Neither the authors, nor the institutions they represent, nor their employees, nor their respective contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any liability or responsibility for accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use will not infringe privately owned rights. Mention of any product, its manufacturer, or suppliers shall not, nor is it intended to, imply approval, disapproval, or fitness for any particular use. A royalty-free, nonexclusive right to use and disseminate same for any purpose whatsoever is expressly granted. Stony Brook University is an affirmative action/equal opportunity employer

The editors (D. Casper, C.K. Jung, C. McGrew and C. Yanagisawa) would like to present this work in honor of our friend and colleague Maurice Goldhaber, on the occasion of his 90th birthday.

The UNO Proto-collaboration

---

ANL,

Argonne, Illinois, U.S.A.
Maury Goodman

BNL,

Upton, New York, U.S.A.
M. Goldhaber, M. Diwan, R. Hahn, B. Viren

University of California, Davis,

Davis, California, U.S.A.
D. Ferenc

University of California, Irvine,

Irvine, California, U.S.A.
S. Barwick, D. Casper, W. Gajewski, W. R. Kropp, S. Mine, M. Smy, H. Sobel, M. R. Vagins, G. Yodh

GRPHE/UHA,

Mulhouse, France
Y. Benhammou

Indiana University,

Bloomington, Indianna, U.S.A.
R. Van Kooten

University of Kansas,

Lawrence, Kansas, U.S.A.
P. Baringer, D. Besson

LANL,

Los Alamos, New Mexico, U.S.A.
T. J. Haines

Louisiana State University,

Baton Rouge, Louisiana, U.S.A.
R. C. Svoboda

University of Minnesota,

Duluth, Minnesota, U.S.A.
A. Habig

University of Minnesota,

Minneapolis, Minnesota, U.S.A.
M. Marshak, J. Nelson, E. Peterson

University of Nebraska,

Lincoln, Nebraska, U.S.A.
D. Claes

National High Magnetic Field Laboratory,

Tallahassee, Florida, U.S.A.
J. Miller

University of New Mexico,

Albuquerque, New Mexico, U.S.A.
S. Seidel

Northwestern University,

Evanston, Illionois, U.S.A.
H. Schellman

State University of New York at Stony Brook,

Stony Brook, New York, U.S.A.
M. Ackerman, J. Hill, C. K. Jung, T. Kato, R. McCarthy, C. McGrew, M. Rijssenbeek, C. Yanagisawa

University of Rochester,

Rochester, New York, U.S.A.
A. Bodek, K. McFarland

Institute de Récherches Subatomiques/ULP,

Strasbourg, France
C. Racca, J. M. Brom

Tufts University,

Medford, Massachusetts, U.S.A.
T. Kafka, T. Mann

University of Utah,

Salt Lake City, Utah, U.S.A.
K. Martens

Warsaw University,

Warsaw, Poland
D. Kielczewska

University of Washington,

Seattle, Washington, U.S.A.
J. Wilkes

Waste Isolation Pilot Plant,

Carlsbad, New Mexico, U.S.A.
R. Nelson, W. Thompson

The UNO Theoretical Advisory Committee

---

University of Arizona,

Tuscon, Arizona, U.S.A.
A. Burrows

BNL,

Upton, New York, U.S.A.
W. Marciano

FNAL,

Batavia, Illinois, U.S.A.
J. Beacom

Institute for Advanced Study,

Princeton, New Jersey, U.S.A.
J.N. Bahcall

University of Maryland,

College Park, Maryland, U.S.A.
J. Pati

Massachusetts Institute of Technology,

Cambridge, Massachusetts, U.S.A.
F. Wilczek

State University of New York at Stony Brook,

Stony Brook, New York, U.S.A.
J. Lattimer, R. Shrock

Other Contributors and Interested Observers

---

Boston University,

Boston, Massachusetts, U.S.A.
E. Kearns, L. R. Sulak, C. W. Walter

BNL,

Upton, New York, U.S.A.
J. C. Gallardo

CEA/Saclay,

Gif-sur-Yvette Cedex, France
M. Spiro

CERN,

Geneva, Switzerland
P. Hernández

FNAL,

Batavia, Illinois, U.S.A.
F. DeJongh, S. Geer, D. Harris, J. Yu

Université de Genève,

Geneva, Switzerland
A. Blondel

ICRR, University of Tokyo,

Tokyo, Japan
T. Kajita, M. Shiozawa, Y. Suzuki

IHEP,

Beijing, P.R. China
Y. Wang

INFN,

Ferrara, Italy
P. Zucchelli

INFN,

Napoli, Italy
V. Palladino

INFN,

Padova, Italy
M. Mezzetto

KEK,

Tsukuba, Japan
K. Nakamura

Kyoto University,

Kyoto, Japan
T. Nakaya, K. Nishikawa

LBL,

Berkeley, California, U.S.A.
A. M. Sessler

Louisiana State University,

Baton Rouge, Louisiana, U.S.A.
W. Metcalf

Massachusetts Institute of Technology,

Cambridge, Massachusetts, U.S.A.
K. Scholberg

University of Michigan,

Ann Arbor, Michigan, U.S.A.
K. Riles

State University of New York at Stony Brook,

Stony Brook, New York, U.S.A.
I. Mocioiu, R. A.M.J. Wijers

University of Pennsylvania,

Philadelphia, Pennsylvania, U.S.A.
K. Lande

Pacific Northwest National Laboratory,

Richland, Washington, U.S.A.
R. T. Kouzes

Queen's University,

Kingston, Ontario, Canada
M.C. Chen

SNO Institute,

Canada
Canadian SNO Collaboration

Universidad de Valencia,

Valencia, Spain
J. Burguet-Castell, J.J. Gomez-Cádenas

Contents

1  Introduction
    1.1  Bibliography
2  The UNO Detector
    2.1  Optimization: Criteria and Constraints
    2.2  Geometry
    2.3  Underground vs. Underwater
    2.4  Baseline Design
    2.5  Light Collection
    2.6  Data Acquisition
    2.7  Overburden
    2.8  Bibliography
3  Nucleon Decay
    3.1  Overview
    3.2  Theoretical Background and Motivation
        3.2.1  Grand Unified Theories and Nucleon Decay
        3.2.2  Predicted Nucleon Decay Rates
    3.3  Current Experimental Results
        3.3.1  Water Cherenkov Detectors
            3.3.1.1  Search for p → e⁺π⁰
            3.3.1.2  Search for p → \mathaccent "7016\relax ν K⁺
        3.3.2  Tracking Calorimeters
            3.3.2.1  Searches for ―νK⁺, l⁺K⁰, and ―νK⁰ modes
            3.3.2.2  Searches for lepton(l⁺,―ν) + meson(S=0) modes
            3.3.2.3  Searches for (B−L) violating processes
    3.4  Nucleon Decay Sensitivity
        3.4.1  Sensitivity to p → e⁺ π⁰
        3.4.2  Sensitivity to p → \mathaccent "7016\relax ν K⁺
        3.4.3  Experimental Determination of the Background
            3.4.3.1  1KT data and simulation
    3.5  Bibliography
4  Neutrino Physics
    4.1  Overview
        4.1.1  Evidence for Neutrino Oscillation
        4.1.2  Neutrino Oscillation Formalism
        4.1.3  Relevant Near- and Mid-Term Experiments
    4.2  Atmospheric Neutrinos
        4.2.1  Direct Observation of the Oscillation Pattern
            4.2.1.1  Experimental Sensitivity to L/E
        4.2.2  Search for ν_τ Appearance
        4.2.3  Global Oscillation Fits
    4.3  Long-Baseline Neutrino Oscillation Experiments
        4.3.1  Overview
        4.3.2  Superbeams
            4.3.2.1  The CERN SPL neutrino beam
            4.3.2.2  Simulation of UNO
            4.3.2.3  ν_μ disappearance
            4.3.2.4  ν_e appearance
            4.3.2.5  θ₁₃ sensitivity
            4.3.2.6  δ_CP sensitivity
        4.3.3  Neutrino Factory
            4.3.3.1  Physics program
            4.3.3.2  Event rates
            4.3.3.3  Charge identification
            4.3.3.4  Detector performance
            4.3.3.5  ν_μ disappearance experiment
            4.3.3.6  \mathaccent "7016\relax ν_μ appearance experiment
            4.3.3.7  Backgrounds
    4.4  Supernova Neutrinos
        4.4.1  Supernova Neutrino Signals
            4.4.1.1  Inverse beta decay
            4.4.1.2  Neutral current from ¹⁶O
            4.4.1.3  Elastic scattering
        4.4.2  High Statistics Measurements
        4.4.3  Black Hole Formation
    4.5  Solar Neutrinos
        4.5.1  Detector Requirements
        4.5.2  Calibration
        4.5.3  Low-Energy Electron Sensitivity
    4.6  Neutrino Astrophysics
        4.6.1  Sources of Astrophysical Neutrinos
        4.6.2  Current Experimental Results
        4.6.3  Point-Source Sensitivity
    4.7  Bibliography
5  Site Studies
    5.1  Homestake Mine
        5.1.1  Homestake Characteristics
        5.1.2  UNO Chamber Construction
        5.1.3  Vertical Cylinder Design
        5.1.4  Next Steps
    5.2  San Jacinto Mountain
        5.2.1  Proposed Facilities and UNO Site
        5.2.2  Schedule
    5.3  WIPP (Waste Isolation Pilot Plant)
        5.3.1  Advantages and Disadvantages of the Site
        5.3.2  Conceptual Layout of an UNO Facility at the WIPP
        5.3.3  Cavity Stability
        5.3.4  Water Containment
        5.3.5  Other Facilities
        5.3.6  Costs
    5.4  Bibliography
6  Detector R&D
    6.1  Overview
    6.2  PMT R&D
    6.3  New Photo-detector R&D: The Novel Photo-sensor ReFerence
        6.3.1  ReFerence Concept
        6.3.2  The ReFerence Photo-sensor
        6.3.3  Outline of the ReFerence Prototype Development
    6.4  Large External Magnet Systems for the UNO Detector
    6.5  Bibliography

