LBNE detector, is shown in Figure 3.10.

In addition to LBNE, LUX and MJD, the Sanford Underground Research Facility science program for the coming five to ten years (Figure 3.14) consists of the expansion of the LUX dark matter search, the Center for Ultralow Background Experiments at Dakota (CUBED), and the geoscience installations. Long-term plans are being developed to host a nuclear astrophysics program involving underground particle accelerators (CASPAR and DIANA), and second- and third-generation dark matter experiments.

4 Beamline

The primary beam, composed of protons in the energy range of 60-120 GeV, will be extracted from the MI-10 straight section of the Main Injector using single-turn extraction. The beam will then be transported to the target area within a beam enclosure embedded in an engineered earthen embankment (hill). The primary-beam transport section is designed for very low losses. The embankment’s dimensions are designed to be commensurate with the bending strength of the required dipole magnets so as to provide a net 5.8∘ downward vertical bend to the neutrino beam (Figures 3.15 and 3.16). The beamline is then buried by soil shielding that is placed at a stable angle of repose, resulting in the embankment final geometry.

The beamline design provides a wide-band neutrino beam with a peak flux at 2.5 GeV, which matches the location of the first $\nu_{\mu}\rightarrow\nu_{e}$ oscillation maximum. The NuMI reference target design used for LBNE allows the target to be moved with respect to Horn 1. The location of the upstream face The proton beam direction determines the upstream and downstream conventions. The upstream (front) face of Horn 1 is therefore the Horn 1 face closest to the proton beam window. of the target with respect to the upstream face of Horn 1 can be varied from $-$35 cm (default location) to $-$2.85 m, thus the LBNE beamline can produce a wide range of beam spectra. Three possible far-site beam spectra, produced by moving the target from $-$35 cm (low-energy) to $-$1.5 m (medium-energy) to $-$2.5 m (high energy) are shown in Figure 3.19.

An array of muon detectors in a small alcove immediately downstream of the absorber measures tertiary-beam muons and thereby indirectly provides information on the direction, profile and flux of the neutrino beam. This will be described in Section 3.5.

The beamline conventional facilities include the civil construction required to house the beamline components in their planned layout as shown in Figures 3.15 and 3.16. Following the beam from southeast to northwest, or roughly from right to left in Figure 3.15, the elements include the underground Extraction Enclosure, the Primary Beam Enclosure (inside the embankment) and its accompanying surface-based Service Building (LBNE 5), the Target Complex (LBNE 20) located in the embankment, the Decay Pipe, the underground Absorber Hall with the muon alcove, and its surface-based Service Building (LBNE 30). The embankment will need to be approximately 290 m long and 18 m above grade at its peak. The planned near neutrino detector facility is located as near as is feasible to the west site boundary of Fermilab, along the line-of-sight indicated in red in Figure 3.15.

The following LBNE beamline design improvements beyond the CD-1 conceptual design are being assessed:

An increase in the length of the decay pipe up to 250 m (the maximum length allowed by the existing Fermilab site boundaries), and also possibly an increase in its diameter up to 6 m. Increases to the decay pipe size would require additional cost of the order several tens of millions of dollars. Increasing the length of the decay pipe from 200 to 250 m increases the overall event rate in the oscillation region by 12%. Increases in the decay pipe diameter produce a 6% increase in the low-energy neutrino event rate as shown in Table 3.3.

It has recently been decided to fill the decay pipe with helium instead of air. The total $\nu_{\mu}$ event rate increases by about 11%, with a decrease in $\overline{\nu}$ contamination in the neutrino beam. Introducing helium in the decay pipe requires the design and construction of a decay pipe window.

An increase in the horn current of the horns by a modest amount (from 200 kA to 230 kA); this is expected to increase the neutrino event rates by about 10-12% at the first oscillation maximum . A Finite Element Analysis simulation and a cooling test of the horns are underway to evaluate this option.

Use of an alternate material to the POCO graphite for the target to increase the target longevity. This would involve additional R&D effort and design work. A beryllium target, for example, could be made shorter, potentially improving the horn focusing.

Development of more advanced horn designs that could boost the low-energy flux in the region of the second oscillation maximum. It should be noted that the target and horn systems can be modified or replaced even after operations have begun if improved designs enable higher beam flux.

5 Near Detector

To achieve the precision required to make a significant advancement in the measurement of neutrino oscillation parameters over current experiments and to reach the desired $5\sigma$ sensitivity to CP violation (discussed in Chapters 4 and 7), LBNE will need to measure the unoscillated flux spectrum, to a few percent, for all neutrino species in the beam: $\nu_{\mu},\,\nu_{e},\,\overline{\nu}_{\mu}$ and $\overline{\nu}_{e}$. This requires a high-resolution, magnetized near neutrino detector with high efficiency for identifying and measuring electrons and muons. To measure the small $\nu_{e}$ contamination in the beam with greater precision, the detector would need to be able to distinguish $e^{+}$ from $e^{-}$; this would require a low-density detector with a commensurately long physical radiation length. In addition, use of an argon target nucleus — similar to the far detector — would allow cancellation of systematic errors. A reference design has been developed for a near neutrino detector that will meet these requirements; in particular it will measure the neutrino event rates and cross sections on argon, water and other nuclear targets for both $\nu_{e}$ and $\nu_{\mu}$ charged current (CC) and neutral current (NC) scattering events.

In addition to the near neutrino detector, a sophisticated array of muon detectors will be placed just downstream of the absorber. The muon detectors, shown in Figure 3.20, detect mostly muons from the two-body decays of $\pi^{+(-)}\rightarrow\mu^{+(-)}\nu_{\mu}(\overline{\nu}_{\mu})$ in the beamline, thus the measured muon and $\nu_{\mu}$ flux distributions are highly correlated. The ionization chamber array will provide pulse-by-pulse monitoring of the beam profile and direction. The variable-threshold gas Cherenkov detectors will map the energy spectrum of the muons exiting the absorber on an on-going basis. The stopped muon detectors will sample the lowest-energy muons, which are known to correlate with the neutrino flux above 3 GeV — equivalent to about half the neutrino flux near the first oscillation maximum — and a decreasing fraction of it at lower energy. This system, together with the existing level of understanding of the similar NuMI beam and experience in previous neutrino oscillation experiments, will provide additional constraints on the understanding of the neutrino beam, and will thus support and complement the near neutrino detector measurements.

The design of the near neutrino detector is the subject of study by the LBNE Collaboration, and alternatives such as a magnetized liquid argon TPC will be investigated further. A detailed description of the fine-grained tracker can be found in , and descriptions of it and the alternative LArTPC design are presented in the March 2012 LBNE CDR (Volume 3 of ).

High-intensity neutrino beams can be used as probes of new physics and given the broad energy range of the LBNE beam, a diverse range of physics measurements is possible in the high-resolution near neutrino detector. These potentially wide-ranging physics measurements would complement other physics programs, such as those at Jefferson Laboratory, that are using proton, electron or ion beams from colliders and fixed-target facilities. A detailed discussion of the physics capabilities of a high-resolution near detector is presented in Chapter 7 and in .

6 Far Detector

The liquid argon TPC technology chosen for LBNE combines fine-grained tracking with total absorption calorimetry to provide a detailed view of particle interactions, making it a powerful tool for neutrino physics and underground physics such as proton decay and supernova-neutrino observation. It provides millimeter-scale resolution in 3D for all charged particles. Particle types can be identified both by their $dE/dx$ and by track patterns, e.g., the decays of stopping particles. The modest radiation length (14 cm) is sufficiently short to identify and contain electromagnetic showers from electrons and photons, but long enough to provide good $e/\gamma$ separation by $dE/dx$ (one versus two minimum ionizing particles) at the beginning of the shower. In addition, photons can be distinguished from electrons emanating from an event vertex by the flight path before their first interaction. These characteristics allow the LArTPC to identify and reconstruct signal events with high efficiency while rejecting backgrounds to provide a high-purity data sample. The principal design parameters of the full-scope LBNE LArTPC far detector are given in Table 3.6.

Other important considerations for the construction of LBNE’s large LArTPC far detector include:

cryogenic safety and the elimination of hazards associated with large cryogenic liquid volumes

attainment of stringent argon purity requirements with respect to electronegative contaminants (e.g., $<0.2\,$ppb O2 concentration)

ease of transport and assembly of TPC mechanical systems

efficient deployment of high-sensitivity/low-noise electronics for readout of the ionization signal

The detector vessels will be constructed using technology standards from the liquefied natural gas (LNG) industry. With similar requirements and geometries, adaptation of industrial LNG cryostat design provides a high-performance, extensively tested approach to the challenge of liquid argon containment for LBNE. The cryostats in large LNG tanker ships are constructed using a thin (1–2 mm), polished, stainless steel inner membrane surrounded by thick foam passive insulation. With stainless steel as the only wetted surface, this is an inherently clean design, ideal for liquid argon detectors where high purity is essential.

The underground detector placement at the 4850L of the Sanford Underground Research Facility was studied in detail during the Conceptual Design Phase of LBNE and presented at the Fermilab Director’s Independent Conceptual Design Review in March of 2012 . Significant effort has been invested to minimize the (dominant) cost of the far site conventional facilities.

Three sense wire planes (two induction planes and one collection plane) with wire pitches of 4.8 mm are mounted on each side of an APA frame, for sensitivity to ionization signals originating within the TPC cell on either side. The wires on these planes are oriented vertically (collection) and at $\pm 45^{\circ}$ (induction) The current design uses a $36^{\circ}$ orientation to remove hit assignment ambiguities.. The induction plane wires are wrapped around the APA frame, and are therefore sensitive to charge arriving from either side of the APA, depending on where the charge arrives along the length of the wires. This configuration allows placement of readout electronics at the top and bottom of each two-APA unit. (Cables from the bottom APA are routed up through the support frame, thereby eliminating any obstruction they would otherwise cause.) In this way, adjacent APA-pairs can be abutted so as to minimize the uninstrumented region in the gaps between them along the length of the detector.

Low-noise, low-power CMOS (Complementary Metal Oxide Semiconductor) preamplifier and ADC ASICS (Application Specific Integrated Circuit) have been developed for deployment on circuit boards mounted directly on the APA frames. This scheme ensures good signal-to-noise performance, even allowing for some attenuation of long-drift ionization signals due to residual impurities in the argon. It also offers the possibility of digital signal processing, including multiplexing and zero suppression at the front end, thereby limiting the cable plant within the cryostat and the number of penetrations required, while also easing requirements on the downstream readout/DAQ systems located outside the cryostat. The ASICS have been laid out following design rules developed explicitly for long-term operation at cryogenic temperatures.

