Prog. Theor. Exp. Phys. 2018, 063C01 (65 pages)
DOI: 10.1093/ptep/pty044

Physics potentials with the second
Hyper-Kamiokande detector in Korea
The Hyper-Kamiokande Proto-Collaboration
K. Abe1,2 , Ke. Abe3 , S. H. Ahn†,4 , H. Aihara2,5 , A. Aimi6 , R. Akutsu7 , C. Andreopoulos8,9 ,I. Anghel10 , L. H. V. Anthony8 , M. Antonova11 , Y. Ashida12 , V. Aushev13 , M. Barbi14 ,G. J. Barker15 , G. Barr16 , P. Beltrame17 , V. Berardi18 , M. Bergevin19 , S. Berkman20 ,L. Berns21 , T. Berry22 , S. Bhadra23 , F. d. M. Blaszczyk24 , A. Blondel25 , S. Bolognesi26 ,S. B. Boyd15 , A. Bravar25 , C. Bronner2 , M. Buizza Avanzini27 , F. S. Cafagna18 , R.
Calland2 , S. Cao28 , S. L. Cartwright29 , M. G. Catanesi18 , C. Checchia6 , Z. Chen-Wishart22 ,B. G. Cheon†,30 , M. K. Cheoun†,31 , K. Cho†,32 , J. H. Choi33 , K. Choi34 , K. Y. Choi†,35 ,E. J. Chun†,36 , A. Cole29 , J. Coleman8 , G. Collazuol6 , G. Cowan17 , L. Cremonesi37 ,T. Dealtry38 , G. De Rosa39 , C. Densham9 , D. Dewhurst16 , E. Drakopoulou17 , F. Di Lodovico37 ,O. Drapier27 , J. Dumarchez40 , P. Dunne41 , M. Dziewiecki42 , S. Emery26 , A. Esmaili43 ,A. Evangelisti39 , E. Fernández-Martinez44,79 , T. Feusels20 , A. Finch38 , G. A. Fiorentini23 ,G. Fiorillo39 , M. Fitton9 , K. Frankiewicz45 , M. Friend28 , Y. Fujii28 , Y. Fukuda46 , D. Fukuda47 ,K. Ganezer48 , M. Ghosh†,49 , C. Giganti40 , M. Gonin27 , N. Grant15 , P. Gumplinger50 ,D. R. Hadley15 , B. Hartﬁel48 , M. Hartz2,50 , Y. Hayato1,2 , K. Hayrapetyan37 , J. Hill48 ,S. Hirota12 , S. Horiuchi51 , A. K. Ichikawa12 , T. Iijima52,53 , M. Ikeda1 , J. Imber27 , K. Inoue54,2 ,J. Insler55 , R. A. Intonti18 , A. Ioannisian56 , T. Ishida28 , H. Ishino47 , M. Ishitsuka57 ,Y. Itow53,58 , K. Iwamoto5 , A. Izmaylov11 , B. Jamieson59 , H. I. Jang60 , J. S. Jang61 ,S. H. Jeon35 , K. S. Jeong†,62 , M. Jiang12 , P. Jonsson41 , K. K. Joo63 , A. Kaboth9,22 ,C. Kachulis24 , T. Kajita7,2 , S. K. Kang†,64 , J. Kameda1,2 , Y. Kataoka5 , T. Katori37 ,K. Kayrapetyan37 , E. Kearns24,2 , M. Khabibullin11 , A. Khotjantsev11 , C. S. Kim†,65 ,H. B. Kim†,30 , H. J. Kim†,66 , J. H. Kim35 , J.-S. Kim†,4 , J. Y. Kim63 , S. B. Kim67 , S. C. Kim†,4,68 ,S.-W. Kim†,4,68 , S. Y. Kim67 , T. J. Kim†,30 , W. Kim†,66 , S. King37 , Y. Kishimoto1,2 , P. Ko†,36 ,T. Kobayashi28 , M. Koga54,2 , A. Konaka50 , L. L. Kormos38 , Y. Koshio47,2 , A. Korzenev25 ,K. L. Kowalik45 , W. R. Kropp69 , Y. Kudenko11,70,71 , R. Kurjata42 , T. Kutter55 , M. Kuze21 ,K. Kwak†,72 , E. H. Kwon†,67 , L. Labarga44 , J. Lagoda45 , P. J. J. Lasorak37 , M. Laveder6 ,M. Lawe38 , J. G. Learned34 , C. H. Lee†,62 , S. J. Lee†,73 , W. J. Lee†,67 , I. T. Lim63 ,T. Lindner50 , R. P. Litchﬁeld41 , A. Longhin6 , P. Loverre74 , T. Lou5 , L. Ludovici74 , W. Ma41 ,L. Magaletti18 , K. Mahn75 , M. Malek29 , L. Maret25 , C. Mariani51 , K. Martens2 , Ll. Marti1 ,J. F. Martin76 , J. Marzec42 , S. Matsuno34 , E. Mazzucato26 , M. McCarthy23 , N. McCauley8 ,K. S. McFarland77 , C. McGrew78 , A. Mefodiev11 , P. Mermod25 , C. Metelko8 , M. Mezzetto6 ,J. Migenda29 , P. Mijakowski45 , H. Minakata7,79 , A. Minamino80 , S. Mine69 , O. Mineev11 ,A. Mitra15 , M. Miura1,2 , T. Mochizuki1 , J. Monroe22 , C. S. Moon†,66 , D. H. Moon63 ,S. Moriyama1,2 , T. Mueller27 , F. Muheim17 , K. Murase81 , F. Muto52 , M. Nakahata1,2 ,Y. Nakajima1 , K. Nakamura28,2 , T. Nakaya12,2 , S. Nakayama1,2 , C. Nantais76 , M. Needham17 ,T. Nicholls9 , Y. Nishimura7 , E. Noah25 , F. Nova9 , J. Nowak38 , H. Nunokawa43 , Y. Obayashi2 ,Y. D. Oh†,66 , Y. Oh†,66 , H. M. O’Keeffe38 , Y. Okajima21 , K. Okumura7,2 , Yu. Onishchuk13 ,E. O’Sullivan82 , L. O’Sullivan29 , T. Ovsiannikova11 , R. A. Owen37 , Y. Oyama28 , J. Pérez44 ,M. Y. Pac33 , V. Palladino39 , J. L. Palomino78 , V. Paolone83 , H. S. Park†,4 , J. C. Park†,84 ,M. G. Park†,85 , S. C. Park†,65 , W. Parker22 , S. Parsa25 , D. Payne8 , J. D. Perkin29 , C. Pidcott29 ,†Author as part of the Korean Neutrino Observatory (KNO) interest group.