Chapter 1
Introduction

Over the past two decades, large underground water Cherenkov experiments - Super-Kamiokande and its predecessors IMB and Kamiokande - have established a remarkable record of success. Their more notable accomplishments include:

• Exclusion of the minimal SU(5) Grand Unified Theory (GUT),
• First real time, directional measurement of solar neutrinos,
• Confirmation of the solar neutrino flux deficit,
• Discovery of atmospheric neutrino oscillation and neutrino mass,
• First detection of accelerator-produced neutrinos at  ∼ 100 km baseline,
• Observation of neutrinos from Supernova 1987A, and
• Establishment of the world's best limits on nucleon decay.

Although originally designed to search for nucleon decay, the above resumé highlights the versatility of these detectors. While, as yet, no unambiguous nucleon decay signal has been identified, the evidence for neutrino oscillation (now firmly established by Super-Kamiokande's atmospheric neutrino data) represents a watershed in particle physics [1]. This breakthrough demonstrates that neutrino masses are very small indeed (if we assume no degeneracy in mass eigenstates), which in turn strongly suggests a new, very high-energy mass scale which generates these small neutrino masses via the ``See-saw" mechanism [2].

Many theoretical models predict nucleon decay, which is a generic consequence of most GUT models. A specific example of such models can be found in Refs. [3,4,5,6], which lay out in detail the connections between neutrino masses, nucleon decay and other Standard Model observables in the G(2,2,4) and SO(10) frameworks. This model predicts proton decay rates within reach of Super-Kamiokande, especially in SUSY-favored decay modes such as p →―ν K⁺. These predictions, along with those of other models, encourage us to extend the search for nucleon decay to even greater sensitivity.

The motivation for redoubled effort in the search for nucleon decay has recently been strengthened by theoretical and experimental advances in other domains, namely:

• an improved calculation of the hadronic nucleon decay matrix element, β_H, based on lattice QCD,
• a smaller value of the strong coupling constant α_s(m_Z) inferred from LEP data, which consequently lowers the unification scale, and
• a larger value of the ratio of Higgs vacuum expectation values tanβ in SUSY models, suggested by both LEP data and recent measurements of the muon anomalous magnetic moment, g−2.

All of these factors increase the expected rate of nucleon decay with respect to earlier predictions, making its detection appear to be an attainable goal.

Discovery of nucleon decay would provide direct evidence that a simpler, yet more fundamental, description of physics lies hidden within the Standard Model. The centuries-old notion of ``unification" in physics, that is, reduction of apparently unrelated phenomena to more general laws, traces its origin from Newton's discovery of a single, universal law which could account for both terrestrial gravitation and celestial mechanics. It reappeared in Maxwell's formulation of electromagnetism, and later in the Glashow-Weinberg-Salaam electroweak theory which, together with QCD, forms the basis of today's Standard Model of particle physics. For two decades, nucleon decay has been the crucible in which attempts at still greater (or ``grand") unification are tested; to date, none have proven equal to the challenge. Observation of nucleon decay would be far more than a mere ``existence proof" for a Grand Unified Theory-it would give us direct experimental clues about precisely which theory nature has chosen. In this respect, the search for nucleon decay is the ultimate experiment at the ``energy frontier": probing physics at a scale ( ∼ 10¹⁶  GeV) far beyond the reach of any imaginable accelerator. In the absence of a signal, five years of UNO data will extend the lifetime limit for two ``benchmark" decay modes (p → e⁺ π⁰ and p → ―ν K⁺) by roughly an order of magnitude over present Super-Kamiokande limits: to  ∼ 5 ×10³⁴  yr and  ∼ 10³⁴  yr, respectively. The expected limit for p → e⁺ π⁰ reaches 10³⁵  yr after a 13-year UNO exposure.

The unrivaled flexibility of the water Cherenkov technique permits us to follow up past breakthroughs even while pursuing new ones: we are fortunate to live in interesting times. In several years, the ``discovery" phase of neutrino flavor physics, which was initiated by ground-breaking measurements of solar and atmospheric neutrinos, will be drawing to a close even as the ``precision measurement" era is dawning. We may hope that in the interim, the solar neutrino puzzle can be resolved by existing or approved experiments such as Super-Kamiokande, SNO, KamLAND and Borexino, and that the dominant channel of ν_μ oscillation will be well-characterized by long-baseline experiments such as K2K and MINOS. Should the MiniBOONE experiment confirm the puzzling LSND effect, the discovery potential of the neutrino sector will multiply considerably. But regardless, even in the most optimistic scenarios, large gaps will remain in our understanding of the neutrino mass hierarchy and leptonic mixing matrix, and direct observation of the oscillatory nature of neutrino flavor violation and ν_τ appearance may remain elusive.

The sinusoidal pattern expected from neutrino oscillation can be established conclusively by measurements of atmospheric neutrinos in a larger detector. Although Super-Kamiokande's directional and hadronic energy resolution are more than sufficient, that detector's dimensions are too small to efficiently contain muons with energies above a few GeV. A larger detector will remedy this ``Achilles Heel"; the resulting gain in L_ν/E_ν resolution, together with a corresponding increase in event rate, will unambiguously establish whether oscillation or some more exotic phenomenon is at work and allow high-precision measurements of the parameters involved.

Probing the subdominant mixing angle θ₁₃ and possible CP-violating terms in the leptonic mixing matrix will require a new generation of neutrino sources and detectors. Two possible types of neutrino sources are presently under intensive study: a muon storage ring (or ``neutrino factory"), or more conventional (``Super-") beams, both fed by very powerful proton drivers. An extremely massive water Cherenkov detector, sensitive to neutrinos over 6 decades of energy, is well-suited to serve as the distant target for any conceivable future high-intensity neutrino source. With a beam of few hundred MeV from a distance of  ∼ 100 km, θ₁₃ sensitivity of 10⁻³ is achievable and CP-violating effects can be observed without complication by matter effects in a variety of plausible scenarios. For a high-energy beam from a muon storage ring, with the addition of internal or external magnets, a water detector's sensitivity to wrong-sign muon appearance is comparable to that of proposed iron spectrometers and liquid detectors, while also offering a much broader complementary program of nucleon decay and particle astrophysics measurements.

Neutrinos from stellar collapse provide a window on neutron star and black hole formation, the supernova explosion mechanism, and heavy element production mechanisms at the very heart of a doomed star, but only 20 such neutrinos have been measured. A much larger detector can increase the chance of future observations by extending the range of detection to a much larger population of stars (the Andromeda Galaxy), and extract much more precise and detailed information from any burst which does occur in our own galaxy. Millisecond timing structure in the collapse is visible if  ∼ 100,000 neutrino interactions are observed. A detector with roughly 20 times the fiducial mass of Super-Kamiokande can collect such a sample from a supernova at the galactic center, and see a clear (if modest) signal even at a distance of 1 Mpc. Such a detector can also search for astrophysical point sources of neutrinos, and dark matter, in an energy range difficult for larger, more coarse-grained undersea and under-ice detectors to cover.

To relentlessly pursue the quest for evidence of grand unification, to unlock the fundamental secrets of neutrino oscillation, and to advance a diverse program of particle astrophysics, we have studied the physics potential and feasibility of a much larger next-generation nucleon decay and neutrino detector. This detector, sited underground and using the robust, versatile and economical water Cherenkov technique, is named UNO (Underground Nucleon decay and Neutrino Observatory) [7].

Preliminary cost estimates indicate the cost of the UNO detector-as described herein with 13 times the total mass of Super-Kamiokande and 20 times the fiducial mass-would be $500M (including excavation), and we find no significant technical obstacles to construction of such a detector. We expect the detector could be completed within ten years of ground-breaking.