In order to separate neutrino beam events from other interactions — particularly for proton decay and supernova neutrino signals — it is necessary to accurately determine the event time relative to the neutrino beam time window or an incoming cosmic muon. If the event time is known at the microsecond level then out-of-time cosmic-ray backgrounds for beam neutrinos can be rejected to the level of $10^{-5}$ (the beam spill duty factor). The slow ionization-electron drift velocity gives the TPC its 3D imaging capability, but an independent fast signal is required to localize events in time and in space along the drift direction. The excellent scintillation properties of liquid argon (${\cal O}(10^{4})$ photons per MeV of energy deposition) are exploited to address this issue. A photon detection system is planned for detection of the 128-nm scintillation light that, in turn, allows determination of the event timing. Several photon detector designs are under study. The most advanced design uses cast acrylic bars coated with wavelength shifter, and SiPMs (silicon photomultipliers) at the ends for read-out. These bars will be assembled into paddles of dimensions 10 cm by 2 m, and mounted on the APA frames, fitting within the 5-cm gap between the sets of wire planes located on both sides of the frames. Initial studies indicate a light yield of 0.1 to 0.5 photoelectrons per MeV.

Given the modular design of the detector and the use of industrial technologies in the cryogenics system, there is a great deal of flexibility in possible contributions from new partners to expand the size of the detector. The details of any scope change would depend on the interests, capabilities and resources of the new partners.

Neutrino Mixing, Mass Hierarchy and CP Violation

The experimental requirements for designing a neutrino oscillation experiment to simultaneously address neutrino CP violation and the mass hierarchy (MH) can be extrapolated as follows from the phenomenology summarized in Chapter 2:

Phenomenology: An appearance experiment is necessary to extract the CP-violating effects.

The experiment will probe oscillations of $\nu_{\mu,e}\rightarrow\nu_{e,\mu}$.

The experiment will identify $\nu_{e}$ and $\nu_{\mu}$ with high efficiency and purity in order to tag (or otherwise know) the flavor of the neutrino before and after flavor transformations.

Phenomenology: In the three-flavor mixing model, the CP-violating Jarlskog invariant arises in the interference term $P_{\sin\delta}$ as given by Equation 2.15; the oscillation scale where the interference term is maximal is that determined by the mixing between the $\nu_{1}$ and $\nu_{3}$ states.

Phenomenology: In the three-flavor model $\nu_{\mu,e}\rightarrow\nu_{e,\mu}$ oscillations depend on all parameters in the neutrino mixing matrix as well as on the mass differences, as shown in Equations 2.12 to 2.15.

The precision with which $\delta_{\rm CP}$ can be determined — and the sensitivity to small CP-violating effects or CP violation outside the three-flavor model — requires precision determination of all the other mixing parameters, preferably in the same experiment. The experiment will be designed so as to minimize dependence on external measurements of the oscillation parameters.

Phenomenology: Observation of CP violation requires the explicit observation of an asymmetry between $P(\nu\rightarrow\nu)$ and $P(\overline{\nu}\rightarrow\overline{\nu})$.

The experiment will probe the oscillations of both neutrinos and antineutrinos in an unambiguous way.

The experiment will be capable of charge tagging in addition to flavor tagging. Charge tagging can be achieved at detection using the lepton charge and/or at production by selecting beams purely of neutrinos or antineutrinos.

Phenomenology: CP asymmetries are maximal at the secondary oscillation nodes.

Coverage of the $L/E$ scale of the secondary oscillation nodes improves experimental sensitivity to small values of $\delta_{\rm CP}$ by enabling measurements of the asymmetry at the secondary nodes where the CP asymmetries are much larger and where there is no degeneracy with the matter asymmetries. The experiment will be performed with a wide-band beam to provide sensitivity to the $L/E$ scale of both the first and second oscillation nodes.

2 Simulation of Neutrino Oscillation Experiments

To evaluate the sensitivity of LBNE and to optimize the experiment design, it is important to accurately predict the neutrino flux produced by the neutrino beamline, the neutrino interaction rate at the far detector, and the far detector performance. This is achieved using Monte Carlo (MC) simulations and the GLoBES package. The simulations and experimental assumptions that are used to evaluate the sensitivity of LBNE to neutrino mixing parameters, to the neutrino mass hierarchy (MH) and to CP violation are described in this section.

2.2 Detector Simulation using the GLoBES Package

For the sensitivity studies presented here, the GLoBES package was used to simulate the detector response using simple smearing and using detector efficiency values based on results from ICARUS and earlier simulation efforts as documented in . The values used in GLoBES are shown in Table 4.2.

The GLoBES implementation used in the sensitivity studies presented here appears to be in good agreement with more recent results from the Fast MC, described in Section A.3. Updated sensitivity and systematics studies are currently underway using the Fast MC for detector simulation, and customized GLoBES-based software for the oscillation fits and propagation of systematics. A full MC simulation of the far detector and automated event reconstruction is being developed; this is also described in Appendix A.

3 Measurements of Mass Hierarchy and the CP-Violating Phase

The neutrino mass hierarchy (MH) and the value of the CP-violating phase, $\delta_{\rm CP}$, are currently unknown. Knowledge of the MH has significant theoretical, cosmological and experimental implications. A determination of the $\delta_{\rm CP}$ value to be neither zero ($0$) nor $\pi$ would constitute the first observation of CP violation in the lepton sector.

In these calculations, experimental sensitivity is quantified using $\Delta\chi^{2}$ parameters, which are determined by comparing the predicted spectra for various scenarios. These quantities are defined, differently for neutrino MH and CP-violation sensitivity, to be:

These sensitivities are evaluated separately for true NH and IH. Since the true value of $\delta_{\rm CP}$ is unknown, a scan is performed over all possible values of $\delta_{\rm CP}^{true}$. The individual $\chi^{2}$ values are calculated using

where n are event rate vectors in $N_{reco}$ bins of reconstructed energy and $f$ represents a nuisance parameter to be profiled. Nuisance parameters include the values of mixing angles, mass splittings, and signal and background normalization. The nuisance parameters are constrained by Gaussian priors; in the case of the oscillation parameters, the Gaussian prior has standard deviation determined by taking 1/6 of the 3$\sigma$ range allowed by the global fit .

With the exception of results reported in Section 4.3.1, where more information on the statistical interpretation of MH sensitivity is provided, the sensitivities presented here are for the typical experiment with no statistical fluctuations considered. In the absence of statistical fluctuations, the $\chi^{2}$ value for the true spectra is identically zero. Statistical fluctuations are incorporated by repeatedly varying the contents of each energy bin in each sample by drawing from a Poisson distribution with the expected number of events in that bin as the mean.

The sensitivity bands in Figures 4.4 and 4.5 represent the variation in sensitivity as a function of the beam design and normalization uncertainties on the signal and background. The solid curve at the lower end of the red band represents the beamline design described in the LBNE CDR Volume 2 for which there is no near detector. The dashed line above the solid curve represents the sensitivity with the beam design improvements currently under study as described in Section 3.4, still without a near detector. The dashed line at the upper end of the red band represents the case in which both the beam design improvements and a high-resolution, highly capable near detector are implemented. The key design goal of the LBNE near detector and beamline simulation software is to enable a prediction of the far detector unoscillated flux with a precision of $\leq 2\%$. Therefore, the total signal and background normalization uncertainties on the $\nu_{\mu}$ disappearance signal are assumed to be 5% and 10%, respectively. The default $\nu_{e}$ appearance signal uncorrelated normalization uncertainties for the full-scope LBNE presented in this chapter are assumed to be 1%. The $\nu_{e}$ appearance background uncertainty is expected to be at least as good as the $\sim 5\%$ achieved by the $\nu_{e}$ appearance search in the MINOS experiment.

A detailed discussion of the systematics assumptions for LBNE is presented in Section 4.3.2. In the case that LBNE has no near neutrino detector, the uncertainties on signal and background are expected to be $5\%$ and $10\%$, respectively, extrapolating from the performance and detailed knowledge of the NuMI beam on which the LBNE beamline is modeled, in situ measurements of the muon flux at the near site as described in , the expectation of improved hadron production measurements with the NA61 and MIPP experiments, and the experience of previous $\nu_{e}$ appearance experiments as summarized in Table 4.4.

In the mass hierarchy (MH) determination, only two possible results are considered, as the true MH is either normal (NH) or inverted (IH). Reference presents the statistical considerations of determining the sensitivity of an experiment to the MH, framed partly in the context of two separate but related questions:

Given real experimental data, with what significance can the MH be determined?

When evaluating future experimental sensitivities, what is the probability that a particular experimental design will be able to determine the MH with a given significance?

Once data are in hand, a number of techniques based either within Bayesian or frequentist statistics make it possible to determine the level of confidence at which one MH hypothesis or the other can be ruled out. In assessing the sensitivity of future experiments, it is common practice to generate a simulated data set (for an assumed true MH) that does not include statistical fluctuations. The expected sensitivity can be reported as $\overline{\Delta\chi^{2}}$, representative of the mean or the most likely value of $\Delta\chi^{2}$ that would be obtained in an ensemble of experiments for a particular true MH. With the exception of Figure 4.7, the sensitivity plots in this document have been generated using this method.

However, addressing the expected sensitivity of an experiment per the second question above requires consideration of the effect of statistical fluctuations and variations in systematics. If the experiment is repeated many times, a distribution of $\Delta\chi^{2}$ values will appear. Studies in and elsewhere (e.g., ) show that the $\Delta\chi^{2}$ metric employed here does not follow the commonly expected $\chi^{2}$ function for one degree of freedom, which has a mean of $\overline{\Delta\chi^{2}}$ and can be interpreted using a Gaussian distribution with a standard deviation of $\sqrt{|\overline{\Delta\chi^{2}}|}$. Rather, these studies show that when the observed counts in the experiment are large enough, the distribution of $\Delta\chi^{2}$ used here approximately follows a Gaussian distribution with a mean and standard deviation of $\overline{\Delta\chi^{2}}$ and $2\sqrt{|\overline{\Delta\chi^{2}}|}$, respectively .

Figure 4.6 shows the expected distribution of $\Delta\chi^{2}$ values in LBNE from toy Monte Carlo studies.

The interpretation of pairs of distributions, such as those in the various panels of this figure, depends on the information being sought. For example, one is not necessarily interested simply in the fraction of experiments where $\Delta\chi^{2}$ has the “right” sign. (An experiment that obtains a small value of $\Delta\chi^{2}$, even with the “right” sign, would not be particularly constraining since there is no way a priori to know which is the right sign — this is what the experiment is attempting to measure.) It should also be noted that in general $|\overline{\Delta\chi^{2}_{\rm MH=NH}}|$ , i.e., true NH, is not necessarily equal to $|\overline{\Delta\chi^{2}_{\rm MH=IH}}|$, i.e., true IH, nor do the corresponding distributions necessarily have the same shape. For some ranges in $\delta_{\rm CP}$, for example, the event rate in LBNE is sufficiently different for the two MH hypotheses that the corresponding distributions in $\Delta\chi^{2}$ are quite distinct.