© The Author(s) 2018. Published by Oxford University Press on behalf of the Physical Society of Japan.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),
which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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E. Pinzon Guerra23 , S. Playfer17 , B. Popov40 , M. Posiadala-Zezula86 , J.-M. Poutissou50 ,A. Pritchard8 , N. W. Prouse37 , G. Pronost1 , P. Przewlocki45 , B. Quilain12 , M. Quinto18 ,E. Radicioni18 , P. N. Ratoff38 , F. Retiere50 , C. Riccio39 , B. Richards37 , E. Rondio45 , H. J. Rose8 ,C. Rott35 , S. D. Rountree51 , A. C. Ruggeri39 , A. Rychter42 , D. Ryu†,72 , R. Sacco37 , M. Sakuda47 ,M. C. Sanchez10 , E. Scantamburlo25 , M. Scott50 , S. Molina Sedgwick37 , Y. Seiya87 , T. Sekiguchi28 ,H. Sekiya1,2 , H. Seo†,67 , S. H. Seo∗,67 , D. Sgalaberna25 , R. Shah16 , A. Shaikhiev11 , I. Shimizu54 ,M. Shiozawa1,2 , Y. Shitov41,22 , S. Short37 , C. Simpson16,2 , G. Sinnis88 , M. B. Smy69,2 ,S. Snow15 , J. Sobczyk89 , H. W. Sobel69,2 , D. C. Son†,66 , Y. Sonoda1 , R. Spina18 , T. Stewart9 ,J. L. Stone24,2 , Y. Suda5 , Y. Suwa90 , Y. Suzuki2 , A. T. Suzuki3 , R. Svoboda19 , M. Taani17,52 ,R. Tacik14 , A. Takeda1 , A. Takenaka1 , A. Taketa91 , Y. Takeuchi3,2 , V. Takhistov69 , H. A. Tanaka76 ,H. K. M. Tanaka91 , H. Tanaka1,2 , R. Terri37 , M. Thiesse29 , L. F. Thompson29 , M. Thorpe9 ,S. Tobayama20 , C. Touramanis8 , T. Towstego76 , T. Tsukamoto28 , K. M. Tsui7 , M. Tzanov55 ,Y. Uchida41 , M. R. Vagins69,2 , G. Vasseur26 , C. Vilela78 , R. B. Vogelaar51 , J. Walding22 , J. Walker59 ,M. Ward9 , D. Wark16,9 , M. O. Wascko41 , A. Weber9 , R. Wendell12,2 , R. J. Wilkes92 , M. J. Wilking78 ,J. R. Wilson37 , E. Won†,73 , T. Xin10 , K. Yamamoto87 , C. Yanagisawa78 , T. Yano3 , O. Yasuda†,49 ,S. Yen50 , N. Yershov11 , D. N. Yeum67 , M. Yokoyama2,5 , H. D. Yoo†,67 , J. Yoo†,93 , S. C. Yoon†,67 ,T. S.Yoon†,85 , T.Yoshida21 , I.Yu35 , M.Yu23 , J. Zalipska45 , K. Zaremba42 , M. Ziembicki42 , M. Zito26
and S. Zsoldos37
1

University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe (WPI), Todai Institutes
for Advanced Study, Kashiwa, Chiba, Japan
3
Kobe University, Department of Physics, Kobe, Japan
4
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
5
University of Tokyo, Department of Physics, Tokyo, Japan
6
INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy
7
University of Tokyo, Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, Kashiwa,
Japan
8
University of Liverpool, Department of Physics, Liverpool, United Kingdom
9STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United
Kingdom
10
Iowa State University, Department of Physics and Astronomy, Ames, Iowa, U.S.A.
11
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
12
Kyoto University, Department of Physics, Kyoto, Japan
13
Kyiv National University, Department of Nuclear Physics, Kyiv, Ukraine
14
University of Regina, Department of Physics, Regina, Saskatchewan, Canada
15
University of Warwick, Department of Physics, Coventry, United Kingdom
16
Oxford University, Department of Physics, Oxford, United Kingdom
17
University of Edinburgh, School of Physics and Astronomy, Edinburgh, United Kingdom
18
INFN Sezione di Bari and Università e Politecnico di Bari, Dipartimento Interuniversitario di Fisica, Bari,
Italy
19
University of California, Davis, Department of Physics, Davis, California, U.S.A.
20
University of British Columbia, Department of Physics and Astronomy,Vancouver, British Columbia, Canada
21
Tokyo Institute of Technology, Department of Physics, Tokyo, Japan
22
Royal Holloway University of London, Department of Physics, Egham, Surrey, United Kingdom
23
York University, Department of Physics and Astronomy, Toronto, Ontario, Canada
24
Boston University, Department of Physics, Boston, Massachusetts, U.S.A.
25
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
26
IRFU, CEA Saclay, Gif-sur-Yvette, France
27
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
28
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
29
University of Shefﬁeld, Department of Physics and Astronomy, Shefﬁeld, United Kingdom
30
Hanyang University, Department of Physics, Seoul 04763, Korea
2

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31

Soongsil University, Origin of Matter and Evolution of Galaxy (OMEG) Institute and Department of Physics,
Seoul 156-743, Korea
32
Korea Institute of Science and Technology Information, Daejeon 34141, Korea
33
Dongshin University, Department of Physics, Naju, Korea
34
University of Hawaii, Department of Physics and Astronomy, Honolulu, Hawaii, U.S.A.
35
Sungkyunkwan University, Department of Physics,Suwon 16419, Korea
36
Korean Institute for Advanced Studies, Seoul, Korea
37
Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom
38
Lancaster University, Physics Department, Lancaster, United Kingdom
39
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy
40
Laboratoire de Physique Nucleaire et de Hautes Energies, UPMC and Universite Paris-Diderot and
CNRS/IN2P3, Paris, France
41
Imperial College London, Department of Physics, London, United Kingdom
42
Warsaw University of Technology, Institute of Radioelectronics and Multimedia Technology, Warsaw, Poland
43
Pontifícia Universidade Católica do Rio de Janeiro, Departamento de Física, Rio de Janeiro, Brazil
44
University Autonoma Madrid, Department of Theoretical Physics, Madrid, Spain45
National Centre for Nuclear Research, Warsaw, Poland
46
Miyagi University of Education, Department of Physics, Sendai, Japan
47
Okayama University, Department of Physics, Okayama, Japan
48
California State University, Department of Physics, Carson, California, U.S.A.
49
Tokyo Metropolitan University, Department of Physics, Tokyo, Japan
50
TRIUMF, Vancouver, British Columbia, Canada
51
Virginia Tech, Center for Neutrino Physics, Blacksburg, Virginia, U.S.A.
52
Nagoya University, Graduate School of Science, Nagoya, Japan
53
Nagoya University, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya, Japan
54
Research Center for Neutrino Science, Tohoku University, Sendai, Japan
55
Louisiana State University, Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.
56
Yerevan Institute for Theoretical Physics and Modeling, Halabian Str. 34; Yerevan 0036, Armenia
57
Tokyo University of Science, Department of Physics, Chiba, Japan58
Nagoya University, Solar-Terrestrial Environment Laboratory, Nagoya, Japan
59
University of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada
60
Seoyeong University, Department of Fire Safety, Gwangju, Korea
61
GIST College, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
62
Pusan National University, Department of Physics, Busan 46241, Korea
63
Chonnam National University, Department of Physics, Gwangju, Korea
64
Seoul National University of Science and Technology, School of Liberal Arts, Seoul 01811, Korea
65
Yonsei University, Department of Physics and IPAP, Seoul 03722, Korea
66
Kyungpook National University, Department of Physics, Daegu 41566, Korea
67
Seoul National University, Department of Physics and Astronomy, Seoul 08826, Korea
68
Korea University of Science and Technology, Daejeon 34113, Korea
69
University of California, Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.
70
National Research Nuclear University (MEPhI), Moscow, Russia
71
Moscow Institute of Physics and Technology, Moscow region, Russia
72
UNIST, Department of Physics, Ulsan, Korea
73
Korea University, Department of Physics, Seoul 02841, Korea
74
INFN Sezione di Roma, Roma, Italy
75
Michigan State University, Department of Physics and Astronomy, East Lansing, Michigan, U.S.A.
76
University of Toronto, Department of Physics, Toronto, Ontario, Canada
77
University of Rochester, Department of Physics and Astronomy, Rochester, New York, U.S.A.
78
State University of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New York,U.S.A.
79
Instituto de Física Teórica, UAM/CSIC, Madrid, Spain
80
Yokohama National University, Faculty of Engineering, Yokohama, Japan81
Pennsylvania State University, Department of Physics, University Park, PA 16802, U.S.A.
82
Stockholm University, Oskar Klein Centre and Department of Physics, Stockholm, Sweden
83
University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, Pennsylvania, U.S.A.
84
Chungnam National University, Department of Physics, Daejeon 34134, Korea
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Kyungpook National University, Department of Astronomy and Atmospheric Sciences, Daegu 41566, Korea
University of Warsaw, Faculty of Physics, Warsaw, Poland
87
Osaka City University, Department of Physics, Osaka, Japan88
Los Alamos National Laboratory, New Mexico, U.S.A.
89
Wroclaw University, Faculty of Physics and Astronomy, Wroclaw, Poland
90
Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto, Japan
91
University of Tokyo, Earthquake Research Institute, Tokyo, Japan
92
University of Washington, Department of Physics, Seattle, Washington, U.S.A.
93
Korea Advanced Institute of Science and Technology (KAIST), Department of Physics, Daejeon 34141, Korea∗
E-mail: sunny.seo@snu.ac.kr
86