At present, the informal UNO proto-collaboration consists of 48 experimental physicists, representing 23 institutions. The collaboration is supported by a Theoretical Advisory Committee (UNO-TAC) and other interested parties from Canada, China, Europe, Japan, and the United States, numbering about 100 in total.

Parallel to the UNO initiative, the possibility of similar next-generation underground water Cherenkov detectors has been discussed in Japan (Hyper-Kamiokande) and in Europe (Fréjus). Also under study in Japan is a large underwater Cherenkov detector (Titanic). The UNO proto-collaboration views these efforts (including our own) as reinforcing, rather than competing with, each other. Taken together, they demonstrate an even broader endorsement of the physics objectives we aim to address, and a global commitment to the shared goal of constructing a next-generation water detector somewhere in the world. Indeed, many of the physicists involved in these other projects have participated fruitfully in our discussions and made very significant contributions to this document, for which we are most grateful.

If realized, UNO will provide a comprehensive nucleon decay and neutrino physics program to the astrophysics, nuclear physics, and particle physics communities world-wide, for decades to come. In the remainder of this document, we present the conceptual configuration, physics potential, candidate sites, and R&D plans for the UNO detector in greater detail.

Bibliography

[1]

Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998)

[2]

M. Gell-Mann, P. Ramond, R. Slansky, in Supergravity, edited by P. van Nieuwenhuizen and D. Freedman (North Holland,Amsterdam, 1979), p.315; T. Yanagida in Proceedings of Workshop on Unified Theory and Baryon Number in the Universe, KEK, 1979.

[3]

J. Pati and A. Salam, Phys. Rev. Lett. 31, 661 (1973); Phys. Rev. D10, 275 (1974).

[4]

C. Albright, K. Babu, and S. Barr, Phys. Rev. Lett. 81, 1167 (1998) (hep-ph/9802314).

[5]

C. Albright and S. Barr, Phys. Rev. Lett. 85, 244 (2000) (hep-ph/0002155); Phys. Rev. D62, 093008 (2000) (hep-ph/0003251); hep-ph/0104294.

[6]

K. Babu, J. Pati, and F. Wilczek, Phys. Lett. B423, 337 (1998); Nucl. Phys. 566, 33 (2000) (hep-ph/9812538).

[7]

C. K. Jung, Feasibility of a Next Generation Underground Water Cherenkov Detector: UNO, (hep-ex/0005046); Next Generation Nucleon Decay and Neutrino Detector, AIP Conference Proceedings 533, edited by M. V. Diwan and C. K. Jung (2000)

Chapter 2
The UNO Detector

UNO's design philosophy begins with the well-established water Cherenkov detector technology of Super-Kamiokande. Extension of the technique to achieve an order of magnitude better sensitivity to nucleon decay and precision measurements of neutrino properties presents no serious technical challenges. In addition to the proven soundness of the fundamental design, UNO can draw on and further refine the twenty years of experience, expertise and analysis tools accumulated from IMB, Kamioka and Super-Kamiokande.

To strike a balance between increased physics reach and practical considerations of cost, the benchmark fiducial volume of the UNO detector is 20 times that of Super-Kamiokande. We aim for broad physics capabilities and a simple, robust detector configuration.

2.1  Optimization: Criteria and Constraints

Several design options have been considered, keeping in mind two practical constraints on the water Cherenkov technique, namely:

• The water depth is limited by the pressure tolerance of the glass bulb of the PMT ( ∼ 8 atm, or roughly 80 meters of water for current 20^′′ Hamamatsu PMTs). This can be overcome only by enclosing each PMT in a high-pressure water-tight container, thereby compromising the Cherenkov collection efficiency, or by using new PMTs specially designed for high-pressure applications.
• The maximum dimension of a detector with only surface instrumentation is limited by the finite attenuation length of Cherenkov light in pure water ( ∼ 80 m at λ = 400  nm is in Super-Kamiokande).

2.2  Geometry

Three detector concepts have been studied: Cubical, Toroidal and Multi-Cubical. Excavation costs are relatively insensitive to the shape of the cavity [1], but the choice of geometry is still important:

• The cost of mining the cavity is proportional to the total volume of the detector, including a  ∼ 2.5 m veto region outside each face of the inner detector and a further 2 m inside the PMT planes which defines the fiducial volume. While these non-fiducial buffer volumes do not contribute directly to our nucleon decay and neutrino rates, experience has shown that they are indispensable for ensuring shielding against entering low energy particles from the surrounding rocks and for background rejection.
• The instrumentation cost (for a fixed photocathode coverage) is proportional to the surface area of the inner detector PMT faces. Equivalently, for a fixed PMT budget, increasing the surface area reduces the amount of information collected for each event, eventually degrading the efficiency for low-energy phenomena and the ability to understand complex higher-energy interactions.

To optimize the detector cost for a fixed fiducial volume (445 kton;  ∼ 20 times Super-Kamiokande), the ratio r_V (fiducial volume/total volume) should be maximized and the ratio r_A (PMT surface area/total volume) should be minimized. These geometrical considerations clearly favor detectors which are large in all dimensions.

To achieve the desired fiducial volume, the Cubical design implies a cavity of 86 ×86 ×86  m³ outer dimensions. While the Cubical detector is close to optimal in terms of r_V and r_A, it runs afoul of the practical constraints. PMTs at the bottom of the detector would be subject to a water pressure of about 9 atmospheres. In addition, the diagonal length of 150 m is almost double the attenuation length in pure water measured by Super-Kamiokande.

The Toroidal design is very inefficient in its use of the excavated volume (r_V). It is not physically possible if the cross-section of the detector is 60 ×60  m². Even with a 50 ×50  m² cross-section the torus would be too tight, making the diameter of the central rock column too small to support the structure. Therefore a Toroidal design requires a small cross-section, making the r_V ratio small and the r_A value large. For example, in a Toroidal design with 40 ×40  m² cross-section, only 60% of the total volume is fiducial, compared to 70% for the Multi-Cubical design option discussed below.

The Multi-Cubical design has outer dimensions of 60 ×60 ×180 m³ and appears to be the optimal geometry consistent with practical constraints. When segmented into three 60 ×60 ×60  m³ cubical subdetector elements, both the maximum water pressure and light travel distance are in acceptable ranges, and the r_V and r_A values are reasonable.

Segmentation naturally increases the cost (by creating 4 additional surfaces to instrument) but provides several significant benefits compared to an open geometry:

• Mitigation of so-called ``flasher" (PMT discharge) instrumental backgrounds (which occur in all water Cherenkov detectors) by confining each event in a smaller optical compartment.
• Reduced inefficiency and associated systematics due to light attenuation in water, by limiting the maximum distance a photon can travel before reaching a sensitive detector.
• Ensuring nearly 100% operational live time, which is essential for a supernova watch. Even with exceptional reliability, Super-Kamiokande is limited to about 90% operational efficiency due to detector calibration. With three optically separated compartments, two subdetectors can remain live even while a third is being calibrated.
• Better trigger performance at low energy, not only from reduced attenuation but also since each subdetector can trigger independently with a lower accidental rate.
• If the divisions between subdetectors are rigid (i.e., water-tight), it would be possible to periodically empty and maintain each compartment separately. It requires four months to drain and refill the present Super-Kamiokande tank, which is less than 1/4 of the total volume in a single UNO subdetector. Rigid segmentation would also facilitate possible reconfiguration of the detector in the future, for instance to install a magnetic tracking system for neutrino factory physics. At present, cost to benefit ratio for rigid segmentation is uncertain, and thus this option requires further study.

2.3  Underground vs. Underwater

The possibility of siting a next-generation detector underwater rather than underground has also been considered. One serious disadvantage of underwater deployment is inaccessibility for calibration and service. Experience with Super-Kamiokande indicates that a well-selected and well-maintained underground site provides an ideal working environment, and that regular and routine access to the detector is indispensable. In contrast, reliable calibration and operation of a deep underwater detector is a challenge which has still not been solved, despite investment of countless man-years of R&D. In addition, other services such as water purification, power, and computing would need to be deployed near any such underwater laboratory, perhaps even maintained at sea. In summary, an underwater detector would raise many technical complications which are absent in the time-tested and more accommodating underground configuration raising the specter of indeterminate delays and cost overruns. The next large underground water Cherenkov detector will be a fourth-generation device; the next large underwater Cherenkov detector will be the first.

2.4  Baseline Design

We conclude that a large underground water Cherenkov detector with a Multi-Cubical, segmented configuration is the best choice for UNO. Such a experiment could be operational within 10 years, with assured performance and reliability, and no large-scale R&D required. The baseline conceptual design of the UNO detector is shown in Figure 2.1.

The detector has three compartments, each measuring 60 ×60 ×60  m³, for a total length of 180 m and a total mass of 648 kton. The outer detector region serves as a veto shield of 2.5 m depth, and is instrumented with 14,901 outward-facing 8^′′ PMTs at a density of 0.33 PMTs/m². The inner detector regions contain the software-defined fiducial volume, beginning 2 m within the PMT planes; the total fiducial mass the three subdetectors is 445 kton. The inner detector regions are viewed by 56,650 20^′′ PMTs, with an average PMT density of approximately 1  PMT/m². Table 2.1 compares UNO's parameters with those of other large water Cherenkov detectors.