The plots shown on the left in Figure 4.6 illustrate the case for a true value of $\delta_{\rm CP}=0^{\circ}$, where the $\Delta\chi^{2}$ distributions for NH and IH scenarios are similar. Shown on the right are the corresponding distributions for the case of $\delta_{\rm CP}=90^{\circ}$, where for NH the matter asymmetry is maximally offset by the CP asymmetry, leading to poorer MH discrimination. For the IH case, these effects go in the same direction, leading to better MH discrimination. The converse is the case for $\delta_{\rm CP}=-90^{\circ}$. Since the true value of $\delta_{\rm CP}$ is unknown (although a best-fit value and confidence interval will emerge from the analysis of the data collected), comparison of a given value of $\Delta\chi^{2}$ with expected distributions for NH and IH cases for the same value of $\delta_{\rm CP}$ does not in general provide the appropriate test. For simplicity, following , the discussion below focuses on the respective values of $\delta_{\rm CP}$ for which the experiment will have poorest sensitivity for NH ($+90^{\circ}$) and IH ($-90^{\circ}$) scenarios.

Given the above introduction to the statistical fluctuation issues, it is natural to employ the statistical language of hypothesis testing in projecting LBNE’s MH sensitivity. Specifically, $\alpha$ is defined as the desired Type-I error rate — that is, the probability of rejecting a particular hypothesis, e.g., NH, in the case where this is the true hypothesis. One can then ask what the corresponding Type-II error rate $\beta$ would be, defined as the probability of accepting the hypothesis being tested (NH in this example), when in fact the alternate hypothesis (IH) is true. The pair of $\alpha$ and $\beta$ would correspond to a particular value of $\overline{\Delta\chi^{2}}$ chosen (in advance of the experiment) as a criterion for deciding whether to rule out the NH (or IH). Historically, many experiments have characterized their anticipated sensitivity by reporting $\alpha$ for the case of $\beta=0.5$, which is nothing more than that given by the median value of the test statistic (in this case, $\Delta\chi^{2}=\overline{\Delta\chi^{2}}$) as described above. Sometimes, the sensitivity is also reported as the square root of $\overline{\Delta\chi^{2}}$.

Due to the approximate symmetry of the MH ambiguity as a function of $\delta_{\rm CP}$ for the two MH scenarios and the desire to be able to reject exactly one of the two possible mass orderings , it is also natural to report a value of $\alpha$ for an experiment such that $\alpha=\beta$ . In this way, it is possible to express just how unlucky an experiment can be while maintaining a corresponding sensitivity $\alpha$. In the case of LBNE, a reasonable benchmark for comparison corresponds to $\overline{\Delta\chi^{2}}=36$. For this case, specifying $\alpha=\beta$ yields $\alpha=0.0013$, which means that the experiment will have a 0.13% probability of ruling out the true MH hypothesis and of accepting the wrong MH hypothesis.

As described above, and as is evident in the plots presented, such as those in Figures 4.4 and 4.5, the sensitivity of LBNE is strongly dependent on the true value of $\delta_{\rm CP}$; Figure 4.7 shows that it also depends on the true value of $\sin^{2}{\theta_{23}}$. While plotting the value of $\alpha$ (for some choice of $\beta$, such as $\beta=0.5$ or $\beta=\alpha$) as a function of these parameters encapsulates the sensitivity, a visually helpful presentation is obtained by plotting the expected mean value, $\overline{\Delta\chi^{2}}$, as well as ranges of possible values corresponding to the expected distribution in $\Delta\chi^{2}$. Thus, Figure 4.7 shows the dependence of $\sqrt{|\overline{\Delta\chi^{2}}|}$ on the true value of $\delta_{\rm CP}$ for the typical LBNE data set, for two possible values of $\sin^{2}\theta_{23}$, as well as the corresponding expectation bands within which 68% (green) and 95% (yellow) of LBNE sensitivities will fall. These expectation bands give a semi-quantitative picture of the likely range of outcomes for the experiment.

The horizontal dashed lines on Figure 4.7 specify the confidence level of an experiment with a particular value of $\Delta\chi^{2}$ such that:

following the convention in , where the notation $P({\rm A}|{\rm B})$ represents the probability of A given condition B, and these probabilities are inferred from the corresponding likelihoods via Bayes’ Theorem. Alternatively, the $\Delta\chi^{2}$ values shown in these plots can be approximately translated to sensitivities in terms of $\alpha$, for whatever choice of $\beta$ is desired, following, for example, the prescription described in .

For the bulk of the range of $\delta_{\rm CP}$, the sensitivity of LBNE is vastly better than for the least favorable value described above. Furthermore, newer data prefer values of $\theta_{23}$ closer to maximal , which results in significantly enhanced LBNE MH sensitivity. As shown in the right-hand plot of Figure 4.7, if $\sin^{2}\theta_{23}=0.5$, the expected MH sensitivity for the typical LBNE experiment at the least favorable $\delta_{\rm CP}$ point is $|\overline{\Delta\chi^{2}}|\approx 64$, which is significantly larger than the sensitivity of $|\overline{\Delta\chi^{2}}|\approx 25$ expected for the same value of $\delta_{\rm CP}$ if $\sin^{2}\theta_{23}=0.39$. This suggests that a typical LBNE data set will determine the MH with $|\Delta\chi^{2}|$ well above the benchmark value of $36$ mentioned above for even the least favorable values of $\delta_{\rm CP}$.

In addition to detailed LBNE-specific frequentist studies reported in , an LBNE-specific update (using both Bayesian and frequentist approaches) to the general statistical studies reported in is in preparation.

3.2 Sensitivities and Systematics

The main systematic uncertainties in any experiment are determined by the analysis strategy employed and the performance of the detector. Figure 4.8 outlines the analysis strategy commonly employed to extract oscillation parameters in two-detector long-baseline neutrino oscillation experiments.

The measured spectrum of $\nu_{\mu}$ events in the near detector, $N^{data}_{\rm ND}(\nu_{\mu})$ is extrapolated to the far detector and is used to predict both the $\nu_{\mu}$ and $\nu_{e}$ appearance signals in the far detector, $N^{expected}_{\rm FD}(\nu_{\mu})$ and $N^{expected}_{\rm FD}(\nu_{e})$ respectively. The measured spectrum of $\nu_{e}$ candidates in the near detector, $N^{data}_{\rm ND}(\nu_{e})$, which comprises mostly the beam $\nu_{e}$ events and NC $\pi^{0}$ misidentified events, is used to predict the background to the $\nu_{e}$ appearance signal in the far detector. In LBNE, neutrino oscillation parameters will be extracted using a fit to four far detector data samples: $\nu_{e}$, $\overline{\nu}_{e}$, $\nu_{\mu}$, and $\overline{\nu}_{\mu}$, which will allow for partial cancellation of uncertainties.

In the current generation of experiments, the measured spectrum of neutrino events in the near detector is a product of beam flux ($\Phi$), detector efficiency and smearing ($\varepsilon$), and neutrino interaction dynamics ($\sigma$). To extrapolate the observed spectra in the near detector to the far detector, corrections have to be made for:

Differences in the beam flux in the near and far detectors, $\Phi_{\rm FD}/\Phi_{\rm ND}$: The near detector is much closer to the neutrino beamline and sees an extended source of neutrinos from the decay pipe as compared to the far detector, which observes a point source. A beam MC is used to correct for these differences. Uncertainties arise from inaccuracies in the simulation of the hadron production from the target, the focusing of the horns, the material in the beamline (which absorbs hadrons before they can decay), and the decay channel geometry.

Differences in near and far detector smearing and efficiencies, $\varepsilon_{\rm FD}/\varepsilon_{\rm ND}$: The largest uncertainties arise from the different event selection efficiencies in the near and far detectors and, in particular, the imperfect modeling of the energy scales of the near and far detectors. Identical near and far detectors allow most of these uncertainties to cancel in the extrapolation in the case of the $\nu_{\mu}$ signal prediction. The $\nu_{e}$ signal prediction is extrapolated from $N^{data}_{\rm ND}(\nu_{\mu})$; thus there are irreducible residual uncertainties arising from different criteria used to select $\nu_{e}$ and $\nu_{\mu}$ candidate events and different detector response functions.

Differences in the interactions of neutrinos in the near and far detector, $\sigma_{\rm FD}/\sigma_{\rm ND}$: In the case in which both near and far detectors use the same target nucleus, the differences cancel for extrapolation of the $\nu_{\mu}$ signal from the near to the far detector. When using the $\nu_{\mu}$ signal in the near detector to predict the $\nu_{e}$ (and $\nu_{\tau}$) signals in the far detector, uncertainties arising from differences in $\nu_{e}$ ($\nu_{\tau}$) and $\nu_{\mu}$ interactions, $\sigma_{\rm FD}(\nu_{e})/\sigma_{\rm ND}(\nu_{\mu})$, dominate. These uncertainties are limited by theoretical uncertainties and are typically smaller at higher energies.

The estimation of the expected signals at the far detector can be summarized thus:

Expected systematic uncertainties on the LBNE $\nu_{e}$ appearance and $\nu_{\mu}$ signal samples in the three-flavor fit for LBNE (Table 4.2) are extrapolated from the current performance of the MINOS and T2K experiments. The dominant uncertainties on the current $\nu_{e}$ appearance analysis from MINOS and T2K and the expected corresponding uncertainties in LBNE are shown in Table 4.5.

The categorization of the dominant experimental uncertainties in Table 4.5 are not always in exact correspondence since T2K and MINOS are very different experiments and deploy different analysis techniques. A detailed description of the expected LBNE performance on each of the dominant uncertainties follows.

Beam flux uncertainties: The LBNE high-resolution near detector is being designed with the goal of accurately measuring the unoscillated beam flux at the near site with a precision $\leq 2\%$ for both shape and absolute normalization. Table 4.6 summarizes the precision that can be achieved using different near detector analysis techniques, described in detail in Section 7.1, to measure the absolute normalization and shape of the different components of this flux.