Received February 7, 2018; Accepted March 16, 2018; Published June 20, 2018...................................................................................................................
Hyper-Kamiokande consists of two identical water-Cherenkov detectors of total 520 kt, with theﬁrst one in Japan at 295 km from the J-PARC neutrino beam with 2.5◦ off-axis angles (OAAs),
and the second one possibly in Korea at a later stage. Having the second detector in Korea would
beneﬁt almost all areas of neutrino oscillation physics, mainly due to longer baselines. There areseveral candidate sites in Korea with baselines of 1000–1300 km and OAAs of 1◦ –3◦ .
We conducted sensitivity studies on neutrino oscillation physics for a second detector, either
in Japan (JD × 2) or Korea (JD + KD), and compared the results with a single detector in Japan.
Leptonic charge–parity (CP) symmetry violation sensitivity is improved, especially when the
CP is non-maximally violated. The larger matter effect at Korean candidate sites signiﬁcantly
enhances sensitivities to non-standard interactions of neutrinos and mass ordering determination.
Current studies indicate the best sensitivity is obtained at Mt. Bisul (1088 km baseline, 1.3◦
OAA). Thanks to a larger (1000 m) overburden than the ﬁrst detector site, clear improvements
to sensitivities for solar and supernova relic neutrino searches are expected.
...................................................................................................................
Subject Index

1.

C03, C04, C12, C32, C43

Introduction

The proposed Hyper-Kamiokande (Hyper-K or HK) experiment [1] builds upon the highly successful
Super-Kamiokande (Super-K or SK) detector [2] by constructing two large water-Cherenkov detectors with 16.8 times the ﬁducial volume of SK to pursue a rich program of neutrino (astro)physics
and proton decay. The Hyper-K design proposes the construction of two identical detectors in stages
with 187 kt (ﬁducial mass) per detector. The ﬁrst one will be constructed near the current Super-K
site, 295 km away and 2.5◦ off-axis from the J-PARC neutrino beam used by the T2K experiment.
The second one is currently under consideration to be built in Korea where the J-PARC neutrino
beam is still reachable. The long-baseline neutrino program observing the J-PARC neutrino beamat Hyper-K aims for a deﬁnitive observation of CP violation (CPV) in neutrino oscillations, that
may result from an irreducible phase δCP in the neutrino mixing matrix. Hyper-K will make precise
measurements of δCP and other oscillation parameters, such as θ23 and m232 , and will have sufﬁcient statistics to make “shape” tests of the three-ﬂavor mixing paradigm. These measurements arevaluable in elucidating the new physics responsible for neutrino mass and mixing and its potential
connections to leptogenesis in the early universe.
Placing the second detector in Korea rather than in Japan will enhance physics sensitivities toalmost all searches and measurements. In the case of proton decay it would not matter where thesecond detector is located since the improvement primarily depends on the detector mass. In othercases—particularly neutrino oscillation measurements using the J-PARC beam—the location of thedetector is a signiﬁcant factor in determining the expected beneﬁts. In this document, we explore thepossibility of placing the second detector in Korea at a baseline of 1000–1300 km; we will refer to
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Fig. 1. Map showing the baseline and off-axis angle of the J-PARC beam in Japan and Korea [8,9].

this as T2HKK in contrast to one detector in Kamioka with 295 km baseline (T2HK). The second
detector in Korea provides the opportunity for Hyper-K to probe oscillation physics at both the ﬁrst
and second oscillation maxima.
South Korea covers a range of angles from the axis of the J-PARC neutrino beam from 1◦ to 3◦(see Fig. 1), which allows for tuning both the baseline and neutrino energy spectrum to maximize thephysics reach of the combined two-baseline experiment. Such a conﬁguration can improve neutrino
oscillation physics sensitivities in Hyper-K in a number of ways: it can break degeneracies related
to the unknown mass ordering, the mixing parameter θ23 , and the CP-violating phase δCP ; it has
better precision (especially on δCP ) in important regions of the parameter space; and it can serve
to mutually reduce the impact of systematic uncertainties (both known and unknown) across allmeasurements. It also provides an opportunity to test the preferred oscillation model in a regime notprobed with existing experiments. Constraints on (or evidence of) exotic neutrino models, such as
non-standard interactions with matter, are also expected to be signiﬁcantly enhanced by the use of alonger baseline conﬁguration for a second detector.
Although the use of a longer baseline in conjunction with the J-PARC beam is the primary feature
distinguishing the use of a detector in Korea from a second detector at Kamioka, there are several
mountains over 1 km in height that could provide suitable sites. This allows for greater overburden
than the site selected for the ﬁrst Hyper-K detector and would enhance the program of low-energy
physics that are impacted by cosmic-ray backgrounds. This includes solar neutrinos, supernova relicneutrinos, dark matter neutrino detection studies, and neutrino geophysics. In the case of supernova
neutrinos there is some beneﬁt from the separation of detector locations.
Further enhancements are possible but not considered in this document. Recent developments ingadolinium doping of water and water-based liquid scintillators could allow for a program based onreactor neutrinos if these technologies are deployed in the detector.
There were earlier studies of a large water-Cherenkov detector in Korea using a J-PARC-based
neutrino beam [3,4]. Originally, an idea for a two-baseline experiment with a second detector in
Korea was discussed by several authors, pointing out possible improvements for measurements of
CP violation and mass hierarchy [5–9]. Three international workshops were held in Korea and Japan
in 2005, 2006, and 2007 [10]. At the time, the mixing angle of θ13 was not yet known, and therefore
the required detector size and mass could not be determined. Now, more realistic studies and a
detector design are possible due to the precisely measured value of θ13 [11–15,17–19].
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2. The Hyper-Kamiokande experiment and the extension to Korea
In this section we present a summary of the proposed Hyper-Kamiokande experiment, with particularreference to the long-baseline neutrino oscillation physics program using the J-PARC neutrino beam.
We then consider the simplest addition of an identical second detector in Korea to this conﬁguration,
focusing on practical considerations such as site selection. The physics case for a Korean detector
and studies of the experiment’s capability with different conﬁgurations are then considered.

2.1.