2.5  Light Collection

UNO's PMT density is chosen to allow excellent sensitivity to a broad range of nucleon decay and neutrino physics while keeping the instrumentation costs under control. Even after fixing the average PMT density, however, additional choices are possible.

The PMTs could be deployed uniformly, providing 20% photo-cathode coverage (equivalent to that of Kamiokande-III) over the entire inner detector. The advantages of this scheme are a uniform detector response, excellent ring-identification and particle ID, and roughly 7 MeV analysis threshold through-out the entire 445 kton fiducial volume. Identification of the 6 MeV γ from nuclear de-excitation following p → ―ν K⁺is still possible in this configuration, notwithstanding the nominal 7 MeV threshold, since these events trigger on the higher energy μ⁺ from K⁺ decay.

Alternatively, the PMT density in the central subdetector module could be doubled to 40% photo-cathode coverage (equivalent to Super-Kamiokande) at the expense of the reducing the two outer modules to 10% each. In this scenario, the trigger threshold for the two wings would be around 10 MeV, while the central detector analysis threshold is reduced to approximately 5 MeV. Only in this configuration is there hope for solar neutrino studies, using the central module. In addition, the lower threshold would allow additional information on core collapse and black-hole formation to be extracted from supernovae neutrinos, along with measurement of the ν_μ and ν_τ fluxes using neutral current excitation of Oxygen.

Several other detector configurations were explored, while keeping the total cost fixed, including four subdetector modules with 10% coverage and five subdetector modules with 4% coverage. While these two options present similar sensitivities for p → e⁺ π⁰ searches, they are inferior to the others for p → ―ν K⁺and low-energy neutrino physics.

A uniform 40% photocathode coverage would clearly enhance UNO's low-energy sensitivity, but it would incur additional cost of  ∼ $160M. To retain the possibility of additional photo-cathode coverage, should a compelling physics case for it arise, the PMT mounting system is designed to accommodate a possible future upgrade.

2.6  Data Acquisition

While UNO does not require cutting-edge readout or triggering, it could benefit from relatively modest improvements to the dual-hit electronics used by Super-Kamiokande. In the conceptual design, waveform digitization of the PMT signals (with roughly 200 MHz sampling frequency and several ms full-scale) opens a number of possibilities for enhancing the detector's sensitivity. Energy resolution and reconstruction of higher energy events (e.g., p → e⁺ π⁰) will benefit from the ability to distinguish direct Cherenkov light from later-arriving scattered and reflected photons. μ→ e identification can be extended to as little as 50 ns after the global trigger, raising the efficiency to nearly 100% and improving background rejection for p → e⁺ π⁰. Freed from the limitations of dual-hit electronics, a multi-level trigger would be implemented, using the digital pattern of hits to eliminate accidental coincidences and lower the effective threshold. Waveform digitization could also be used (after the fact) to find lower-energy coincidences during a supernova burst, again allowing more physics to be done with less light collection.

While the potential benefits of improved electronics are many, they are not yet firmly established. Existing analysis software, designed for dual-hit electronics, was not designed to take advantage of the much more detailed event data provided by waveform digitizers. Next-generation reconstruction algorithms are now under development, and will permit more quantitative study of our data acquisition concept.

2.7  Overburden

The optimal detector overburden is influenced by a number of factors, including physics goals, cosmic ray background, excavation and installation costs, structural stability and rock temperature. Thus, the question is non-trivial and the choice depends on the specific characteristics of a given site. With an outer detector veto and waveform electronics, cosmic ray background even at modest depth ( ∼ 2000 mwe) will not compromise nucleon decay studies, however the greater demands of a solar neutrino physics program would require a depth of at least 3000 mwe to avoid unacceptable inefficiency or background from muon-induced spallation products.

Bibliography

[1]

Talk by D. Lee Petersen at NNN99 Workshop at Stony Brook; See his talk on http://superk.physics.sunysb.edu/NNN99.

Chapter 3
Nucleon Decay

3.1  Overview

Proton decay offers a unique window to view physics at truly short distances ( < 10⁻³⁰ cm). It is one of the crucial predictions made by the hypothesis of grand unification of the fundamental particles and of their forces: Thus the discovery of proton decay would have far-reaching consequences on our understanding of nature at the highest energy scale.

Baryon number conservation was first proposed by Stueckelberg (1938) [1] and Wigner (1949) [2]. This conservation law can be proved exact to an extremely good approximation from such evident data as the ambient level of radioactivity. If we assume that each violation is associated with the emission of a charged particle or a gamma-ray, the resultant limit is greater than 10¹⁶ years. A series of tests, starting with one by Reines et al. (1954) [3] that yielded a limit of greater than 10²² years, produced increasingly stringent limits.

Until the 1970's, there was no compelling theoretical reason to question baryon-number conservation. Instead, experiments were motivated by the conviction that fundamental laws should be tested as the means become available. The situation changed with the success of Weinberg and Salam's ideas regarding unification of the weak and electromagnetic forces and with the development of quantum chromodynamics describing the strong interaction. Theorists proposed to unify these three interactions in a way that called for quarks to change into leptons with the result that nucleons would decay. The simplest of these grand unification theories, SU(5) [4], predicted a proton lifetime in the range 10²⁸ to 10³⁰ years and specified the decay modes. These predictions stimulated world-wide, dedicated searches for proton decay and led to the construction of the Frejus, IMB, Kamiokande, Kolar and NUSEX underground experiments during the 1980's. In its initial report in 1983, the largest of these detectors, IMB, set a lower limit on SU(5)'s dominant decay process (p→ e⁺ π⁰) at τ/ β = 6.5 ×10³¹yr, effectively ruling out the minimal theory. With additional data collected over the remainder of the decade, the lower limit on the lifetime was improved to 8.5 ×10³² yr.

Results obtained by LEP experiments provided high precision measurements of electroweak and strong coupling constants at the M_Z scale and allowed for more conclusive extrapolations to high energies in search of the unification scale. In a non-supersymmetric Standard Model with only one Higgs doublet, the convergence of coupling constants at a single point is excluded. With additional Higgs doublets, unification can be obtained. However, this unification is at a scale conflicting with the experimental limits on the proton lifetime. In the supersymmetric extension of SU(5) with a minimal Higgs sector of two doublets, a single convergence point is obtained by fitting both the unification scale M_GUT and the SUSY breaking scale M_SUSY. This in turn predicted a proton decay lifetime of τ/ β ∼ 10^{34 ±1.2} yr if the decay is dominated by gauge boson exchange. In many SUSY models, Higgs exchange interactions further reduced the proton lifetime. In unification models with dominant baryon violation amplitude generated by the Higgs exchange, the decay rates of p→ ―νK⁺ and n→ ―ν K⁰ would be dominant. For experimenters, those decay modes demand sensitivity to visible energies well below the 1 GeV typical of gauge boson mediated decay modes. Although strange particle production is strongly suppressed in the soft atmospheric neutrino spectrum, excellent topological and kinematic resolution (which allows kaon identification) is essential for background reduction.

These considerations suggested the possibility of observing proton decay with the operation of a larger, more sensitive, detector and were the primary motivation for construction of the Super-Kamiokande experiment in Japan. The search for nucleon decay requires massive detectors. A search with a sensitivity of 10³³ years requires a detector with approximately 10³³ nucleons. Since there are 6×10²⁹ nucleons per metric ton of material, this implies detectors of the multi-kiloton scale. The 50,000 kt Super-Kamiokande detector is the most recently constructed detector and began taking data in 1996. A summary of the limits currently established by Super-Kamiokande along with the limits obtained by other nucleon decay experiments is given in Table 3.1.

Background for nucleon decay arises from interactions of muons and neutrinos produced by cosmic-ray interactions in the upper atmosphere. By locating the detectors underground, experimenters can reduce cosmic-ray muons to a manageable level, but neutrino background is unavoidable. The vast majority of atmospheric neutrino interactions bear little resemblance to nucleon decay, but a small fraction are indistinguishable (based on topology and kinematic parameters) from the signal. Recently, data from a scaled down version of Super-Kamiokande installed in the neutrino beamline at KEK (K2K 1kton detector) has allowed a high-statistics study of these backgrounds in a controlled environment, and will permit a far more precise estimation of their incidence once fully analyzed. More sophisticated calculations of atmospheric neutrino production in the atmosphere, coupled with data on primary cosmic-ray fluxes (BESS) and secondary particle production (HARP and E907), will likewise refine our understanding of the atmospheric neutrino fluxes themselves in the near future.