$\boldmath{\nu_{\mu}}$ energy-scale uncertainty: Both T2K and MINOS use the reconstructed $\nu_{\mu}$ event spectrum in the near detector to predict the $\nu_{e}$ appearance signal at the far detector. Therefore the $\nu_{\mu}$ energy-scale uncertainty in the near detector is propagated as an uncertainty on the $\nu_{e}$ appearance signal at the far detector. In MINOS — which has a high proportion of non-QE events — the $\nu_{\mu}$ energy-scale uncertainty is dominated by uncertainty in the hadronic energy scale (7% for $E_{\nu}<3$ GeV) and the muon energy scale (2.5%). Utilization of the low-$\nu_{0}$ method for energies less than 3 GeV in LBNE reduces the hadronic energy-scale contribution to the uncertainty in the $\nu_{\mu}$ energy scale in the near detector. As discussed in Chapter 7, it is expected that both the muon and hadronic energy-scale uncertainties in the near detector will be $<$1%, so far detector energy-scale uncertainties will dominate the uncertainty in the $\nu_{\mu}$ signal prediction. The high-resolution LArTPC far detector and an active program of hadron test-beam experiments planned for LBNE will reduce far detector hadronic energy-scale uncertainties, which also contribute to uncertainty in the energy scale of the far detector $\nu_{\mu}$ signal used in the three-flavor analysis. Extrapolating from MINOS, the LBNE $\nu_{\mu}$ energy-scale uncertainty is thus estimated to be $\sim 2\%$.

In MINOS, the 7% $\nu_{\mu}$ energy-scale uncertainty resulted in a residual uncertainty of 3.5% on the $\nu_{e}$ signal prediction. In the LBNE full three-flavor analysis, this uncertainty is 100% correlated between the predicted $\nu_{\mu}$ and $\nu_{e}$ signal samples; therefore a $E_{\nu_{\mu}}$ energy-scale uncertainty of 2% is assigned to the $\nu_{\mu}$ signal prediction in LBNE. The residual uncorrelated uncertainty on the $\nu_{e}$ signal prediction is considered to be negligible.

Absolute $\boldmath{\nu_{e}}$ energy-scale uncertainties: In Figure 4.9, the MH and CP-violation sensitivity obtained using a rate-only, a shape-only and a rate+shape analysis of $\nu_{e}$ appearance is shown. This study demonstrates that a critical component of LBNE’s oscillation sensitivity is an accurate measurement of the shape of the $\nu_{e}$ appearance signal.

This measurement depends on the precision with which the detector response to $\nu_{e}$ interactions is understood. The $\nu_{e}$ energy-scale uncertainty, which is not yet included in the current sensitivity calculation with the GLoBES framework, is therefore expected to be an important systematic uncertainty in the LBNE oscillation analysis.

The effect of $\nu_{e}$ energy-scale uncertainty on the $\nu_{e}$ signal normalization, determined by the precision of detector calibration, was 2.7% in MINOS and 3.4% in T2K, where the T2K uncertainty actually includes most far detector effects. LBNE’s LArTPC detector technology is expected to outperform both the MINOS sampling calorimeter and the T2K water Cherenkov detector in reconstruction of the $\nu_{e}$ interaction. For example, the proton produced from the $\nu_{e}$-QE interaction — the interaction with potentially the best $\nu_{e}$ energy resolution — is clearly visible in a LArTPC , whereas it is often below Cherenkov threshold in T2K. An active program of test beam experiments with LArTPCs is currently being planned to address the detector response to electrons and hadrons. Results from the test beam experiments and the projected performance of the in situ calibration will enable LBNE to limit the detector energy-scale uncertainties below the level achieved by the current generation of experiments.

Hadronic energy is expected to contribute more than half of the total energy deposit for many $\nu_{e}$ and $\nu_{\mu}$ interactions in LBNE. The hadronic energy scale does not depend on neutrino flavor; since it should be identical for $\nu_{e}$ and $\nu_{\mu}$ interactions, this portion of the absolute energy-scale uncertainty is expected to largely cancel in the LBNE three-flavor analysis. This cancellation may be reduced to the extent that event-selection criteria vary the hadronic energy fraction among the samples.

Simulation uncertainties: The simulation uncertainties listed in Table 4.5 refer primarily to uncertainties in modeling neutrino interactions with the target nucleus in the near and far detectors. These uncertainties include $\nu_{e}$ and $\nu_{\mu}$ cross-section uncertainties, uncertainties arising from the modeling of the structure of the target nucleus, modeling of final-state interactions within the nucleus, and hadronization model uncertainties arising from the break up of the target nucleus in higher-energy inelastic interactions. The deployment of identical nuclear targets in the MINOS (iron) and LBNE (argon) near and far detectors allows for a larger cancellation of the simulation uncertainties as compared to T2K, which used dissimilar target nuclei in its near detector (carbon) and far detector (oxygen). A high-resolution near detector such as that being designed for LBNE will enable further constraints on the hadronization models by resolving many of the individual particles produced in resonance and deep inelastic interactions, which represent $\sim$75% of LBNE neutrino interactions.

The MINOS $\nu_{e}$ appearance analysis achieved a 2.7% residual uncertainty from simulation after the near-to-far extrapolation. The MINOS simulation uncertainty is dominated by hadronization uncertainties, because cross-section uncertainties largely cancel between the identical nuclei in the near and far detectors. The T2K residual uncertainty after near-to-far extrapolation is 7%. Additionally, the T2K analysis includes more sources of cross-section uncertainties than MINOS and, at the lower T2K energies, larger differences in $\nu_{\mu}$/$\nu_{e}$ cross sections (2.9 %) persist after extrapolating the $\nu_{\mu}$ spectrum in the near detector to the $\nu_{e}$ signal prediction in the far.

It is important to note that some $\nu/\overline{\nu}$ simulation uncertainties may not cancel out in the near-to-far extrapolation or in the combined fit; in particular, uncertainties due to nuclear models and intra-nuclear effects are different for $\nu/\overline{\nu}$ interactions. New models of intra-nuclear effects are being evaluated to determine the size of these irreducible residual uncertainties. Additionally, there are uncertainties at the level of 1-2% in the cross sections that will not cancel between $\nu_{e}$ and $\nu_{\mu}$ . In the absence of theoretical progress, these should also be considered irreducible.

$\boldmath{\nu_{e}}$ appearance background systematic uncertainties: The $\nu_{e}$ appearance normalization uncertainty is expected to be at least as good as the $\sim 5\%$ achieved by the $\nu_{e}$ appearance search in the MINOS experiment, using the technique of predicting intrinsic-beam and neutral current (NC) background levels from near detector measurements. The LBNE far detector should be able to provide additional constraints on the background level by independently measuring NC and $\nu_{\tau}$ background.

In comparing Figures 4.11, 4.12 and 4.13, the dependence on the true value of $\theta_{23}$ is particularly striking. As $\sin^{2}\theta_{23}$ increases, the sensitivity to CP violation decreases because the CP asymmetry that LBNE measures is inversely proportional to $|\sin\theta_{23}|$ as demonstrated in Equation 2.20. For the same reason, as $\theta_{23}$ increases, the degeneracy between the CP and matter asymmetries is broken, which increases the LBNE sensitivity to neutrino MH. The explicit dependence of MH sensitivity on the value of $\sin^{2}\theta_{23}$ is shown in Figure 4.14.

As this plot makes clear, LBNE resolves the MH with a significance of $\sqrt{\overline{\Delta\chi^{2}}}>6$ for nearly all allowed values of $sin^{2}\theta_{23}$ and $\delta_{\rm CP}$.

3.3 Summary of CP-Violation and Mass Hierarchy Sensitivities

3.4 CP-Violating and Mass Hierarchy Sensitivities with Increased Exposures

4 Measurement of θ23\theta_{23} and Determination of the Octant

The value of $\textrm{sin}^{2}2\theta_{23}$ is measured to be $>$ 0.95 at 90% CL using atmospheric neutrino oscillations . This corresponds to a value of $\theta_{23}$ near 45∘, but leaves an ambiguity as to whether the value of $\theta_{23}$ is in the lower octant (less than 45∘), the upper octant (greater than 45∘) or exactly 45∘. The value of $\sin^{2}\theta_{23}$ from the 2013 global fit reported by is $\sin^{2}\theta_{23}=0.425^{+0.029}_{-0.027}(1\sigma)$ for normal hierarchy (NH), but as shown in Figure 4.15, the distribution of the $\chi^{2}$ from the global fit has another local minimum — particularly if the MH is inverted — at $\sin^{2}\theta_{23}\approx 0.59$. A maximal mixing value of $\sin^{2}\theta_{23}=0.5$ is therefore still allowed by the data and the octant is still largely undetermined. As discussed in Chapter 2, a value of $\theta_{23}$ exactly equal to 45∘ would indicate that $\nu_{\mu}$ and $\nu_{\tau}$ have equal contributions from $\nu_{3}$, which could be evidence for a previously unknown symmetry. It is therefore important experimentally to determine the value of $\sin^{2}\theta_{23}$ with sufficient precision to determine the octant of $\theta_{23}$.

The measurement of $\nu_{\mu}\rightarrow\nu_{\mu}$ oscillations is sensitive to $\sin^{2}2\theta_{23}$, whereas the measurement of $\nu_{\mu}\rightarrow\nu_{e}$ oscillations is sensitive to $\sin^{2}\theta_{23}$. A combination of both $\nu_{e}$ appearance and $\nu_{\mu}$ disappearance measurements can probe both maximal mixing and the $\theta_{23}$ octant. With the large statistics and rich spectral structure in a wide-band, long-baseline experiment such as LBNE (Figure 4.2), precision measurements of $\sin^{2}\theta_{23}$ can be significantly improved compared to existing experiments, particularly for values of $\theta_{23}$ near $45^{\circ}$.

5 Precision Measurements of the Oscillation Parameters in the Three-Flavor Model

The rich oscillation structure that can be observed by LBNE and the excellent particle identification capability of the detector will enable precision measurement in a single experiment of all the mixing parameters governing $\nu_{1}$-$\nu_{3}$ and $\nu_{2}$-$\nu_{3}$ mixing. As discussed in Chapter 2, theoretical models probing quark-lepton universality predict specific values of the mixing angles and the relations between them. The mixing angle $\theta_{13}$ is expected to be measured accurately in reactor experiments by the end of the decade with a precision that will be limited by systematics. The systematic uncertainty on the value of $\sin^{2}2\theta_{13}$ from the Daya Bay reactor neutrino experiment, which has the lowest systematics, is currently $\sim 4$% .

6 Oscillation Studies Using Atmospheric Neutrinos

A Fast MC runs on the produced four-vectors, placing events into containment and flavor categories. Containment is evaluated by tracking leptons through the liquid argon detector box geometry and classifying events as either fully contained (FC) or partially contained (PC). A detection threshold of 50 MeV is assumed for all particles. Flavor determination, in which events are placed into electron-like or muon-like categories, is based on properties of the primary and secondary particles above detection threshold. Electrons are assumed to be correctly identified with 90% probability and other electromagnetic particles (e.g., $\pi^{0}$, $\gamma$) are misidentified as electrons 5% of the time. Muons are identified with 100% probability and charged pions are misidentified as muons 1% of the time. Events in which neither of the two leading particles is identified as a muon or electron are placed into an NC-like category. With these assumptions, the purities of the flavor-tagged samples are 97.8% for the FC electron-like sample, 99.7% for the FC muon-like sample, and 99.6% for the PC muon-like sample. The NC-like category is not used in this analysis, but would be useful for $\nu_{\tau}$ appearance studies.