J-PARC neutrino beam

The neutrino beam for Hyper-K is produced at J-PARC (Japan Proton Accelerator Research Complex), located in Tokai Village, Ibaraki prefecture on the east coast of Japan, which is 295 km fromthe Kamioka detector sites. The 30 GeV (kinetic energy) proton beam is extracted from the J-PARC
main ring (MR) by single-turn fast extraction and transported to the production target after being
deﬂected about 90◦ by 28 superconducting combined-function magnets to direct the beam toward
Kamioka. The beam pulse consists of eight bunches spaced 581 ns apart to give a pulse of duration
4.2 μs. As of 2017, the repetition period of the pulses is 2.48 s. The production target is a graphiterod 26 mm in diameter and 90 cm long (corresponding to two interaction lengths). About 80% of theincoming protons interact in the target. The secondary pions (and kaons) from the target are focusedby three consecutive electromagnetic horns operated by a 250 kA pulsed current. It is expected thatby the time of Hyper-K, the horn currents will be increased to 320 kA. The focused pions and kaons
enter a decay volume (DV) of length 96 m ﬁlled with helium gas, and decay in ﬂight into neutrinos
and charged leptons. The beam dump, which consists of graphite blocks of about 3.15 m thickness
followed by iron plates of 2.5 m total thickness, is placed at the end of the DV to absorb remnant
hadrons. Muon monitors (MUMONs) are placed just behind the beam dump to monitor on a spill-byspill basis the intensity and the proﬁle of muons with initial energy over 5 GeV which pass throughthe beam dump.
T2K adopted the ﬁrst ever off-axis scheme to produce a narrow energy neutrino spectrum centeredon the oscillation maximum to maximize the physics sensitivity. The J-PARC beam is aligned toprovide a 2.5◦ degree off-axis beam to the Super-Kamiokande detector.
As of summer 2017, stable operation of the MR at 470 kW beam power has been achieved. The
design power of the J-PARC main ring will be realized through the upgrade of the magnet power
supplies, RF core, and other components. These upgrades will increase the repetition rate of the beamfrom 0.40 Hz to 0.77 Hz. Preparation for the upgrade has begun, and the upgrade may be completed as
early as 2019. Further beam power increases will require upgrades to secondary beamline components
such as the beam window, target, and horns. Upgrades primarily to the RF power supply will gradually
increase the number of protons per pulse (ppp) and repetition rate further to 3.3 × 1014 p and 1/1.16 s,
respectively, to reach > 1.3 MW by around 2025 before Hyper-K becomes operational.

2.2.

Hyper-Kamiokande tank conﬁguration

The Hyper-K experiment employs a ring-imaging water-Cherenkov detector technique to detect rareinteractions of neutrinos and the possible spontaneous decay of protons and bound neutrons. The
baseline conﬁguration of the experiment consists of a single cylindrical tank built in the Tochibora
mine at a baseline of 295 km from the J-PARC neutrino source.
A full overview of the cavern and detector design research and development, upgraded beam andnear detector suite, and expected physics sensitivities can be found in the Hyper-Kamiokande Design
Report [25]. A schematic view of the tank is shown in Fig. 2. The design is an upright cylindrical tank
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Fig. 2. Schematic view of the ﬁrst tank.

with a diameter of 74 m and height of 60 m. The total (ﬁducial) mass of the detector is 258 (187) kt,
giving a ﬁducial mass that is eight times larger than Super-K. The Hyper-K detector candidate
site is in the Tochibora mine, which is used by the Kamioka Mining and Smelting Company, near
Kamioka town in Gifu Prefecture, Japan. This is 8 km south of Super-K and 295 km away from
J-PARC. The J-PARC neutrino beamline is directed so that the existing Super-Kamiokande detector
in the Mozumi mine and the Hyper-K candidate site in the Tochibora mine have the same off-axis
angle. The detector will lie under the peak of Nijuugo-yama, with an overburden of 650 m of rockor 1750 meters-water-equivalent (m.w.e.), at geographic coordinates N36◦ 21 20 , E137◦ 18 49(world geographical coordinate system), and an altitude of 514 m above sea level (a.s.l.).
The Hyper-K detector is designed to employ newly developed high-efﬁciency and high-resolution(timing) PMTs (Hamamatsu R12860), which will collect more photons compared to the current
Super-K PMTs, and improve sensitivity to low-energy events such as neutron captures and nuclear
de-excitations. This increased sensitivity contributes signiﬁcantly to the major goals of the Hyper-K
experiment such as clean proton decay searches via p → e+ + π 0 and p → ν̄ + K + decay modes
and the observation of supernova electron antineutrinos. The inner detector region of the single tankis viewed by 40,000 PMTs, corresponding to a PMT density of 40% photo-cathode coverage (thesame as that of Super-K). The detector will be instrumented with front-end electronics and a readout
network/computer system that is capable of high-efﬁciency data acquisition for two successive eventsin which Michel electron events follow muon events with a mean interval of 2 μs. It is also able torecord data from the vast number of neutrinos that would come from a nearby supernova in a nominal
time period of 10 s. Similar to Super-K, an outer detector (OD) with a layer width of 1–2 m is envisaged. In addition to enabling additional physics, this would help to constrain the external background.
The photo-coverage of the OD can be sparser, and use smaller PMTs than those used for the ID.
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Near and intermediate detector complex

The neutrino ﬂux and cross-section models can be probed by data collected at near detectors, situatedclose enough to the neutrino production point that oscillation effects are negligible. Near detector
data is extremely important to constrain uncertainties in these models.
The existing T2K ND280 detector suite comprises two detectors [26]: INGRID, which consistsof 14 iron-scintillator modules in a cross pattern centered on the neutrino beam axis, and ND280,
a multi-component detector at an angle of 2.5◦ from the beam direction. The primary purpose of
the INGRID detector is to monitor the neutrino beam direction, while the off-axis detector is used
to characterize the spectrum and interactions of neutrinos in the beam before oscillation. T2K has
successfully applied a method of ﬁtting to ND280 data with parametrized models of the neutrino
ﬂux and interaction cross-sections. Using the ND280 measurements, the systematic uncertainties on
the parts of the models constrained by ND280 have been reduced to a typical 3% uncertainty on the
Super-K (SK) predicted event rates. An upgrade of the current ND280 detector is planned before thestart of Hyper-K.
Moreover, it is proposed to build a water-Cherenkov detector at ∼1–2 km, before Hyper-K becomes
operational [28].A water-Cherenkov intermediate detector can be used to measure the cross section on
H2 O directly, with the same acceptance of lepton scattering angle as the far detector and with no needto account for the different target nuclei in a heterogeneous detector. Additionally, water-Cherenkov
detectors have shown excellent particle identiﬁcation capabilities, allowing for the detection of pure
νμ -CC, νe -CC, and NCπ 0 samples. The CCπ 0 rate and kaon production in neutrino interactions,which are backgrounds to nucleon decay searches, can also be measured. The proposed waterCherenkov detector will have the capability to make measurements at OAAs of 1.0◦ –4.0◦ , covering
the potential OAAs of detectors in Korea.
These additional water-Cherenkov measurements are essential to achieve the low systematic errors
required by Hyper-K, but are complemented by the magnetized ND280 tracking detector, whichis capable of tracking particles below the Cherenkov light threshold in water and of separating
neutrino and antineutrino beam components via lepton charge measurement. The design anticipates that a combination of a magnetized tracking detector such as ND280 and an “intermediate”
water-Cherenkov detector will provide the greatest reduction in systematic uncertainties affecting
the oscillation measurement.