While data from existing experiments have yet to reveal evidence for proton decay, it demonstrates that still more sensitive searches are possible. Recent papers by Babu, Pati, Wilczek [5] and others stress the significance of Super-Kamiokande's discovery of neutrino oscillations to the mechanisms for nucleon stability. Their work, based on an SUSY SO(10) framework, can describe the masses and mixings of all quarks and leptons. It predicts proton lifetimes in the range of 10³³ to 10³⁴ yrs, with ―ν K⁺ being the dominant decay mode, and suggests that an improvement in the current Super-Kamiokande sensitivity by a factor of five to ten might allow the observation of proton decay.

Grand unified theories continue to predict a broad range of possible proton lifetimes. There is evidence that our fundamental approach to unification is sound, and nucleon decay is one of the few accessible regimes where grand unified theories can be directly confronted with experimental data. Further progress toward detection of this unique process may be crucial to the future development of physics; this dictates that the search for evidence for nucleon decay be pursued with renewed vigor.

3.2  Theoretical Background and Motivation

3.2.1  Grand Unified Theories and Nucleon Decay

There has been great interest in searches for baryon number violation and proton decay after the development of grand unified theories (GUTs) in the early 1970's. These theories embed the standard model G_SM = SU(3) × SU(2) × U(1)_Y gauge group in a simple gauge group G_GUT. The Pati-Salam idea that lepton number could be considered as the fourth color was an early step in the direction of unification; an associated gauge group was SU(4) × SU(2) × SU(2) [6]. Considering fully unified models with simple embedding groups, since G_GUT ⊃ G_SM, it follows that the rank r(G_GUT) ≥ r(G_SM) = 4. Since r(SU(N))=N−1, it follows that in the SU(N) series of groups, a minimal GUT would be SU(5), and this was the first one to be studied, by Georgi and Glashow [4]. In this theory, the 15 Weyl fermions of a given generation fit nicely into a 10-dimensional second rank antisymmetric tensor representation ψ_L^αβ and a conjugate fundamental representation ψ^{c α}_L. Specifically, for the first generation, the ―5_L contains the d^c_L and (ν_e, e)_L^T, while the 10_L contains the (u,d)_L^T, u^c, and e^c. In terms of SU(3) × SU(2) SM representations, we have

5 = (3,1) + (1,2)

(3.1)

10 = (3,2) + ( - 3   ,1) + (1,1)

(3.2)

The model contains N²−1=24 gauge bosons in the adjoint representation. The decomposition relative to the SM is given by

24 = (8,1) + (1,3) + (1,1) + (3,2) + ( - 3   ,2)

(3.3)

Thus, of the 24 gauge bosons in SU(5), 12 are the gauge bosons of the standard model: 8 gluons, the W^±, Z, and γ. The other 12 consist of (X,Y) and (X^f,Y^f), where X and Y are color triplets with electric charges −4/3 and −1/3, respectively. The contributions to the anomaly in gauged currents cancel between the two fermion representations. The full SU(5) gauge symmetry must be broken at a high scale to that of the standard model. This is done via a Higgs field in the adjoint representation. The further breaking of the electroweak symmetry is done via an electroweak-doublet Higgs in the fundamental representation of SU(5).

A more complete, although less minimal, grand unification is achieved with the GUT group SO(10), with rank 5 [7]. Maximal subgroups of SO(10) include SU(5) × U(1) and SO(6) ×SO(4)  ∼ SU(4) ×SU(2) ×SU(2). It thus contains both the Georgi-Glashow SU(5) group and the Pati-Salam SU(4) ×SU(2) ×SU(2) (422) group. In terms of the decomposition with respect to SU(5) representations we have

16 = 10 + - 5   + 1

(3.4)

so that in addition to the known fermions of each generation, the model also contains a G_SM-singlet field, denoted χ_L^c, which is the conjugate of a χ_R with the quantum numbers of (an electroweak singlet) neutrino. The gauge boson sector is expanded relative to that of SU(5) and contains 45 fields.

In general, GUTs introduce a number of attractive features to particle physics:

• Because of the embedding of the standard model in a simple group, they predict the ratios of the three gauge couplings for the SU(3), SU(2), and U(1)_Y factor groups. As discussed below, the predictions of supersymmetric GUTs for this gauge coupling unification are in general agreement with the data.
They provide a simple and natural explanation of charge quantization, since the charge operator is a generator (equivalently, a linear combination of generators) of the Lie algebra associated with G_GUT.
They unify quarks and (anti)leptons, since these are placed together in irreducible representation(s) of the gauge group G_GUT. Indeed, as a consequence, they predict new interactions that transform quarks into antiquarks and into (anti)leptons, and these, in turn, lead to the decay of the proton and the (otherwise stable) bound neutron.
Because of the unification of quarks and leptons, these theories yield viable predictions for fermion mass relations and the Cabibbo-Kobayashi-Maskawa quark mixing matrix.
The SO(10) GUT incorporates an elegant seesaw mechanism [8] that yields naturally small neutrino masses of the generic form m_ν  ∼ m_D²/m_R, where m_D is a Dirac-type mass, related to the up-type quarks, and m_R is a mass associated with a bilinear consisting of electroweak-singlet neutrinos, of order the GUT scale. This yields values for neutrino masses that are consistent with the values suggested by current atmospheric and solar data.
The violation of B and L in these theories, together with effects of electroweak instantons at finite temperature, can provide a mechanism for baryogenesis and leptogenesis.
String theories are appealing candidates for theories of quantum gravity. Ideally, one hopes that it will be possible to deduce the structure of the quantum field theory below the string scale from this framework. While it is still an outstanding challenge to deduce the low-energy field theory from the underlying string theory, one can at least plausibly motivate the appearance of grand unified theories.

Specific appeals of SO(10) include the following:

• All of the the fermions in a given generation can be placed into a single irreducible representation, the 16-dimensional spinor representation of SO(10).
Rather than having the anomaly in gauged currents cancel between different fermion representations as in SU(5), the theory has the technical property of being ``safe'', i.e., free of any gauge anomaly, despite having complex representations [9].
The fermion mass predictions are more complete than in SU(5), involving not just the down-type quarks and charged leptons, but also the up-type quarks and neutrinos. In particular, one gets the seesaw mechanism for neutrino masses.
If one considers generalizing N_c from three and inquires under what conditions one can achieve minimal grand unification, with all of the fermions of a single generation fitting into a single representation, one is led to a GUT group SO(2(N_c+2)) and the condition [10]


2Nc+1 = 4(Nc+1)

(3.5)
The only solution of this condition is for N_c=3, which provides a deeper insight into why there are three colors.

In these theories, proton and bound neutron decay occurs via Feynman diagrams involving the exchange of X and Y gauge bosons in SU(5) and similar gauge bosons in SO(10). For example, in one such diagram, two u quarks in a proton combine to form a virtual X^f in the s-channel, which then produces a d^c e⁺ pair. The d^c binds with the spectator d in the proton to form an outgoing π⁰, thereby yielding the decay p →e⁺ π⁰. An example of another diagram contributing to this decay is a t-channel exchange in which a u emits a virtual X^f and changes into a u^c; the X^f is absorbed by a d quark, changing it to a e^c, and then the u^c combines with the spectator u to form a π⁰, thereby yielding the final state e⁺ π⁰. Higgs scalars can also contribute to proton and bound neutron decay.

As one moves below the mass scale M_GUT where the GUT gauge symmetry is spontaneously broken to the SM, one has three, rather than one, gauge couplings, and these run separately. Working back from the observed values of the electroweak couplings g₁ and g₂, or equivalently, sin²θ_W and α_em, in conjunction with the value of the strong coupling parameter α_s, early estimates suggested a unification point around 10¹⁴ GeV, which would then play the role of M_GUT. Based on this, estimates of the proton lifetime for minimal non-SUSY SU(5) were of order 10^{29 ±1.5} yrs. This prediction is long excluded by experiments. But supersymmetric GUTs brings a few complexion to proton decay as discussed below.

Although grand unified theories achieve a number of desirable theoretical goals, they bring with them some new problems. One is the gauge hierarchy problem, namely that the condition that the GUT scale is much larger than the electroweak scale, M_GUT >> M_ew, is unstable to radiative corrections. That is, considering the Higgs potential terms in the SM Lagrangian, V = μ²φ^f φ+ λ(φ^f φ)², one-loop radiative corrections would modify μ² →μ² + O(λM_GUT²). Thus, preserving μ << M_GUT would require extreme fine-tuning. One promising solution to this problem is supersymmetry which naturally suppresses the large radiative correction to Higgs mass, and this gave rise to the development of supersymmetric (SUSY) GUTs. Of course, supersymmetry is not observed at lower energies, and must be broken. However, the scale at which it is broken cannot be very much larger than the electroweak scale, M_ew  ∼ 250 GeV, or else the role of supersymmetry in protecting the Higgs sector against large radiative corrections would be lost. Current models hypothesize a SUSY breaking scale of several hundred GeV to a TeV. The proton would decay much too rapidly in such theories if one did not impose a certain discrete symmetry known as R-parity. This is defined to take the value R=1 for each of the usual fields, i.e., matter fermions, gauge bosons, and Higgs, and R=−1 for each of their superpartners, i.e., squarks, sleptons, gauginos, Higgsinos. Henceforth, we assume that this symmetry is imposed.