In performing oscillation fits, the data in each flavor/containment category are binned in energy and zenith angle. Figure 4.23 shows the zenith angle distributions for several ranges of reconstructed energy, where oscillation features are clearly evident.

The power to resolve the mass hierarchy (MH) with atmospheric neutrinos comes primarily from the MSW enhancement of few-GeV neutrinos at large zenith angles. This enhancement occurs for neutrinos in the normal hierarchy and antineutrinos in the inverted hierarchy. Figure 4.24 shows zenith angle distributions of events in the relevant energy range for each of the three flavor/containment categories. Small differences are evident in comparing the NH and IH predictions.

Since the resonance peak occurs for neutrinos in the NH and antineutrinos in the IH, the MH sensitivity can be greatly enhanced if neutrino and antineutrino events can be separated. The LBNE detector will not be magnetized; however, its high-resolution imaging offers possibilities for tagging features of events that provide statistical discrimination between neutrinos and antineutrinos. For the sensitivity calculations that follow, two such tags are included: a proton tag and a decay-electron tag. For low-multiplicity events, protons occur preferentially in neutrino interactions; protons are tagged with 100% efficiency if their kinetic energy is greater than 50 MeV. Decay electrons are assumed to be 100% identifiable and are assumed to occur 100% of the time for $\mu^{+}$ and 25% of the time for $\mu^{-}$, based on the $\mu^{\pm}$ capture probability on 40Ar.

In the oscillation analysis, 18 nuisance parameters are included, with detector performance parameters correlated between beam and atmospheric data. In all cases, $\sin^{2}\theta_{12}$, $\Delta m^{2}=1/2(\Delta m_{32}^{2}+\Delta m_{31}^{2})$, and $\Delta m_{21}^{2}$ are taken to be fixed at the values given in Table 4.10. The fits then range over $\theta_{23}$, $\theta_{13}$, $\delta_{\rm CP}$, and the MH. A 2% constraint is assumed on the value of $\theta_{13}$; this value is chosen to reflect the expected ultimate precision of the current generation of reactor-neutrino experiments. The systematic errors included in this analysis are given in Table 4.14.

For all values of the MH and $\delta_{\rm CP}$, the MH can be determined at $\sqrt{\overline{\Delta\chi^{2}}}>3$. The resolution depends significantly on the true value of $\theta_{23}$; the sensitivity for three $\theta_{23}$ values is shown. The sensitivity depends relatively weakly on the true hierarchy and the true value of $\delta_{\rm CP}$. This is in sharp contrast to the MH sensitivity of the beam, which has a strong dependence on the true value of $\delta_{\rm CP}$. Figure 4.26 shows the MH sensitivity as a function of the fiducial exposure. Over this range of fiducial exposures, the sensitivity goes essentially as the square root of the exposure, indicating that the measurement is not systematics-limited.

Figure 4.30 shows the combined sensitivity to beam and atmospheric neutrinos for the $\theta_{23}$ octant determination and CPV. The role played by atmospheric data in resolving beam-neutrino degeneracies is also clear from considering the combined and beam-only sensitivities in these plots.

7 Searches for Physics Beyond the Standard Three-Flavor Neutrino Oscillation Model

This section explores the potential of the full-scope LBNE design to pursue physics beyond the three-flavor neutrino oscillation model.

Neutral current (NC) nonstandard interactions (NSI) can be understood as nonstandard matter effects that are visible only in a far detector at a sufficiently long baseline. They can be parameterized as new contributions to the MSW matrix in the neutrino-propagation Hamiltonian:

To assess the sensitivity of LBNE to NC NSI, the NSI discovery reach is defined in the following way: the expected event spectra are simulated using GLoBeS, assuming true values for the NSI parameters, and a fit is then attempted assuming no NSI. If the fit is incompatible with the simulated data at a given confidence level, the chosen true values of the NSI parameters are considered to be within the experimental discovery reach. In Figure 4.31, the NSI discovery reach of LBNE is shown; only one of the $\epsilon^{m}_{\alpha\beta}$ parameters at a time is taken to be non-negligible.

7.2 Search for Long-Range Interactions

The small scale of neutrino-mass differences implies that minute differences in the interactions of neutrinos and antineutrinos with currently unknown particles or forces may be detected through perturbations to the time evolution of the flavor eigenstates. The longer the experimental baseline, the higher the sensitivity to a new long-distance potential acting on neutrinos. For example, some of the models for such long-range interactions (LRI) as described in (Figure 4.32) could contain discrete symmetries that stabilize the proton and give rise to a dark-matter candidate particle, thus providing new connections between neutrino, proton decay and dark matter experiments. The longer baseline of LBNE improves the sensitivity to LRI beyond that possible with the current generation of long-baseline neutrino experiments. The sensitivity will be determined by the amount of $\nu_{\mu}/\overline{\nu}_{\mu}$-CC statistics accumulated and the accuracy with which the unoscillated and oscillated $\nu_{\mu}$ spectra can be determined.

7.3 Search for Mixing between Active and Sterile Neutrinos

Searches for evidence of active-sterile neutrino mixing at LBNE can be conducted by examining the NC event rate at the far detector and comparing it to a precise estimate of the expected rate extrapolated from $\nu_{\mu}$ flux measurements from the near detector and from beam and detector simulations. Observed deficits in the NC rate could be evidence for mixing between the active neutrino states and unknown sterile neutrino states. The most recent such search in a long-baseline experiment was conducted by the MINOS experiment .

7.4 Search for Large Extra Dimensions

Several theoretical models propose that right-handed neutrinos propagate in large compactified extra dimensions, whereas the standard left-handed neutrinos are confined to the four-dimensional brane . Mixing between the right-handed Kaluza-Klein modes and the standard neutrinos would change the mixing patterns predicted by the three-flavor model. The effects could manifest, for example, as distortions in the disappearance spectrum of $\nu_{\mu}$. The rich oscillation structure visible in LBNE, measured with its high-resolution detector using both beam and atmospheric oscillations, could provide further opportunities to probe for this type of new physics. Studies are underway to understand the limits that LBNE could impose relative to current limits and those expected from other experiments.

8 Comparison of LBNE Sensitivities to other Proposed Experiments

It is important to note that the precision on $\delta_{\rm CP}$ in the off-axis experiments shown in Figure 4.34 assumes the mass hierarchy (MH) is resolved. If the MH is unknown, the resolution of T2K, NO$\nu$A and T2HK will be much poorer than indicated. LBNE does not require external information on the MH to reach the precisions described in this section. Only a neutrino factory can possibly out-perform a wide-band, long-baseline experiment — but not by much — for equivalent power, target mass and years of running. To achieve this precision, however, LBNE will need to tightly control the systematic uncertainties on the $\nu_{e}$ appearance signal. Its high-resolution near detector will enable it to reach this level of precision, as described in Section 3.5.

An independent study comparing LBNE’s sensitivity to the mass ordering to that of current and future proposed experiments highlights its potential . The study uses frequentist methods of hypothesis testing to define sensitivities. The validity of the approach is tested using toy MC simulations of the various experiments. The comparison of expected MH sensitivities for a variety of current and proposed experiments using different approaches with reasonable estimates as to the start time of the different experiments is summarized in Figure 4.35.

Nucleon Decay Motivated by Grand Unified Theories

The uniqueness of proton decay signatures in a LArTPC and the potential for reconstructing them with redundant information has long been recognized as a key strength of this technology. A LArTPC can reconstruct all final-state charged particles and make an accurate assessment of particle type, distinguishing between muons, pions, kaons and protons. Electromagnetic showers are readily measured, and those that originate from photons generated by $\pi^{0}$ decay can be distinguished to a significant degree from those that originate from $\nu_{e}$ charged-current (CC) interactions. Kiloton-per-kiloton, LArTPC technology is expected to outperform water Cherenkov in both detection efficiency and atmospheric-neutrino background rejection for most nucleon decay modes, although intranuclear effects, which can smear out some of the proton decay signal, are smaller for oxygen and nonexistent for hydrogen.

2 Signatures for Nucleon Decay in Liquid Argon

For modes with no electron in the final state, the same displaced vertex performance that underpins long-baseline neutrino oscillation measurements allows the rejection of CC interactions of atmospheric $\nu_{e}$’s. As will be stressed for the key mode of $p\rightarrow K^{+}\overline{\nu}$ described in detail below, the capability to reconstruct the charged kaon with the proper range and $dE/dx$ profile allows for a high-efficiency, background-free analysis. In general, these criteria favor all modes with a kaon, charged or neutral, in the final state. Conversely, the efficiency for decay modes to a lepton plus light meson will be limited by intranuclear reactions that plague liquid argon to a greater extent than they do 16O in a water Cherenkov detector.

An extensive survey of nucleon decay efficiency and background rates for large LArTPCs with various depth/overburden conditions, published in 2007, provides the starting point for the assessment of LBNE’s capabilities. Table 5.1 lists selected modes where LArTPC technology exhibits a significant performance advantage (per kiloton) over the water Cherenkov technology. The remainder of this chapter focuses on the capabilities of LBNE for the $p\to K^{+}\overline{\nu}$ channel, as the most promising from theoretical and experimental considerations. Much of the discussion that follows can be applied to cover the other channels with kaons listed in the table.

In LArTPC detectors, the $K^{+}$ can be tracked, its momentum measured by range, and its identity positively resolved via detailed analysis of its energy-loss profile. Additionally, all decay modes can be cleanly reconstructed and identified, including those with neutrinos, since the decaying proton is essentially at rest. With this level of detail, it is possible for a single event to provide overwhelming evidence for the appearance of an isolated kaon of the right momentum originating from a point within the fiducial volume. The strength of this signature is clear from cosmogenic-induced kaons observed by the ICARUS Collaboration in the cosmic-ray (CR) test run of half of the T600 detector, performed at a surface installation in Pavia and in high-energy neutrino interactions with the full T600 in the recent CNGS (CERN Neutrinos to Gran Sasso) run . Figure 5.1 shows a sample event from the CNGS run in which the kaon is observed as a progressively heavily-ionizing track that crosses into the active liquid argon volume, stops, and decays to $\mu\nu$, producing a muon track that also stops and decays such that the Michel-electron track is also visible. The 3D reconstruction of the event is shown in Figure 5.2.

If it can be demonstrated that background processes mimicking this signature can be rejected at the appropriate level, a single $p\to K^{+}\overline{\nu}$ candidate could constitute evidence for proton decay.