2.4. T2HKK experimental conﬁguration
The axis of the J-PARC neutrino beam emerges upwards out of the sea between Japan and Korea.
The southern part of the Korean peninsula is exposed to the beam at a 1◦ –3◦ range of off-axis angles.
From east to west, baselines of 1000–1300 km are possible, as shown in Fig. 1. The topographyof South Korea is quite mountainous, especially in the east of the country, and provides plenty ofsuitable candidate sites.
The Korean rocks are in general made of granite, hard enough to build a large cavern. A search
for mountains higher than 1000 m has been made to ﬁnd several candidates for the Korean detector.
Mountains in the national or provincial parks were not considered in the search. Six suitable sites arelisted in Table 1, along with their location with respect to the J-PARC neutrino beam. The baselines
and energy options of the six sites are shown in Fig. 3. All sites would provide a signiﬁcant ﬂux atthe second oscillation maximum, and depending on the site it is possible to sample neutrinos fromas far apart as the ﬁrst and third maxima.
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Table 1. Detector candidate sites with off-axis angles between 1◦ and 2.5◦ . The baseline is the distance fromthe production point of the J-PARC neutrino beam.
Site
Mt. Bisul
Mt. Hwangmae
Mt. Sambong
Mt. Bohyun
Mt. Minjuji
Mt. Unjang

Height (m)
1084
1113
1186
1124
1242
1125

Baseline (km)
1088
1141
1169
1043
1145
1190

Off-axis angle
◦

1.3
1.9◦
2.1◦
2.3◦
2.4◦
2.2◦

Composition of rock
Granite porphyry, andesitic breccia
Flake granite, porphyritic gneiss
Porphyritic granite, biotite gneiss
Granite, volcanic rocks, volcanic breccia
Granite, biotite gneiss
Rhyolite, granite porphyry, quartz porphyryFig. 3. Comparison of baseline and energy regime of various recent and proposed long-baseline experiments.
The event rates for Kamioka and Korean sites are based on calculated ﬂuxes, using the quasi-elastic chargedcurrent cross section from NEUT. The ESSnuSB event rates are calculated from publicly available ﬂux
histograms [20] and the NEUT cross section. The event rates from MINOS [22], NOνA [23], and the DUNE[24] optimized design use publicly available spectra, which typically assume inclusive charged-current crosssections.

At an off-axis angle similar to that of the Kamioka site (2.5◦ ) the neutrino interaction rate peaks
at an energy of around 0.7 GeV. At this energy the second oscillation maximum occurs at a baseline of roughly 1100 km, with longer baselines corresponding to maxima for higher energies andvice versa.
The novel aspect of a detector built in Korea becomes clear if we compare it to similar longbaseline neutrino experiments. Figure 3 shows the regime of baseline (L) and neutrino energy (E)covered by recent and proposed experiments. T2HKK provides a baseline almost as long as the
proposed DUNE experiment but in a similar energy band to the existing T2K experiment, whichallows it to probe oscillations at the second oscillation maximum, a capability not available toany existing experiment, and only shared by the proposed ESS neutrino beam [20,21]. Furthermore, the fact that oscillations become more rapid at higher-order maxima means that the T2HKK
conﬁguration can probe more of the oscillation shape than existing experiments. It is also worth
noting that a double-baseline conﬁguration using similar ﬂuxes and different (non-trivial) baselines
within one experiment is only possible because the axis of the J-PARC beam passes below the
Kamioka site. Equivalent conﬁgurations using the NuMI or proposed LBNF and ESS beamlines
do not exist.
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Fig. 4. Two candidate sites for the second Hyper-K detector in Korea. Mount Bisul is located near the city of
Daegu at 1.3◦ off-axis, and Mt. Bohyun atYoungcheon at 2.3◦ off-axis. Mount Bisul is 1084 m high and provides
excellent accessibility with an existing highway nearby. Mount Bohyun is 1124 m high and accommodates
an optical telescope on the top. A detector at Bisul is expected to have ∼1000 m overburden with a slightly
inclined access tunnel 2.8 km long. An electromagnetic geological survey shows excellent bedrock for the
candidate site, suitable for a large cavern.

2.4.1. Investigation of candidate sites
We can roughly partition the candidate sites into two groups. For ﬁve of the six sites the (unoscillated)interaction rate is expected to peak near or slightly below the energy of the second oscillation
maximum. The exception is Mt. Bisul; at 1.3◦ it is much closer to the beam axis, so the typicalneutrino is more energetic and the spectrum overall is broader. A detector at this site could stillsample the second maximum but also sample a signiﬁcant part of the ﬁrst oscillation maximum andthe region between the ﬁrst and second oscillation maxima. Physics studies therefore treat Bisul asa distinct case.
The variation in L/E between the other sites is less substantial, and discriminating between thephysics reach of each requires detailed simulations. The Bohyun site, being closest to J-PARC, is
expected to provide the highest event rate after Bisul. Based on these considerations, Mt. Bisul and
Mt. Bohyun are the ﬁrst sites considered for more detailed investigation of their suitability.
Mount Bisul is located at Dalseong in the city of Daegu, the fourth largest city in population inSouth Korea, as shown in Fig. 4. Its accessibility is excellent. It takes one hour and forty minutes
to get to Daegu from Seoul by the KTX (Korean bullet train). The mountain is 1084 m high andmade of hard rocks: granite porphyry and andesitic breccia. A detector at Bisul is expected to have∼1000 m overburden with a slightly inclined access tunnel and to be exposed to a 1.3◦ off-axis
neutrino beam. The site coordinates are N35◦ 43 00 in latitude and E128◦ 31 28 in longitude.
The baseline from J-PARC is 1088 km. A recent geological survey using a magnetotelluric method
shows excellent bedrock for the candidate site, belonging to the hardest rock classes 1 or 2. Basedon nearby lakes and rivers, sufﬁcient underground water could be available in the site. The survey
result obtains an estimate of ∼2.7–3.2 m3 km−1 min−1 underground water ﬂow into the access tunnel
through rock fractures. The expected water would be sufﬁcient to be supplied for the detector. We ﬁnd
excellent access roads up to the candidate location of tunnel entrance, and easy access to electricity
supply lines.
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Fig. 5. Mount Bohyun as a candidate site for the second Hyper-K detector in Korea. It is 1124 m high andprovides ∼1000 m overburden with a slightly inclined access tunnel that is 3.9 km long. A geological survey
shows excellent bedrock for the candidate site, suitable for a large cavern.

Mount Bohyun is located at Youngcheon and is also the site of the Bohyunsan Optical Astronomy
Observatory, as shown in Fig. 5. The mountain is 1124 m high and made of fairly hard rocks: granite,
volcanic rocks, and volcanic breccia. It is an excellent candidate site for a large cavern. A detector
at Bohyun is expected to have ∼1000 m overburden and to be exposed to a 2.3◦ off-axis neutrino
beam. The site coordinates are N36◦ 09 47 in latitude and E128◦ 58 26 in longitude. The baselinefrom J-PARC is 1040 km. The geological survey also shows excellent bedrock for the candidate site.
Based on nearby rivers, sufﬁcient underground water is expected in the site. The survey result obtains
an estimate of ∼3.7 m3 km−1 min−1 underground water ﬂow into the access tunnel. Its accessibility
is reasonably good.
In summary, both candidate sites seem to be suitable for building a second Hyper-K detector, andcan provide roughly 1000 m overburden for low-energy neutrino measurements. Investigation of
the suitability of the sites for a larger cavern is already advanced, and initial estimates suggest the
excavation cost in Korea would be comparatively low.

3.

Physics motivation for the T2HKK conﬁguration

In this section we explain in more detail the expected beneﬁts of a detector sited in Korea, and why
these are sufﬁcient to make the proposal attractive despite the inevitable loss of statistics from using
a longer baseline.
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Fig. 6. The likelihood function versus cos δCP for normal-ordering neutrino mass spectrum for different typesof ﬂavor symmetries assuming the prospective 1 σ uncertainties in the determination of the neutrino mixing
angles [29].