3.2.2  Predicted Nucleon Decay Rates

As the data from LEP and SLC, in conjunction with other data for sin²θ_W and α_s, have shown, in the minimal supersymmetic standard model (MSSM), the gauge couplings approximately unify, at a scale M_GUT  ∼ 10¹⁶ GeV, which thus characterizes a SUSY GUT [11]. (Here the MSSM contains the usual particle content of the SM with the addition of a second Higgs doublet whose hypercharge is opposite to that of the usual Higgs doublet, together with the addition of all of the corresponding superpartners.) In contrast, although early data in the 1970's was consistent with gauge coupling unification in nonsupersymmetric GUTs, the more accurate data obtained in the 1990's has shown that the gauge couplings fail to unify in such theories. In view of this, the role of SUSY in protecting the gauge hierarchy, and the fact that the first generation of dedicated proton decay searches ruled out nonsupersymmetric GUTs, we henceforth restrict our discussion to supersymmetric GUTs, for now. One can consider both SUSY SU(5) and SO(10), with the MSSM embedded in either. While the regular known fermion and gauge boson sectors of these theories, and hence also the full corresponding chiral and vector superfields, are fixed, the full set of Higgs chiral superfields varies from model to model. A general statement is that realistic SUSY GUTs contain at least a pair of color-triplet Higgs fields H_ic, i=1,2. (Even in nonsupersymmetric GUTs a color-triplet Higgs field was present, e.g., as the first three components of the 5 of Higgs in the original SU(5) model. Since it contributed at tree level to proton decay, its mass had to be be of order the GUT scale, and the huge splitting between this and the mass of the electroweak doublet Higgs forming the 4,5 components of the 5 of Higgs was known as the second hierarchy problem. Unlike the gauge hierarchy problem, which was solved with the hypothesis of supersymmetry, the second hierarchy problem, that of doublet-triplet Higgs mass splitting, remains even in SUSY GUTs and requires further devices for its solution.)

As noted above, the evidence for neutrino masses provides, via the seesaw mechanism, further support for SUSY SO(10). Examples of recent SO(10) models that fit Super-Kamiokande data on atmospheric and solar neutrinos include  [12,13,14].

In general, in grand unified theories, the lowest-dimension operator products that mediate nucleon decay contain a part of the form QQQ, coupled to a color singlet, to annihilate the three quarks in the nucleon. The fourth field is a lepton, so that the full Lorentz-invariant operator product is of the form QQQL. This is a dimension-six operator, and hence involves a c-number coefficient with dimensions of inverse mass squared. In conventional nonsupersymmetric GUTs, as discussed above, the exchange of the massive gauge bosons with propagators of the form 1/M_GUT² yield c-number coefficients for these operator products of the form α_GUT/m_GUT² in the amplitudes.

In SUSY GUT theories, there are two main contributions to proton decay. The dominant one arises from one-loop graphs involving the fermionic superpartners of the Higgs color triplets and the scalar superpartners of the fermions. Because the Higgs couplings to fermions are proportional to fermion masses, and the same couplings hold for the corresponding Higgsinos, it follows that the decays into higher-generation particles are preferred, subject to obvious constraints from phase space. Because the only GUT-scale mass in the diagram occurs on a fermion, rather than a boson, line, the amplitude involves only an external factor of 1/M_GUT rather than 1/M_GUT² as for the gauge boson-induced amplitude. For this reason, this type of operator is often called ``dimension-5'', although of course the actual operator is still the dimension-6 QQQL operator. The other factor with dimensions of inverse mass that multiples the QQQL operator in these types of theories is 1/m_SUSY, where m_SUSY is the SUSY breaking scale.

Recall that SUSY GUTs introduce two new features to proton decay: (i) First, by raising M_X to a higher value about 2×10¹⁶ GeV (contrast with the non-SUSY case of nearly 3×10¹⁴), they strongly suppress the gauge-boson-mediated d=6 proton decay operators, for which e⁺π⁰ would have been the dominant mode (for this case, one typically obtains: Γ⁻¹(p→e⁺π⁰)|_d=6 ∼ 10^35.3±1.5 yrs). (ii) Second, they generate d=5 proton decay operators [15] of the form Q_iQ_jQ_kL_l/M in the superpotential, through the exchange of color triplet Higgisinos, which are the GUT partners of standard Higgs(ino) doublets, such as those in the 5+―5 of SU(5) or 10 of SO(10). Assuming that a suitable doublet-triplet splitting mechanism provides heavy GUT-scale masses to these color triplets and at the same time light masses to the doublets, these ``standard'' dimension-5 operators, suppressed by just one power of the heavy mass and the small Yukawa couplings, are found to provide the dominant mechanism for proton decay in SUSY GUT  [16,17].

Now, owing to (a) Bose symmetry of the superfields in QQQL/M, (b) color antisymmetry, and especially (c) the hierarchical Yukawa couplings of the Higgs doublets, it turns out that these standard d=5 operators by themselves lead to dominant ―ν K⁺ and comparable ―νπ⁺ modes, but in all cases to highly suppressed e⁺π⁰, e⁺K⁰ and even μ⁺K⁰ modes.

It has recently been pointed out that in SUSY GUTs based on SO(10) or G(224)=SU(2) × SU(2) × SU(4) which assign heavy Majorana masses to the right-handed neutrinos, there exists a new set of color triplets, and thereby very likely a new source of d=5 proton decay operators [5], which are related to neutrino masses. In general, these new operators compete favorably with the standard ones. They can, however, lead to prominent μ⁺K⁰ modes, with ―ν K⁺ still being dominant. The color-triplet Higgsino-exchange leads to transitions of the type ~q~qq→―l. Supplemented by wino-exchange in a loop, they lead to transitions of the type qqq→ ―l, which in turn induce proton decay. The expression for the inverse rate of proton decay, induced via such a loop, is given by [14,18]

Γ−1(p→ ν   τ  K+) ≈ (4 ×1030yrs) ×(  0.67 As )2 [  0.014GeV3 βH ]2 [  1/6 m~w/m~q ]2[  m~q 1  TeV ]2 [  2×10−24 GeV−1 ^ A   ( ν   ) ]2

(3.6)

This is a general expression that applies to both SUSY SU(5) and SUSY SO(10). The model dependence enters through the entity ∧A(―ν), which denotes the strength of the d=5 operator, multiplied by the CKM mixing parameters that enter into the wino-vertices. Thus ∧A depends for example on the mass of the color triplet, on the SUSY-parameter tanβ and also on the way the different contributions to the amplitude interfere with each other. The entity β_H measures the matrix element of the three quark-operator between the proton and the vacuum state. Two early lattice gauge theory calculations of β_H are, in units of GeV³, 0.029(6) [19] and  ∼ 0.050 [20]. The recent lattice calculation in Ref. [21] yields the more precise accurate value β_h = 0.014(1) GeV³, which is used in (3.6). In order for SUSY to protect the Higgs sector from large radiative corrections, one normally would not take the SUSY breaking scale too much larger than the electroweak scale of v/√2 = 175 GeV; in eq. (3.6) we use 1 TeV. A similar estimate was obtained in Ref. [22] from a different SO(10) SUSY GUT.

It may also be noted that if one attributes the 2.6 σ discrepancy, a_{μ, exp.}−a_μ,thy = (4.3 ±1.6) ×10⁻⁹ between the recent measurement by a Brookhaven experiment of the anomalous magnetic moment of the μ⁺ [23] and the theoretical calculation supersymmetric contributions [24], one is led to infer that

4.3 ×10−9 = (1.4 ×10−9) ⎛ ⎝  100  GeV MSUSY ⎞ ⎠ 2   tanβ

(3.7)

where we recall that tanβ = v_u/v_d is the ratio of the vacuum expectation values of the two Higgs doublets in the MSSM. Thus, for example, for the illustrative value M_SUSY ≅ 400 GeV, one would have tanβ ≅ 50. (The LEP limit on the mass of the lightest Higgs in the MSSM also suggests independently that tanβ\mathrel [ > ||  ∼ ]4.) If one substituted these values into the proton decay rate, it would substantially shorten the lifetime (for large tanβ, the rate goes like tanβ²; the original estimate in (3.6) assumed a a value of tanβ of about 2-3.