3 Background Levels and Rejection Capabilities

This section discusses the key background processes and their signatures, focusing on the $p\to K^{+}\overline{\nu}$ channel as the benchmark mode Much of this discussion applies equally well to other nucleon decay modes involving charged or neutral kaons.. The two potential sources of background are cosmic-ray muons and atmospheric neutrinos, described separately below.

Cosmic-ray (CR) muons contribute background signals when they penetrate the detector. Hence, the self-shielding feature of the LArTPC and the depth of the site are important assets for controlling the rate of signals that can mimic a proton decay event. Additionally, the energy deposition associated with spallation products is well below the hundreds-of-MeV range for depositions from proton decay final-state particles.

The most pernicious CR-muon background in liquid argon for proton decay with kaon final states thus comes from particular pathological processes. Specifically, CR muons that produce kaons via photonuclear interactions in the rock near the detector or in the liquid argon itself but outside the active volume are capable of producing signatures that mimic $p\to K^{+}\overline{\nu}$ and other modes with kaons. CR-induced kaon backgrounds as a function of depth have been studied for liquid argon .

One class of such backgrounds involves production of a charged kaon outside the active volume, which then enters the active region. Assuming unambiguous determination of the drift time (via the scintillation-photon detection system and other cues such as detailed analysis of the $dE/dx$ profile of the kaon candidate), it will be possible to identify and reject such entering kaons with high efficiency. It should be noted that, through studies of CR muons that interact within the active volume of the detector, backgrounds of this type can be well characterized with data from the detector itself.

No muon is in the detector active volume.

In addition to the impact of an active veto system for detectors at various depths, the studies of also consider impacts of progressively restrictive fiducial volume cuts. Together, these and the above studies demonstrate that proton decay searches in the LBNE LArTPC at the 4,850-ft level can be made immune to CR-muon backgrounds, without the requirement of an external active veto system. To the extent that there are uncertainties on the rate of kaon production in CR-muon interactions, one has flexibility to suppress background from this source further by application of modest fiducial volume cuts.

3.2 Background from Atmospheric-Neutrino Interactions

Super–Kamiokande has given considerable attention to atmospheric-neutrino backgrounds in its nucleon decay searches (e.g., ). In the SK analyses, data obtained with relaxed cuts have been studied to validate the atmospheric-neutrino flux and interaction models employed. Consequently, the atmospheric-neutrino backgrounds for nucleon decay searches are well established at the level required for the water Cherenkov detector approach to this physics.

For the case of LBNE, however, with a different detector technology, and with a goal of being sufficiently background-free to enable a discovery based on observation of a single candidate event, one would like to go further to understand at a detailed level what the rates for the specific background processes are. The first question to ask is what are the physical processes that could produce the exact signature of a $p\to K^{+}\overline{\nu}$ event? Some possibilities are discussed below.

Strange particle production in $\Delta S=0$ processes: An identified source of background events for SK involves associated production of a pair of strange hadrons, nominally in the strong decay of a nucleonic resonance excited via an inelastic NC neutrino-nucleon interaction. This could be in the form of a kaon accompanying a $\Lambda$ baryon. Again, conservation of strangeness holds that the baryon cannot be absorbed, and thus a weak decay of the strange quark is guaranteed. For water Cherenkov detectors the strange baryon is produced with a small enough momentum that its decay products are typically below Cherenkov threshold. For a liquid argon detector, these final state particles should be detectable, leaving distinctive signatures that can be reconstructed. Thus in principle, this source of background can be suppressed with appropriate event reconstruction and analysis tools. To understand this prospect in quantitative terms, the range of kinematic distributions are currently under investigation.

It is possible to imagine yet more contrived scenarios, for example where the meson produced is a $K^{0}_{L}$ that escapes detection, while a charged kaon ($K^{-}$ in this case) results from the decay of an excited $\Lambda$ or $\Sigma$ baryon produced in association. However, one would expect such processes to be even more rare than those described above. Thus if the rates for (say) the $K^{+}\Lambda$ production channel described above can be constrained as being sufficiently small, it can be argued that the more contrived scenarios can be ignored.

Strange particle production in $\Delta S=1$ processes: A potentially challenging source of background is production of a single charged kaon (in this case a $K^{-}$) in a $\Delta S=1$ process. In the simplest case, one could think of it as the Cabibbo-suppressed version of single $\pi$ production in a CC antineutrino interaction. In contrast to the $\Delta S=0$ processes described above, no strange baryon is produced in association, and so there are no other hadrons to detect. (Similarly, one could imagine the kaon originating in the decay of a strange baryon resonance produced in a Cabibbo-suppressed neutrino interaction, accompanied by a neutron that goes undetected.) On the other hand, such processes can only occur in CC interactions, and thus a charged lepton will accompany the kaon. This therefore constitutes a background only for cases where the charged lepton is missed, which should be rare. The combination of probabilities associated with (1) Cabibbo-suppression, (2) single hadron production, and (3) circumstances causing the charged lepton to be missed, lead to an overall suppression of this source of background. Thus it should be possible to rule it out as a source of concern for LBNE on the basis of these features alone.

One variant of this background source occurs for the case where the pion decays in flight. Two experimental handles on this background can be immediately identified. First is the deviation from the expected $dE/dx$ profile for a kaon, which will be more dramatic than in the case of the stopping pion. Second is the correlation of the direction of the decay muon with that of the pion, which is absent in the decay of a particle at rest. Assessment of the cumulative impact of event rejection based on these features is under study. However, the decaying kaon observed in the ICARUS CNGS run displayed in Figure 5.1 can be used to give a sense of the $\pi/K$ discrimination possible in a LArTPC via $dE/dx$. In Figure 5.3, the measurements of $dE/dx$ versus residual range for the anode wires registering signals from the kaon and muon tracks in this event are plotted against the expected $dE/dx$ profiles . The data from the kaon track (cyan points) agree very well with the expected $dE/dx$ profile (blue curve) and are quite distinguishable from the expected pion profile (dashed curve).

Event reconstruction pathologies: While consideration of rare event topologies in atmospheric-neutrino interactions is important, it will be equally important to understand ways in which more typical events might be misreconstructed so as to mimic nucleon decay processes. For example, a quasi-elastic $\nu_{\mu}$-CC interaction will produce a muon and a recoil proton from a common vertex. However, it may be possible to interpret the vertex as the kink associated with the decay of a stopping kaon, where the proton track is confused with a kaon traveling in the opposite direction. Tools are still under development to be able to understand the degree to which this possibility poses a potential background. Naively, the $dE/dx$ profile of the proton as a function of residual range will not match the time-reversed version of this for a kaon, and distributions of kinematic quantities will be distinct. Additionally, such a background will only affect the portion of the $p\to K^{+}\overline{\nu}$ analysis focused on $K^{+}\to\mu^{+}\nu$; other $K^{+}$ decays will be immune to this pathology.

The point of this example is to illustrate that although the exquisite performance characteristics of the LArTPC technique enables unambiguous identification of nucleon decay signatures, an extensive program of detailed analysis will be required to fully exploit these capabilities.

Conclusions on atmospheric-neutrino backgrounds: The above examples suggest that it will be possible to demonstrate the desired level of suppression of atmospheric-neutrino background without undue reliance on simulations via a combination of arguments based on existing experimental data (from SK proton decay searches, as well as data from various sources on exclusive and inclusive neutrino-interaction processes that yield rare topologies), physics considerations, and detailed analysis of anticipated detector response. For the latter, ongoing LBNE event-reconstruction efforts will play a role with simulated atmospheric-neutrino samples. Additionally, useful input is expected to come in over the short/intermediate term from analyses of LArTPC data from ArgoNeuT, MicroBooNE and the proposed LArIAT. Finally, while the state of neutrino flux and interaction models is already quite advanced, vigorous theoretical work is ongoing to improve these further, exploiting existing data from neutrino and electron-scattering experiments. In particular, kaon production in neutrino interactions in relevant energy ranges is receiving renewed attention .

4 Summary of Expected Sensitivity to Key Nucleon Decay Modes

Based on the expected signal efficiency and the upper limit on the background rates estimated in Section 5.3, the expected limit on the proton lifetime as a function of running time in LBNE for $p\rightarrow K^{+}\overline{\nu}$ is shown in Figure 5.4.

Core-Collapse Supernova Neutrinos

A core-collapse supernova Supernova always refers to a core-collapse supernova in this chapter unless stated otherwise. occurs when a massive star reaches the end of its life, and stellar burning can no longer support the star’s weight. This catastrophic collapse results in a compact remnant such as a neutron star, or possibly a black hole, depending on the mass of the progenitor. The infall is followed by a bounce when sufficiently high core density is reached, and in some unknown (but nonzero) fraction of cases, the shock wave formed after the bounce results in a bright explosion . The explosion energy represents only a small fraction of the enormous total gravitational binding energy of the resulting compact remnant, however — thanks to the neutrinos’ weak coupling, which allows them to escape — within a few tens of seconds almost all of the energy is emitted in the form of neutrinos in the tens-of-MeV range. In spite of their weak coupling, the neutrinos are copious enough to (very likely) play a significant role in the explosion.

Neutrinos from the celebrated SN1987A core collapse in the Large Magellanic Cloud outside the Milky Way were observed; however, the statistics were sparse and a great many questions remain. A high-statistics observation of a neutrino burst from a nearby supernova would be possible with the current generation of detectors. Such an observation would shed light on the nature of the astrophysical event, as well as on the nature of neutrinos themselves. Sensitivity to the different flavor components of the flux is highly desirable.

The core-collapse neutrino signal starts with a short, sharp neutronization burst primarily composed of $\nu_{e}$ (originating from $p+e^{-}\rightarrow n+\nu_{e}$, as protons and electrons get squeezed together), and is followed by an accretion phase lasting some hundreds of milliseconds, as matter falls onto the collapsed core. The later cooling phase over $\sim$10 seconds represents the main part of the signal, over which the proto-neutron star sheds its gravitational binding energy. The neutrino flavor content and spectra change throughout these phases, and the supernova’s temperature evolution can be followed with the neutrino signal. Some fairly generic supernova signal features are illustrated in Figure 6.1, based on and reproduced from .

The supernova-neutrino spectrum at a given moment in time is expected to be well described by a parameterization given by:

where $E_{\nu}$ is the neutrino energy, $\langle E_{\nu}\rangle$ is the mean neutrino energy, $\alpha$ is a pinching parameter, and $\mathcal{N}$ is a normalization constant. Large $\alpha$ corresponds to a more pinched spectrum (suppressed high-energy tail). This parameterization is referred to as a pinched-thermal form. The different $\nu_{e}$, $\overline{\nu}_{e}$ and $\nu_{x},\,x=\mu,\tau$ flavors are expected to have different average energy and $\alpha$ parameters and to evolve differently in time.