To do so, it is ﬁrst worth restating the goals of the next generation of neutrino oscillation experiments. A general goal is to test the three-neutrino PMNS model. By using a different range of
L/E we subject the model to a broader range of checks than existing long-baseline experiments. An
example of these kinds of checks is the study of non-standard interactions (between neutrinos andnormal matter), which is described in Sect. 7. Even without resorting to any particular new model,
an expanded range of L/E values provides a check of the complete model used to analyze neutrino
experiments. In the broadest sense, this includes the models used for systematic uncertainties, suchas the modeling of neutrino ﬂuxes and cross sections.
Assuming that the three-neutrino oscillation model is correct and the uncertainties we assign tothe broader model are sensible, the primary goals of the next generation of neutrino oscillation
experiments are:◦ Establish the ordering of neutrino masses. That is, whether or not m23 > m21 .
◦ Establish the existence (or not) of CP violation in the neutrino sector. That is, whether or notδCP = 0, π.
◦ Make precision measurements of all oscillation parameters. Most important is to make aprecision measurement of δCP (as opposed to simply determining that it is not zero or π).
The ﬁrst two of these are well known, and need not be elaborated. As an example of the third goal,
Fig. 6 shows the prediction of GUTs with different ﬂavor symmetries for the value of cos δ. Four of
the ﬁve models predict a sizable CP violation effect (CP conservation occurs for cos δ = ±1), andare only separated by precision measurement.
At the second maximum, the effect on the observed spectrum from both the CP-phase and mass
hierarchy are enhanced in comparison to the Kamioka site, but the exact behavior is dependent on
the site. At the Bisul site (or any hypothetical site with an off-axis angle below about 1.5◦ ; see Fig. 8
later in this section) the beam spectrum peaks at around 1 GeV with a wider energy band, making
it possible to sample events from both the ﬁrst and second oscillation maxima. In addition, becauseof the energy dependence of matter-enhancement effects, the maximum sensitivity for determining
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the neutrino mass ordering is achieved by going to higher neutrino energies, so the Bisul site will
provide better discrimination between normal and inverted orderings.
Alternatively, the off-axis angle can be chosen in the region of 2.5◦, to provide a similar ﬂux(without oscillations) to that seen at Kamioka. In that case, the J-PARC neutrino beam spectrum
peaks at Eν = 0.6 GeV, with a narrower energy band in the vicinity of the second oscillation
maximum. With identical off-axis angles for HK and HKK, the combined analysis is essentially aratio measurement between the two sites, which can be expected to greatly reduce the uncertainties
from ﬂuxes and cross sections.
Both alternatives sample a wider range of L/E than the Kamioka site, and this enables improved
measurement resolution of the CP phase, especially near the maximally CP-violating values.
In the following section we examine the oscillation probabilities to explain the enhancements
seen at various Korean sites, and how measurements at HKK would differ from the baseline HK.
Following this, sensitivity studies are presented using both generic sites at a typical baseline of1100 km and the Bisul and Bohyun sites identiﬁed above.

3.1.

Neutrino oscillation probabilities

The sensitivity enhancement of a second detector in Korea can be understood by ﬁrst examining theP(νμ → νe ) and P(ν μ → ν e ) probabilities. We do this by ﬁrst studying the probabilities in vacuum
and then the probabilities with the matter effect included. The approximate oscillation probability invacuum is:P((−)ν μ →(−)ν e ) ≈ sin2 θ23 sin2 2θ13 sin2 (31 )+ sin2θ23 sin2θ13 sin2θ12 cos θ13 sin(31 ) sin(21 ) cos(32 ) cos δ∓ sin2θ23 sin2θ13 sin2θ12 cos θ13 sin(31 ) sin(21 ) sin(32 ) sin δ+ cos2 θ13 cos2 θ23 sin2 2θ12 sin2 (21 ).

(1)

m2 L

Here, we use the shorthand ji = 4Eji . The ﬁrst line represents the oscillations at the atmosphericmass splitting, and this term dominates for L/E values of ∼500 km/1 GeV typical of acceleratorbased long-baseline oscillation experiments. The fourth line gives the oscillations driven by the solar
mass splitting, which are small for the L/E values of interest. The second and third lines are theCP-conserving and CP-violating parts, respectively, of the interference term. The sign of the thirdline ﬂips to positive when considering antineutrinos, introducing the CP violation effect.
To understand the beneﬁt of a second-maximum experiment, note that the CP-violating interferm2 L

ence term depends on sin( 4E21 ). Since the argument is small for the L/E values of interest, thisdependence is approximately linear. Thus, for a given energy, a larger CP effect will be observed
at longer baselines. This is illustrated in Fig. 7, where the intrinsic CP-driven neutrino–antineutrino
probability difference is shown for baselines of 300, 900, and 1100 km.
m2 L

We identify the “oscillation maxima” as points where 4E32 = nπ/2 and n is an odd integer.
For a ﬁxed baseline, the second oscillation maximum will be located at 1/3 the energy of the ﬁrst
oscillation maximum. Alternatively, for a ﬁxed energy, the necessary baseline to observe the second
oscillation maximum will be three times larger than the baseline needed to observe the ﬁrst oscillation
maximum. The neutrino ﬂux will decrease by the ratio of the baselines squared—a factor of 1/9 inthis case—which means the statistical sensitivity decreases by a factor of three. At the same time,
the CP effect is around three times larger at the second oscillation maximum. The result is that CP
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Fig. 7. The neutrino–antineutrino probability difference for δ = 3π/2 at 300, 900, and 1100 km baselines foroscillations in vacuum. As the effects of matter are ignored here, this indicates the empirical size of “true” CPviolation, driven only by δCP .

violation measurements made at the second oscillation maximum have similar sensitivity to the ﬁrst
maximum, despite the reduction in event rate that comes with a three-times-larger baseline.
The signiﬁcant beneﬁt for second-maxima experiments is that this near indifference of the statisticalsensitivity to the baseline does not apply in relation to systematic uncertainties. Most important systematic errors are not signiﬁcantly constrained by data from the oscillated neutrino beam. This can bebecause parameters are better constrained by a near detector in the same beamline, by other independent experiments, or perhaps by using data taken with local calibration sources. Such uncertainties
do not grow with the baseline and as such are reduced relative to the larger CP violation effect.
Another uncertainty that potentially impacts the CP measurement is that associated with the leading
atmospheric term. This dominates the overall appearance probability at the ﬁrst maximum, so in arealistic case where we cannot do a perfect neutrino–antineutrino comparison, there will be some
contribution to the overall uncertainty arising from our imperfect measurement of the parameters thatappear in this term. But at the second maximum, where the size of the interference term is roughly
as large as the leading term, the ﬁnite precision to which the latter is known has less impact. In
essence, there is less “background” due to contributions that are independent of δCP . The picture is
not that simple in practice, but this effectively means that correlations between oscillation parametermeasurements at Kamioka and a Korean detector can be different, leading to potential synergies by
having both.
When neutrinos propagate in matter, the matter potential is added to the Hamiltonian of the system, modifying the neutrino oscillation probabilities. There are few expressions of the approximate
probability in matter [31–34] and one of them can be written as [31]:sin (31 ∓ aL) 2
P((−)ν μ →(−)ν e ) ≈ sin2 θ23 sin2 2θ13
31
(31 ∓ aL)2
2