The central value of Γ⁻¹=τ/B for p →―ν K⁺ in SUSY SO(10) models in eq. (3.6) is somewhat less than the current Super-Kamiokande limit of 1.6×10³³ years. (This difference would be rendered more severe if one were to substitute values such as the illustrative ones M_SUSY = 400 GeV and tanβ = 50 from fitting the discrepancy in the muon anomalous magnetic moment to SUSY.) In view of these estimates, one could argue that current Super-Kamiokande data disfavor the simplest SUSY GUTs. However, the idea of supersymmetric grand unification is sufficiently attractive that one would not like to give it up, and instead one concentrates on carefully examining possibilities that yield longer proton lifetimes. If one tries to make color triplet Higgs much heavier than the SUSY GUT scale, this produces large corrections to gauge coupling unification, although one can try to arrange further cancellations to maintain this coupling unification (e.g., [22]). However, as discussed in [14,18], what enters the calculation is an effective color triplet mass, which can be greater than the SUSY GUT scale without producing problems with gauge coupling unification. Moreover, one can entertain the possibility of having a simple group at the string scale break immediately to the SU(4) × SU(2) × SU(2) group, removing the problem with proton decay mediated by Higgs color triplets. Another alternative is denoted the ESSM (extended supersymmetric standard model) [18,25], and involves the addition of chiral superfields transforming as 16 and ―16 of SO(10); these are vectorlike as regards the standard model gauge group but have different charges under a string-motivated U(1)_A. Adding such complete SO(10)-multiplets would of course preserve gauge coupling unification. In this model the partial lifetime for p → ―ν K⁺ can be increased by factors of order 10² relative to the prediction (3.6) in usual SUSY SO(10). A similar increase in τ/B(p → ―ν K⁺) can be achieved in models in which a presumed underlying string theory yields the gauge group G(224) at a high scale instead of SO(10), which could still satisfy gauge coupling unification at the string scale. In this case the usual box diagrams involving colored triplet higgsinos would not occur, but the other class of contributions proportional to M_GUT⁻¹ in the amplitude would occur [18]. In these types of theories, τ/B(p → ―ν K⁺) could also be increased substantially relative to (3.6) and could also lead to prominent decays of the form p→ μ⁺ K⁰ with typical branching ratios of 10 to 50 %.

A rather different theoretical possibility is illustrated by models with a low scale of quantum gravity,  ∼ 10-100 TeV, and associated large extra dimensions [26]. Estimates for proton decay rates vary widely in these models.

Taking account of the range of SUSY GUTs and other theoretical possibilities, a rough estimate for an upper limit might be

Γ−1(p → - ν   K+) \mathrel <  ∼    1034  yrs

(3.8)

Concerning other proton decay modes, there is also, for example, p →μ⁺K⁰; typically this has a somewhat smaller, but still sizable, branching ratio, relative to p →―ν K⁺. Correspondingly, there are also the bound neutron decays n →―ν K⁰ and n →μ⁺ K⁻, again with comparable respective rates.

In addition to these favored decay modes, SUSY GUTs also lead to the same type of decays, such as p →e⁺ π⁰, as nonsupersymmetric GUTs. These have much smaller branching ratios than the favored modes. A typical estimate in an SO(10) SUSY GUT is [27]

Γ−1(p →e+ π0) ≅ 1 ×1035  yrs   ⎛ ⎝  0.015  GeV3 βh ⎞ ⎠ 2   ⎛ ⎝  MGUT 1016  GeV ⎞ ⎠ 4

(3.9)

where we have included the most uncertain factors. Since this decay mode is mediated by the GUT gauge bosons, its rate is much less model-dependent than the favored p → ―ν K⁺ decay mode, which depends on details of the SUSY GUT Higgs sector.

The current Super-Kamiokande limit on p → ―ν K⁺ partial lifetime is in the vicinity of the predicted upper limits from the simplest SUSY GUTs. Thus, if this appealing theoretical framework is correct, this decay mode should be clearly observed by UNO given its increased sensitivity. Furthermore the central values of the simplest SUSY predicted p →e⁺ π⁰ decay mode partial lifetimes are few times 10³⁴ to 10³⁵ within reach of UNO.

The increased sensitivity of UNO for the p →e⁺ π⁰ decay mode, which many consider the fundamental decay mode of proton, enhances its potential for a major discovery not only in the framework of SUSY GUTs but also in the framework of other variety of non SUSY GUT models. This provides a very strong motivation for the UNO project.

3.3  Current Experimental Results

The current and the past experimental searches for nucleon decays can be grouped into water Cherenkov detectors and calorimeters. The former is represented by IMB, Kamiokande and Super-Kamiokande and the latter by Soudan-2 and Fréjus. In particular, it is interesting to consider the strengths and weaknesses of the various detectors so that we can appreciate the challenges faced by the UNO detector.

3.3.1  Water Cherenkov Detectors

Ring imaging water Cherenkov detectors have searched for nucleon decay since the early 1980's when the IMB detector was constructed. This detector in combination with the Kamiokande detector in Kamioka, Japan pushed the limits on the partial lifetime in the various decay modes into charged particles to more than 10³² years. The most recently constructed and largest of these detectors is Super-Kamiokande, also located in Kamioka. This detector has been extremely successful and has pushed the limit for the partial lifetime of the proton by the p → e⁺ π⁰ mode to 5.0×10³³ yr.

The partial lifetime limits set by Super-Kamiokande for several possible decay modes are shown in Table 3.2 along with the recovery efficiency, the estimated background, and the number of candidates that have been found. No unambiguous evidence has been found for nucleon decay.

3.3.1.1  Search for p → e⁺π⁰

All of the final particles generated by a proton decay p → e⁺ π⁰ are all visible (an e⁺ and two γ's) in a water Cherenkov detector, so it is possible to reconstruct the proton mass. Further, all of the products are effectively massless and can be identified so the invariant mass of the proton can be reconstructed unambiguously.

Candidate p → e⁺ π⁰ events are selected from the sample of fully contained events. While several interactions can create events which may be confused with the p → e⁺ π⁰ signal, the dominant sources of background events are the atmospheric electron neutrino interactions where an electron (or positron) plus a single pion is produced (for instance ―ν_e + N → e⁺+N′+ π⁰). Even if there is no neutral pion produced, a charged pion may interact via charge exchange to become a neutral pion.

The contained event sample is reconstructed to find the event vertex, the number of rings, the particle type associated with each ring, and the momentum of each particle. A sample of p → e⁺ π⁰ candidates is selected by requiring (a) two or three Cherenkov rings which are (b) identified as electron-like, (c) in events with three reconstructed rings, the invariant mass of two rings must be consistent with the π⁰ mass (85 MeV/c² < m_π⁰ < 185 MeV/c²), (d) there must be no decay electron signals, (e) the total invariant mass must be consistent with the proton mass (800 MeV/c² < M_total < 1050 MeV/c²), and (f) the total momentum must be consistent with the Fermi momentum of a proton in an oxygen nucleus (P_total < 250 MeV/c).

Most of the background events have a total momentum far from zero while a proton decay candidate will have a momentum near zero. Excluding detector resolution effects, a proton decay candidate will have a total momentum less than the maximum Fermi momentum of a proton within an oxygen nucleus. Figure 3.1 shows the reconstructed total momentum and invariant mass distributions for samples of simulated p → e⁺ π⁰ candidates, simulated atmospheric neutrino background, and events from a 79.3 kt·yr exposure of Super-Kamiokande which have been selected by criteria (a)-(d). There are no candidate events. The events near the signal region are summarized in Figure 3.2. The invariant mass of events with a total momentum P_total < 250 MeV/c is shown on the left. The total momentum of events with an invariant mass consistent with proton decay is shown on the right. In both cases, the data is consistent with the expectation.

The efficiency and estimated background for this analysis are summarized in Table 3.2. Using the data corresponding to 79kt·yr Super-Kamiokande found no candidate while 0.2 background events were expected. This information is used to obtain a lower limit on the proton partial lifetime of 5×10³³ years at 90% C.L.

3.3.1.2  Search for p → ―ν K⁺

The momentum of the K⁺ from p → ―ν K⁺ is 340 MeV/c and is below the Cherenkov threshold in water. Fortunately, K⁺ production by atmospheric neutrinos is an extremely rare process and the existence of p → ―ν K⁺ can be inferred from the existence of a K⁺ signal where the K⁺ is in turn inferred by the decays into μ⁺ν_μ or π⁺π⁰. Further, the K⁺ has a small interaction probability in water, it exits the ¹⁶O 97% of time, and it is estimated that 90% of K⁺ decay at rest. Significantly, if a proton in the p_3/2 state of ¹⁶O decays, the ¹⁶O becomes an excited state of ¹⁵N nucleus which promptly decays to the ground state by emitting a 6.3 MeV γ with a 41% probability. This is extremely important since the γ ray occurs simultaneous with the proton decay, and the K⁺ has the lifetime of 12 ns. A requirement of a 6.3 MeV γ preceding the decay products from K⁺ makes it possible to eliminate the majority of the background events.

The Super-Kamokande experiment uses three methods to search for the p → ―ν K⁺ mode: (1) K⁺→ μ⁺ν_μ where the μ⁺ decays to e⁺ν_μ―ν_e, (2) with a 6.3 MeV prompt γ and (3) K⁺→π⁺π⁰ where the π⁰ decays to two γ's.