A wide variety of astrophysical phenomena affect the flavor-energy-time evolution of the spectrum, including neutrino oscillation effects that are determined by the mass hierarchy (MH) and collective effects due to neutrino-neutrino interactions. A voluminous literature exists exploring these collective phenomena, e.g., .

This list is far from comprehensive. Furthermore, signatures of collective effects and signatures that depend on the MH will make an impact on many of the above signals (examples will be presented in Section 6.2). Certain phenomena are even postulated to indicate beyond-the-Standard-Model physics such as axions, extra dimensions and an anomalous neutrino magnetic moment; non-observation of these effects, conversely, would enable constraints on these phenomena.

The supernova-neutrino burst signal is prompt with respect to the electromagnetic signal and therefore can be exploited to provide an early warning to astronomers . Additionally, a LArTPC signal is expected to provide some pointing information, primarily from elastic scattering on electrons.

Even non-observation of a burst, or non-observation of a $\nu_{e}$ component of a burst in the presence of supernovae (or other astrophysical events) observed in electromagnetic or gravitational wave channels, would still provide valuable information about the nature of the sources. Moreover, a long-timescale, sensitive search yielding no bursts will also provide limits on the rate of core-collapse supernovae.

2 Expected Signal and Detection in Liquid Argon

As discussed in Section 2.4, liquid argon is known to exhibit a singular sensitivity to the $\nu_{e}$ component of a supernova-neutrino burst. This feature is especially important, as it will make LBNE a unique source in the global effort to combine data from a variety of detectors with different flavor sensitivities to obtain a complete picture of the physics of the burst.

Work is currently underway using the full Geant4 simulation framework and the LArSoft software package to characterize low-energy response for realistic LBNE detector configurations. Preliminary studies of the detector response with the full simulation are summarized in Section A.1.2 and are found to be consistent with the parameterized response implemented in SNOwGLoBES.

Table 6.1 shows rates calculated with SNOwGLoBES for the dominant interactions in argon for the Livermore model , and the GKVM model . Figure 6.3 shows the expected observed differential event spectra for these fluxes. Clearly, the $\nu_{e}$ flavor dominates.

Figure 6.4 gives another example of an expected burst signal, for which a calculation with detailed time dependence of the spectra is available out to nine seconds post-bounce. This model has relatively low luminosity but a robust neutronization burst. Note that the relative fraction of neutronization-burst events is quite high.

In Figure 6.5, different oscillation hypotheses have been applied to Duan fluxes . The Duan flux represents only a single late time slice of the supernova-neutrino burst and not the full flux; MH information will be encoded in the time evolution of the signal, as well. The figure illustrates, if only anecdotally, potential MH signatures.

Another potential MH signature is shown in Figure 6.6, for which a clear time-dependent shock-wave-related feature is visible for the normal MH case.

Figure 6.7 shows yet another example of a preliminary study showing how one might track supernova temperature as a function of time with the $\nu_{e}$ signal in liquid argon. Here, a fit is made to the pinched-thermal form of Equation 6.1. Not only can the internal temperature of the supernova be effectively measured, but the time evolution is observably different for the different hierarchies.

3 Low-Energy Backgrounds

3.2 Local Radiation Sources

It is possible that radioactive decays will directly overlap with the energy spectrum created by supernova-neutrino events in LBNE. It is also possible for an ensemble of radioactive-decay events in and around higher-energy particle interactions (e.g., from beam neutrinos) to obscure the edges of electromagnetic showers from highly scattering particles such as electrons and pions; this would appear as the radiological equivalent of dark noise in a digital image, and could potentially introduce a systematic uncertainty in the energy calculated for events, even at much higher energy than the decays themselves. It is therefore very important to calculate the radioactive-decay backgrounds in the LBNE far detector with sufficient accuracy to properly account for their presence, either as direct backgrounds or as systematic effects in energy calculations. To this end, LBNE collaborators are in the process of creating a physics-driven, radioactive-background budget and associated event generator for low-energy background events in the far detector.

The radioactive-background budget will have many components, each of which will fall into one of two categories:

intrinsic radioactive contamination in the argon or support materials, or

cosmogenic radioactivity produced in situ from cosmic-ray showers interacting with the argon or the support materials.

3.3 Intrinsic Radioactive Background Mitigation

Since a large body of work has been compiled on the control of radiological background in previous experiments that have encountered similar conditions, much of the work in this area will be cited from these experiments (e.g., DARKSIDE , EXO , ICARUS, BOREXINO, KamLAND and Super–Kamiokande). Work remains, however, on understanding the background particular to the LBNE far detector location/depth (e.g., radon levels and dust activity, for instance), and on integrating existing and new work into the LBNE simulation, reconstruction and analysis framework.

4 Summary of Core-Collapse Supernova Sensitivities

Precision Measurements with a High-Intensity Neutrino Beam

The reduction of systematic uncertainties for the neutrino oscillation program requires excellent resolution in the reconstruction of neutrino events. Combined with the unprecedented neutrino fluxes available — which will allow the collection of ${\cal{O}}$(${10}^{8}$) inclusive neutrino charged current (CC) interactions for ${10}^{22}$ protons-on-target (POT) just downstream of the beamline — the near detector (ND) will significantly enhance the LBNE long-baseline oscillation program and produce a range of short-baseline neutrino scattering physics measurements. The combined statistics and resolution expected in the ND will allow precise tests of fundamental interactions resulting in a better understanding of the structure of matter.

This chapter presents a short description of some of the studies that can be performed with LBNE’s fine-grained near neutrino detector and gives a flavor of the outstanding physics potential. A more detailed and complete discussion of the ND physics potential can be found in .

Appendix B describes neutrino scattering kinematics and includes definitions of the kinematic variables used in this chapter.

From the studies of uncertainties and the impact of the spectral shape presented in Section 4.3.2, it is evident that to fully realize the goals of the full LBNE scientific program — in particular, sensitivity to CP violation and the precision measurement of the three-flavor oscillation parameters — it is necessary to characterize the expected unoscillated neutrino flux with high precision. In addition to the precise determination of the neutrino flux, shape and flavor composition, the characterization of different neutrino interactions and interaction cross sections on a liquid argon target is necessary to estimate physics backgrounds to the oscillation measurements. The high-resolution near tracking detector described in Section 3.5 can measure the unoscillated flux normalization, shape and flavor to a few percent using systematically independent techniques that are discussed in the following sections.

The most promising method of determining the shape of the $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ flux is by measuring CC events with low hadronic-energy deposition (low-$\nu$) where $\nu$ is the total energy of the hadrons that are produced after a neutrino interaction, $E_{\nu}-E_{\mu}$. It is important to note that not all the hadrons escape the remnant nucleus, and intranuclear effects will smear the visible energy of the hadronic system. A method of relative flux determination known as low-$\nu_{0}$ — where $\nu_{0}$ is a given value of visible hadronic energy in the interaction that is selected to minimize the fraction of the total interaction energy carried by the hadronic system — is well developed . The method follows from the general expression of the $\nu$-nucleon differential cross section:

where the coefficients are ${\cal A}={\cal F}_{2}$, ${\cal B}=({\cal F}_{2}\pm{\cal F}_{3})/2$, ${\cal C}=({\cal F}_{2}\mp{\cal F}_{3})/6$, and ${\cal F}_{i}=\int^{1}_{0}\int^{\nu_{0}}_{0}F_{i}(x)dxd\nu$ is the integral of structure function $F_{i}(x)$. The dynamics of neutrino-nucleon scattering implies that the number of events in a given energy bin with hadronic energy $E_{\rm had}<\nu_{0}$ is proportional to the (anti)neutrino flux in that energy bin up to corrections ${\cal O}(\nu_{0}/E_{\nu})$ and ${\cal O}(\nu_{0}/E_{\nu})^{2}$. The number ${\cal N}(\nu<\nu_{0})$ is therefore proportional to the flux up to correction factors of the order ${\cal O}(\nu_{0}/E_{\nu})$ or smaller, which are not significant for small values of $\nu_{0}$ at energies $\geq\nu_{0}$. The coefficients ${\cal A}$, ${\cal B}$ and ${\cal C}$ are determined for each energy bin and neutrino flavor within the ND data.

LBNE’s primary interest is the relative flux determination, i.e., the neutrino flux in one energy bin relative to that in another; variations in the coefficients do not affect the relative flux. The prescription for the relative flux determination is simple: count the number of neutrino CC events below a certain small value of hadronic energy ($\nu_{0}$). The observed number of events, up to the correction of the order ${\cal O}(\nu_{0}/E_{\nu})$ due to the finite $\nu_{0}$ in each total visible energy bin, is proportional to the relative flux. The smaller the factor $\nu_{0}/E_{\nu}$ is, the smaller is the correction. Furthermore, the energy of events passing the low-$\nu_{0}$ cut is dominated by the corresponding lepton energy.

The empirical parameterization of the pion and kaon neutrino parents produced from the proton target, determined from the low-$\nu_{0}$ flux at the ND, allows prediction of the $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ flux at the far detector location. This parameterization provides a measure of the $\pi^{+}/K^{+}/\mu^{+}(\pi^{-}/K^{-}/\mu^{-})$ distributions of neutrino parents of the beam observed in the ND. Additionally, with the capability to identify $\overline{\nu}_{e}$ CC interactions, it is possible to directly extract the elusive $K^{0}_{L}$ content of the beam. Therefore, an accurate measurement of the $\nu_{\mu},\overline{\nu}_{\mu}$ and $\overline{\nu}_{e}$ CC interactions provides a prediction of the $\nu_{e}$ content of the beam, which is an irreducible background for the $\nu_{e}$ appearance search in the far detector:

Based on the NOMAD experience, a precision of $\leq 0.1\%$ on the flux ratio $\nu_{e}/\nu_{\mu}$ is expected at high energies. Taking into account the projected precision of the $\nu_{\mu}$ flux discussed in Section 7.1.1, this translates into an absolute prediction for the $\nu_{e}$ flux at the level of $2\%$.

Finally, the fine-grained ND can directly identify $\nu_{e}$ CC interactions from the LBNE beam. The relevance of this measurement is twofold:

It provides an independent validation for the flux predictions obtained from the low-$\nu_{0}$ method.

It can further constrain the uncertainty on the knowledge of the absolute $\nu_{e}$ flux.