+ sin2θ23 sin2θ13 sin2θ12 cos θ13

sin(31 ∓ aL)
sin(aL)31
21 cos(32 ) cosδ(31 ∓ aL)aL∓ sin2θ23 sin2θ13 sin2θ12 cos θ13

sin(31 ∓ aL)
sin(aL)31
21 sin(32 ) sinδ(31 ∓ aL)aL+ cos2 θ13 cos2 θ23 sin2 2θ12

sin2 (aL) 2
21 .
(aL)2
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√
The matter effect depends on a = GF Ne / 2, where GF is Fermi’s constant and Ne is the number
density of electrons in the matter. The signs of the aL terms ﬂip for antineutrinos, introducing aneffect that can mimic CP violation for some experimental conﬁgurations.
From here, note that the amplitudes of the ﬁrst, second, and third terms are dependent on the ratio

−1
31
= 1∓A ,
31 ∓ aL(3)√
where A = aL/31 = 2 2GF Ne E/m231 is directly proportional to E and inversely proportional
to the signed value of m231 . Similarly, the vacuum oscillation phase 31 in sin(31 ) is scaled
by a factor of (1 ∓ A). Since A is signed, this factor is less than unity for the combination of
normal ordering with neutrinos or inverted ordering with antineutrinos, but greater than unity for the
opposite combinations. As a result, both the amplitude of the appearance probability and the locationof the oscillation maxima shift depending on the mass ordering, and can be used to determine it
experimentally.
The shift in the amplitude of the probability depends only on E, and this is the reason the sensitivityof ﬁrst-maxima experiments increases with L and E at ﬁxed L/E. Among the Korean sites, it alsomeans that a detector at Mt. Bisul will have greater sensitivity to the mass ordering than otherlocations.
The shift in the phase is more interesting. It also depends on energy, but when considering a ﬁxed
value of E, the physical effect will grow linearly as the baseline increases. Thus, even Korean sites at a2.5◦ off-axis angle are more sensitive to the effect compared to Kamioka, even though the amplitudedifference is not larger.
This enhanced sensitivity to the mass ordering and δCP are illustrated ﬁrst in Fig. 8 and further in thefollowing section. Figure 8 shows the oscillation probabilities as a function of energy, at a baselineof L = 1100 km. In the region of the ﬁrst oscillation maximum above 1.2 GeV, the matter effect has
separated the oscillation probabilities for normal and inverted ordering for all values of the CP phase.
In the region of the second oscillation maximum, 0.5–1.2 GeV, the CP probability differences are
signiﬁcant, while the matter effect also affects the height and position of the oscillation maximum.
The spectrum of neutrino interactions (ignoring oscillations) for a 1.5◦ off-axis beam is also shownfor comparison.
3.1.1. Bi-probability plots
While it is relatively straightforward for the eye to interpret the way the oscillation probabilities
depend on δCP and the mass ordering near the ﬁrst oscillation maximum, e.g. above 1.2 GeV in Fig. 8,
these plots become complicated around the second maximum, and it becomes difﬁcult to understandthe overall pattern.A popular alternative is the “bi-probability” plot, in which the νμ → νe appearance
probability is plotted along the horizontal axis, and the ν μ → ν e probability along the vertical. Suchplots in principle show CP violation in a very direct way—the diagonal is CP conserving, andeverywhere in the space is CP violating, although that includes induced CP violation due to matter
effects.
Assuming a speciﬁc baseline and energy, the probabilities approximated by Eq. (2) can be calculated
for various values of the oscillation parameters. In particular, by allowing δ to vary with otherparameters held constant, a closed ellipse is traced out on the bi-probability plot. The binary choiceof mass orderings can then also be displayed as a second ellipse. The center point of the ellipse will
depend on the ﬁrst and fourth lines of the probability, and the binary choice of mass orderings will
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Fig. 8. The oscillation probabilities for δ = 0, π/2, π , 3π/2 and normal and inverted mass ordering are shownfor neutrinos (top) and antineutrinos (bottom). Expected muon (anti)neutrino spectra at 1.5◦ off-axis with
arbitrary normalization are shown for comparison.

(if the matter density is non-zero) appear as a separation into two separated ellipses, one for eachordering.
Such plots have one particular weakness when considering long-baseline experiments: the ellipses
are plotted for a ﬁxed energy. An experiment that measures oscillations over a range of energies
is summarized by a single value. This single-energy simpliﬁcation is reasonable when comparing
two experiments at the ﬁrst oscillation maximum, where the oscillation is typically rather broad incomparison to the ﬂux, but it does not represent the situation in T2HKK well, as this conﬁguration
samples a much wider range of L/E.
In order to use these plots for showing the more complex oscillation patterns at T2HKK it isnecessary to show multiple neutrino energies. It is not sufﬁcient to average the probability overthe interaction spectrum; this is equivalent to doing a rate-only measurement, and suppresses all
the shape information that a real analysis would use. Instead, in the following plots three curves
are shown: one (in blue) for the peak interaction rate, as normal, and two more from the upper (red)and lower (green) tails of the spectrum, chosen so that 50% of the (potentially) interacting neutrinos
lie between these two ellipses. (The exact method by which these points are calculated is describedin Appendix A.) This results in a set of six representative ellipses instead of two.
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Fig. 9. Appearance bi-probabilities at the Hyper-K site in Kamioka. The gray ellipses show the relative sensitivity (left) for a ten-year exposure of one Hyper-K tank and (right) for the original T2K design goal. Full
explanation is given in the text.

Figure 9 shows the resulting ellipses for the Kamioka site. The three ellipses differ in size andeccentricity, but the separation between the two mass orderings, and the dependence of the appearance
probabilities on the value of sin(δ), is similar for all three energies. The similarity of the three pairs of
ellipses explains why the narrow-band, ﬁrst-maximum conﬁguration can be reasonably approximatedas a single (“rate-only”) measurement.
Two more details are added to the plots. The ﬁrst is a summary of the L/E value probed (at thepeak energy) at the given site. The quantity
2 m232  L
32 =
(4)
π
4E
is deﬁned, which has (near) odd-integer values for oscillation maxima, and (near) even-integer
values for oscillation minima. For calculation of 32 and drawing all bi-probability plots, a value of
2.5 × 10−3 eV2 is assumed for m232 .
The second detail is the gray ellipses, which provide a comparative scale for the statistical powerof the measurement: this depends on the number of events seen with energy similar to each coloredellipse. Since this will depend on the νe appearance probabilities and the relative size of the background contamination, this varies across the measurement space. Since this is essentially unrelated
to how the analysis is actually performed, it is not possible to accurately indicate the absolute sensitivity, but does give an indication of the relative sensitivity at different sites. Full details are given
in Appendix A.
Since the ﬂux at the Hyper-K site near Kamioka should be the same as the existing T2K experiment,
the beneﬁt of a larger detector and upgraded beam is entirely due to the higher statistics. In termsof the bi-probability plots, the probability ellipses remain the same, but the statistical error ellipses
shrink. This is illustrated by a comparison of the left and right panels of Fig. 9, showing that Hyper-K
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Fig. 10. Appearance bi-probabilities at the Mt. Bisul site at 1088 km.