The first method makes use of the fact that the decay is two-body and the μ⁺ is mono-energetic with a momentum of 236 MeV/c. The selection criteria are that there is a μ-like ring whose momentum is between 215 and 260 MeV/c, no prompt gamma-ray signal exist, and a decay electron is found. These requirements substantially reduce the background, although a relatively large contamination of atmospheric neutrino events remains in the sample. The detection efficiency including the branching ratios is estimated to be 33%. Figure 3.3 shows the spectrum of muon momenta near the expected energy of muons from a K⁺ decay at rest. No significant excess above the background is observed. The limit is derived by fitting the shape of the spectrum to the expected atmospheric neutrino spectrum plus the spectrum expected from the decay of a K⁺. The limit from this method on the partial proton lifetime was found to be 4.4×10³² years at 90% C.L.

In the second method an additional requirement of a prompt γ preceding the μ signal is applied by requiring that between 8 and 59 PMT hits occur outside a 50^° cone around the muon ring in a sliding 12 ns window. The hits must occur between 0 ns and 120 ns prior to the muon signal. This additional requirement completely eliminates the background and no candidate is found. The expected background is 0.5 events. However, most of estimated background results from mis-reconstructed events. The reconstruction failure is understood and the background rejection will likely be improved in the near future. Figure 3.3 shows the distribution of the number of PMT hits found proceeding the muon signal. The atmospheric neutrino distribution extends well beyond a total of 8 PMT hits within the window. However, these events result from the misreconstruction of the primary particle in the event. The detection efficiency including the branching ratio is estimated to be 8.8%. The lower limit on the partial proton lifetime is thus obtained to be 1.0×10³³ years at 90% C.L.

Unlike the first two methods the third method uses the K⁺ decay to π⁺π⁰ where π⁺ and π⁰ both carry approximately 205 MeV/c in the opposite directions. While the π⁰ is identified from the existence of two γs which are used to reconstruct π⁰ mass, the π⁺ is barely above the Cherenkov threshold and is reconstructed with very low efficiency. To maximize the p → ―ν K⁺ reconstruction efficiency, the reconstruction of the π⁺ is not required. Instead, the charge in a 50^° cone opposite the π⁰ direction is summed (referred to as the backward charge, Q_back) and must be consistent with the expectation for a π⁺ near threshold. The selection criteria for this decay mode are: (i) two e-like rings, (ii) one decay electron, (iii) 85 MeV/c² < m_γγ < 185 MeV/c², (iv) 175 MeV/c < P_γγ < 250 MeV/c, and (v) 40 p.e. < Q_b < 100 p.e.

Figure 3.4 shows the distribution of the backward charge versus the reconstructed invariant mass of the e-like rings. The left plots show the expectation for the atmospheric neutrino background and the possible p → ―ν K⁺ signal. The right plot shows the distribution found during a 79.3 kt·yr exposure. After all cuts one event survives while 1.7 background events are expected. The detection efficiency including the branching ratios is estimated to be 6.8%, and the lower limit on the partial proton lifetime is found to be 5.9×10³² years.

The three independent methods just discribed can be combined to set a total lower limit on the proton partial lifetime. The combined limit is 1.6×10³³ years using the data corresponding to an exposure of 79.3kt·yr.

3.3.2  Tracking Calorimeters

The detection capabilities for nucleon decay which have been demonstrated by water Cherenkov experiments, especially for resolving two-body decays in a large mass of monitored medium, are difficult to match using other techniques. However there are some decay channels for which the information provided by Cherenkov detection seems less than optimal. These channels involve higher multiplicities of track and shower prongs in the final state, and/or charged particles which are non-relativistic and hence are invisible to a Cherenkov experiment. Multiprong nucleon decays which have various degrees of these attributes are among the modes favored by supersymmetric (SUSY) grand unification theories (GUTs), e.g. p → μ⁺ K⁰, K⁰ → π⁺ π⁻. Motivated in part by these considerations, development of fine-grained tracking calorimeters for nucleon decay has proceeded in parallel with development of the water Cherenkov technique as an alternative experimental approach [28].

Tracking calorimeters used in non-accelerator experiments are ionization sensitive devices which are generally dense since they use iron or liquid argon as the monitored mass. The various calorimeters deployed underground differ in the method used for observing ionization and in the granularity of the sampling. The generic design goal for tracking calorimeters is to achieve bubble-chamber-like imaging for vertices and for non-relativistic as well as relativistic charged particles. In pursuit of this goal, detector geometries of iron plate calorimeters have evolved over the years from planar layered configurations, e.g. NUSEX and Fréjus, to the honeycomb lattice geometry utilized by Soudan 2. In the latter detector a spatial resolution of about 1 cm has been realized, and ionizing particles are imaged with dE/dx sampling thereby allowing proton tracks to be distinguished from charged pion and muon tracks. In general, tracking calorimeter detectors can provide relatively uniform detection efficiencies for a wide variety of nucleon decay channels, making them well-suited to branching ratio measurements in the case that signals are observed.

It has been demonstrated with prototype liquid argon time projection chambers (TPC) developed for the ICARUS project, that performance characteristics of underground calorimeters can be substantially improved. Indeed, a spatial resolution of  ∼  3 mm with ionization dE/dx sampling is feasible with this approach. However, the extent to which performance and costing for such devices can be scaled to multi-kiloton detectors remains to be seen [29].

An oft-cited ``advantage'' attributed to fine-grained calorimeters is that discovery of nucleon decay is made possible with the observation of one or few well-imaged events. Unfortunately this advantage entails substantial cost; in all calorimeter experiments to date, fine granularity has been achieved by trading off monitored mass, thereby limiting the decay lifetime reach of the experiments. As it has turned out, there appears to be no nucleon decay signal at lifetimes below the maximum reach of deployed calorimeters ( ∼ 2 ×10³² years), and so these experiments have not been able to capitalize on high resolution imaging of individual events. Contrastingly, the water Cherenkov technique has proven readily extendable to higher fiducial masses while being remarkably amenable to refinements in light collection and in search strategies. The result is that no tracking calorimeter to date has approached the nucleon decay search capability realized by the Super-Kamiokande experiment. The current situation is made clear by the relatively modest lifetime limits reported by calorimeter experiments; examples are given below. For the foreseeable future, the only plausible calorimeter alternative to water Cherenkov detectors lies with ICARUS-type liquid argon TPCs.

3.3.2.1  Searches for ―νK⁺, l⁺K⁰, and ―νK⁰ modes

Supersymmetric grand unification models introduce new processes involving SUSY particle loops for nucleon decay amplitudes. Nucleon decay diagrams of this type give integrals which vanish unless the transitions involve intergenerational mixing. Consequently final states containing strange mesons are predicted; in particular, two-body (B−L) conserving decays involving strangeness +1  K⁺ or K⁰ mesons are expected to be prominent.

Of keen interest to SUSY GUTs models is the mode p → ―ν K⁺, for which a number of detailed lifetime calculations have been published. In Soudan 2, a search was carried out using a 3.56 fiducial kiloton year (kt·yr) exposure. The search utilized the visibility of the K⁺ in the calorimeter together with the visibility of the decay electron from a stopped μ⁺ (K⁺ → μ⁺ ν, μ⁺ → e⁺ ν―ν) to minimize background from atmospheric neutrino interactions. Two K⁺ decay channels were investigated: K⁺ → μ⁺ ν and K⁺ → π⁺ π⁰. One marginal candidate event was observed with total background estimated to be 1.54 events. The combined lower lifetime limit at 90% CL without (with) background subtraction is 4.3(4.6) ×10³¹ years [30].

Searches for nucleon decay into two-body modes involving K⁰ mesons have been carried out by Soudan 2 using a 4.41 fiducial kt·yr exposure. Channels investigated included proton decay into μ⁺ K⁰ and e⁺ K⁰ with K⁰ → K⁰_s or K⁰_l, and neutron decay into ν K⁰_s. Event selection criteria were developed by studying Monte Carlo samples of nucleon decay and atmospheric neutrino events. These simulations included the full detector response and were processed in conjunction with data events.

For these final states, the distributions of event invariant mass and of magnitude of net three-momentum are approximately Gaussian. Consequently the density distribution of points on the invariant mass versus net momentum plane can be represented by a bi-variate Gaussian probability distribution function. Projections of this bi-variate Gaussian surfaces onto the M_inv versus |→P_net| plane enable kinematic selections to be defined in an optimal way. Figure 3.5a shows the kinematic selection contour in the M_inv versus |→P_net| plane which was used for p → l⁺ K⁰_s searches in four separate channels.

Backgrounds from neutrinos and from cosmic ray interactions in the cavern rock distribute diffusely with respect to the search region as shown in Figs 3.5b,c. Only three data events satisfy this kinematic selection (Figure. 3.5d); one of the data events is shown in Figure. 3.6.

No evidence for a nucleon decay signal was observed; the lifetime lower limits reported by Soudan 2 at 90% CL are summarized in Table 3.3 [31].