1.3 Constraining the Unoscillated 𝝂\boldsymbol{\nu} Spectral Shape with the QE Interaction

In any long-baseline neutrino oscillation program, including LBNE, the quasi-elastic (QE) interactions are special. First, the QE cross section is substantial at lower energies . Second, because of the simple topology (a $\mu^{-}$ and a proton), the visible interaction energy provides, to first order, a close approximation to the neutrino energy ($E_{\nu}$). In the context of a fine-grained tracker, a precise measurement of QE will impose direct constraints on nuclear effects related to both the primary and final-state interaction (FSI) dynamics (Section 7.6), which can affect the overall neutrino energy scale and, thus, the entire oscillation program. To this end, the key to reconstructing a high-quality sample of $\nu_{\mu}$ QE interactions is the two-track topology where both final-state particles are visible: $\mu^{-}$ and $p$. A high-resolution ND can efficiently identify the recoil proton and measure its momentum vector as well as $dE/dx$. Preliminary studies indicate that in a fine-grained tracking detector the efficiency (purity) for the proton reconstruction in QE events is $52\%$ ($82\%$). A comparison between the neutrino energy reconstructed from the muon momentum through the QE kinematics (assuming a free target nucleon) with the visible neutrino energy measured as the sum of $\mu$ and $p$ energies is sensitive to both nuclear effects and FSI. Furthermore, comparing the two-track sample ($\mu$ and $p$) with the single-track sample (in which only $\mu$ is reconstructed) empirically constrains the rate of FSI.

1.4 Low-Energy Absolute Flux: Neutrino-Electron NC Scattering

Neutrino neutral current (NC) interaction with the atomic electron in the target, $\nu_{\mu}e^{-}\rightarrow\nu_{\mu}e^{-}$, provides an elegant measure of the absolute flux. The total cross section for NC elastic scattering off electrons is given by :

1.5 High-Energy Absolute Flux: Neutrino-Electron CC Scattering

1.6 Low-Energy Absolute Flux: QE in Water and Heavy-Water Targets

Another independent method to extract the absolute flux is through the QE-CC scattering ($\nu_{\mu}n(p)\to\mu^{-}p(n)$) on deuterium at low $Q^{2}$. Neglecting terms in $(m_{\mu}/M_{n})^{2}$ at $Q^{2}=0$, the QE cross section is independent of neutrino energy for $(2E_{\nu}M_{n})^{1/2}>m_{\mu}$:

which is determined by neutron $\beta$ decay and has a theoretical uncertainty $<1\%$. The flux can be extracted experimentally by measuring low $Q^{2}$ QE interactions ($\leq 0.05$ GeV) and extrapolating the result to the limit of $Q^{2}=0$. The measurement requires a deuterium (or hydrogen for antineutrino) target to minimize the smearing due to Fermi motion and other nuclear effects. This requirement can only be achieved by using both H2O and D2O targets embedded in the fine-grained tracker and extracting the events produced in deuterium by statistical subtraction of the larger oxygen component. The experimental resolution on the muon and proton momentum and angle is crucial. Dominant uncertainties of the method are related to the extrapolation to $Q^{2}=0$, to the theoretical cross section on deuterium, to the experimental resolution and to the statistical subtraction. Sensitivity studies and the experimental requirements are under study.

1.7 Neutral Pions, Photons and 𝝅±\boldsymbol{\pi^{\pm}} in NC and CC Events

The principal background to the $\nu_{e}$ and $\overline{\nu}_{e}$ appearance comes from the NC events where a photon from the $\pi^{0}$ decay produces a signature similar to that produced by $\nu_{e}$-induced electron; the second source of background is due to $\pi^{0}$’s from $\nu_{\mu}$ CC where the $\mu^{-}$ evades identification — typically at high $y_{Bj}$. Since the energy spectra of NC and CC interactions are different, it is critical for the ND to measure $\pi^{0}$’s in NC and CC interactions in the full kinematic phase space.

The proposed ND is designed to measure $\pi^{0}$’s with high accuracy in three topologies:

Both photons convert in the tracker ($\simeq$25%).

One photon converts in the tracker and the other in the calorimeter ($\simeq$50%).

Both photons convert in the calorimeter; the first two topologies afford the best resolution because the tracker provides precise $\gamma$-direction measurement.

The $\pi^{0}$ reconstruction efficiency in the proposed fine-grained tracker is expected to be $\geq$75% if photons that reach the ECAL are included. By contrasting the $\pi^{0}$ mass in the tracker versus in the calorimeter, the relative efficiencies of photon reconstruction will be well constrained.

Finally, the $\pi^{\pm}$ track momentum and $dE/dx$ information will be measured by the tracker. An in situ determination of the charged pions in the $\nu_{\mu}/\overline{\nu}_{\mu}$ CC events — with $\mu$ID and without $\mu$ID — and in the $\nu$ NC events is crucial to constrain the systematic error associated with the $\nu_{\mu}$( $\overline{\nu}_{\mu}$) disappearance, especially at low $E_{\nu}$.

1.8 Signal and Background Predictions for the Far Detector

In order to achieve reliable predictions for signal and backgrounds in the far detector, near detector measurements — including (anti)neutrino fluxes, nuclear cross sections and detector smearing — must be unfolded and extrapolated to the far detector location. The geometry of the beam and detectors (point source versus extended source) as well as the expected neutrino oscillations imply differences in the (anti)neutrino fluxes in the near and far detectors. These differences, in turn, will result in increased sensitivity of the long-baseline analysis to cross-section uncertainties, in particular between neutrinos and antineutrinos and for exclusive background topologies. Furthermore, the much higher event rates at the near site and the smaller detector size (i.e., reduced containment) make it virtually impossible to achieve identical measurement conditions in both the near and far detectors. However, as discussed in Sections 7.1.1 to 7.1.7, the energy, angular and space resolution of the low-density ND are key factors in reducing the systematic uncertainties achievable on the event predictions for the far detector; the ND can offer a precise in situ measurement of the absolute flux of all flavor components of the beam, $\nu_{\mu},\nu_{e},\bar{\nu}_{\mu},\bar{\nu}_{e}$, resulting in constraints on the parent $\pi^{\pm}/K^{\pm}/\mu^{\pm}$ distributions. In addition, measurements of momenta and energies of final-state particles produced in (anti)neutrino interactions will allow a detailed study of exclusive topologies affecting the signal and background rates in the far detector. All of these measurements will be used to cross-check and fine-tune the simulation programs needed for the actual extrapolation from the near to the far detector.

It is important to note that several of these techniques have already been used and proven to work in neutrino experiments such as MINOS and NOMAD . The higher segmentation and resolution in the LBNE ND with respect to past experiments will increase the available information about the (anti)neutrino event topologies, allowing further reduction of systematic uncertainties both in the ND measurements and in the Monte Carlo extrapolation.

For a more detailed discussion of the impact of ND measurements on the long-baseline oscillation analysis see Section 4.3.2.

2 Electroweak Precision Measurements

The weak mixing angle can be extracted experimentally from three main NC physics processes:

deep inelastic scattering off quarks inside nucleons: $\nu N\to\nu X$

elastic scattering off electrons: $\nu e^{-}\to\nu e^{-}$

elastic scattering off protons: $\nu p\to\nu p$

Figure 7.1 shows the Feynman diagrams corresponding to the three processes.

The most precise measurement of $\sin^{2}\theta_{W}$ in neutrino deep inelastic scattering (DIS) comes from the NuTeV experiment, which reported a value that is $3\sigma$ from the Standard Model . The LBNE ND can perform a similar analysis in the DIS channel by measuring the ratio of NC and CC interactions induced by neutrinos:

Here $\rho$ is the relative coupling strength of the neutral-to-charged current interactions ($\rho=1$ at tree-level in the Standard Model) and $r$ is the ratio of antineutrino to neutrino cross section ($r\sim 0.5$). The absolute sensitivity of ${\cal R}^{\nu}$ to $\sin^{2}\theta_{W}$ is 0.7, which implies that a measurement of ${\cal R}^{\nu}$ to 1% precision would in turn provide a 1.4% precision on $\sin^{2}\theta_{W}$. This technique was used by the CDHS , CHARM and CCFR experiments. In contrast to the NuTeV experiment, the antineutrino interactions cannot be used for this analysis at LBNE due to the large number of $\nu_{\mu}$ DIS interactions in the $\overline{\nu}_{\mu}$ beam compared to the $\overline{\nu}_{\mu}$ DIS interactions.

The use of a low-density magnetized tracker can substantially reduce systematic uncertainties compared to a massive calorimeter. Table 7.2 shows a comparison of the different uncertainties on the measured ${\cal R}^{\nu}$ between NuTeV and LBNE. While NuTeV measured both ${\cal R}^{\nu}$ and ${\cal R}^{\overline{\nu}}$, the largest experimental uncertainty in the measurement of ${\cal R}^{\nu}$ is related to the subtraction of the $\nu_{e}$ CC contamination from the NC sample. Since the low-density tracker at LBNE can efficiently reconstruct the electron tracks, the $\nu_{e}$ CC interactions can be identified on an event-by-event basis, reducing the corresponding uncertainty to a negligible level. Similarly, uncertainties related to the location of the interaction vertex, noise, counter efficiency and so on are removed by the higher resolution and by changing the analysis selection. The experimental selection at LBNE will be dominated by two uncertainties: the knowledge of the $\overline{\nu}_{\mu}$ flux and the kinematic selection of NC interactions. The former is relevant due to the larger NC/CC ratio for antineutrinos. The total experimental systematic uncertainty on $\sin^{2}\theta_{W}$ is expected to be about 0.14%.

The measurement of ${\cal R}^{\nu}$ will be dominated by theoretical systematic uncertainties on the structure functions of the target nucleons. The estimate of these uncertainties for LBNE is based upon the extensive work performed for the NOMAD analysis and includes a Next-to-Next-Leading-Order (NNLO) QCD calculation of structure functions (NLO for charm production) , parton distribution functions (PDFs) extracted from dedicated low-$Q$ global fits, high-twist contributions , electroweak corrections and nuclear corrections . The charm quark production in CC, which has been the dominant source of uncertainty in all past determinations of $\sin^{2}\theta_{W}$ from $\nu$N DIS, is reduced to about 4% of the total $\nu_{\mu}$ CC DIS for $E_{\rm had}>5$ GeV with the low-energy beam spectrum at LBNE. This number translates into a systematic uncertainty of 0.14% on ${\cal R}^{\nu}$ (Table 7.2), assuming the current knowledge of the charm production cross section. It is worth noting that the recent measurement of charm dimuon production by the NOMAD experiment allowed a reduction of the uncertainty on the strange sea distribution to $\sim 3\%$ and on the charm quark mass $m_{c}$ to $\sim 75$ MeV . The lower neutrino energies available at LBNE reduce the accessible $Q^{2}$ values with respect to NuTeV, increasing in turn the effect of non-perturbative contributions (high twists) and $R_{L}$. The corresponding uncertainties are reduced by the recent studies of low-$Q$ structure functions and by improved modeling with respect to the NuTeV analysis (NNLO vs. LO). The total model systematic uncertainty on $\sin^{2}\theta_{W}$ is expected to be about 0.21% with the reference beam configuration. The corresponding total uncertainty on the value of $\sin^{2}\theta_{W}$ extracted from $\nu$N DIS is 0.35%.