will be much more sensitive than the design goal of T2K-I (7.8×1021 POT) by virtue of much smaller
statistical errors. In contrast, at the Korean sites the statistical uncertainties are about three times
larger than the default Hyper-K conﬁguration, but they gain sensitivity due to the fact the probability
ellipses change drastically.
The ﬁrst example shown is for the most on-axis site under consideration—Mt. Bisul—in Fig. 10.
A detector at Bisul would see completely separated ellipses depending on the mass ordering, i.e.
the measurement is completely non-degenerate with CP violation for events at the peak, and in thehigh-energy tail. This reﬂects the beneﬁt of high-energy neutrinos for resolving the mass ordering.
At the peak energy, however, the normal ordering enhances the antineutrino probabilities relative toneutrinos, which is opposite to the amplitude-dominated effect seen at the ﬁrst maximum. This isdue to the matter effect also changing the effective oscillation length for neutrinos and antineutrinos,
so that the neutrinos are closer to an appearance minimum than are antineutrinos of the same energy.
Unlike a ﬁrst-maximum experiment, the experimental signature determining the mass ordering uses
shape as well as rate information, and the impact of systematic uncertainties (most obviously on
neutrino versus antineutrino cross sections and detection efﬁciencies) is correspondingly different.
Although most pronounced at the higher beam energies of the Bisul site, this characteristic is seenfor some energies at any Korean site.
The low-energy tail of the Bisul site corresponds to an (L, E) regime more similar to the other
Korean sites. Figure 11 shows the Bohyun site, which has the shortest baseline of the sites underconsideration, and a ﬂux more similar to that at Kamioka. It is immediately apparent (as it wasfor the lower-energy ellipse at Bisul) that the ellipses are much larger, demonstrating a greatly
enhanced CP-violation signal. For the energy peak at Bohyun (which is close to the oscillation maximum), the overlap between the normal and inverted ordering ellipses is still large, but
the effect for the higher and lower energy ellipses is quite different, so information provided
by the spectrum of observed events is less degenerate, and correspondingly more interesting,than it is for ﬁrst-maxima experiments. The larger effect size almost entirely compensates forthe lower statistics compared to T2HK at Kamioka, but the absolute scale of detector systematic
errors does not grow for a more distant site, so systematic errors are expected to be much lessimportant.
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Fig. 11. Appearance bi-probabilities at the Mt. Bohyun site at 1043 km.

Fig. 12. Appearance bi-probabilities at the Mt. Minjuji site at 1145 km.

Finally, Fig. 12 shows the Minjuji site, which probes the largest values of L/E. For Minjuji, the lowenergy tail is actually probing the region near the third oscillation maximum. The independence of
information available at different energies is again clearly apparent—for the peak energy and below
the ellipses are noticeably “fatter.” More precisely, we can say that dP/dδ is larger in the vicinity ofδ = ±π/2. Narrow ellipses are characteristic of an energy band near the oscillation maximum, where
the dependence on δ is dominated by a sin δ dependence. This is optimal for making a measurementof δ near 0, π, and therefore for establishing (or not) CP violation. However, if the true value of δ
is in the vicinity of ±π/2, this provides the least precision on the value. The wider L/E band of a
Korean detector improves the sensitivity to cos δ and the measurement precision on the CP phase inlarge CP-violation scenarios.
However, we reiterate that although these kinds of plots are useful for understanding the meritsof a Korean detector, they are largely unrelated to how the actual analysis is done: using binned
energy spectra, multiple backgrounds, and ﬁnite energy resolution. To determine real sensitivities,
more detailed studies must be done with full simulations. Such studies are presented in the following
sections.
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Table 2. The default oscillation parameter values and prior uncertainties used in the studies presented in thissection.

4.

Parameter

Value

Prior error

δCP
m232
sin2 θ23m221
sin2 θ12
sin2 θ130
2.5 × 10−3 eV2
0.5
7.53 × 10−5 eV2
0.304
0.0219No prior constraint
No prior constraint
No prior constraint
0.18 × 10−5 eV2
0.041
0.0012

Improved neutrino mass ordering and CP sensitivities

This section describes the sensitivity in measuring the neutrino mass ordering and discovering CP
violation using a conﬁguration of Hyper-K with one tank in Japan and the second tank in Korea.
Expected reconstructed event spectra for the Korean detector are presented and the effect of theoscillation parameters on these spectra are considered. A model of systematic uncertainties is added,
and studies of the resulting sensitivity for mass ordering measurement, CP violation discovery, andthe precision of CP phase measurement are presented.

4.1.

Event rates at Korean detectors

For the purpose of the sensitivity studies presented here, we consider generic detector locations inSouth Korea at a baseline of 1100 km and off-axis angles of 1.5◦ , 2.0◦ , or 2.5◦ . The expected event
rates are estimated by using the NEUT [35] 5.3.2 neutrino interaction generator and a GEANT3based simulation of the Super-K detector, where the ﬁducial mass has been scaled from 22.5 kt
to 187 kt. The simulated events are scaled to give good agreement with NEUT 5.1.4.2, which has
been tuned against T2K near-detector data. Following the running plan of Hyper-K, an exposureof (1.3 MW)×(10 × 107 s) is assumed with a 3 : 1 ratio of antineutrino-mode to neutrino-mode
operation. This corresponds to ten years of Hyper-K operation, or 27 × 1021 protons on target. Oscillation probabilities are calculated using Prob3++ [36], and a constant matter density of
3.0 g cm−3 is assumed for the 1100 km baseline [37]. Unless otherwise speciﬁed, simulated event
rates are calculated with the oscillation parameters shown in Table 2. When ﬁtting, the parameterssin2 θ13 , sin2 θ12 , and m221 are constrained by Gaussian constraint terms with the 1 σ uncertainties shown in Table 2, which are extracted from the Particle Data Group (PDG) 2016 Review ofParticle Physics [38]. For each detector conﬁguration, reconstructed events are classiﬁed in four
categories:◦ Neutrino mode, 1Re: single electron-like ring candidates collected in neutrino-mode operationof the beam.
◦ Antineutrino mode, 1Re: single electron-like ring candidates collected in antineutrino-mode
operation of the beam.
◦ Neutrino mode, 1Rμ: single muon-like ring candidates collected in neutrino-mode operationof the beam.
◦ Antineutrino mode, 1Rμ: single muon-like ring candidates collected in antineutrino-mode
operation of the beam.
The selection cuts for these candidate samples are identical to the selection cuts used in recent T2K
oscillation measurements [39], except for the reconstructed energy Erec <1.25 GeV cut on the 1Re
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Fig. 13. Predicted 1Re candidate rates for neutrino mode (left) and antineutrino mode (right) with the detector
at a 1.5◦ (top), 2.0◦ (middle), or 2.5◦ (bottom) off-axis angle. The oscillation parameters are set to δCP = 0,m232 = 2.5 × 10−3 eV2 (normal mass ordering), sin2 θ23 = 0.5, sin2 θ13 = 0.0219.

samples. This cut has been removed, since the matter effect that constrains the mass ordering is moststrongly manifested in events with reconstructed energy greater than 1.25 GeV.
Predicted event rates for normal mass ordering and δCP = 0 are shown for 1Re and 1Rμ samples
in Fig. 13/Table 3 and Fig. 14/Table 4, respectively. In Tables 3 and 4, the predicted event rates forthe nominal Hyper-K tank location are shown for comparison. The 1Re candidate rates in Korea are
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Table 3. The expected number of νe and ν̄e 1Re candidate events. Normal mass ordering with sin2 θ13 = 0.0219
and δCP = 0 are assumed. Background is categorized by the ﬂavor before oscillation. “Signal” are 1Re
candidates produced by νe in neutrino-mode operation and ν̄e in antineutrino-mode operation. “Wrong-sign
signal” are 1Re candidates produce by ν̄e in neutrino mode-operation and νe in antineutrino-mode operation.
Detector location

SignalOAA, L
2.5◦ , 295 km
2.5◦ , 1100 km
2.0◦ , 1100 km
1.5◦ , 1100 km

1426.1
87.9
122.6
140.6

OAA, L
2.5◦ , 295 km
2.5◦ , 1100 km
2.0◦ , 1100 km
1.5◦ , 1100 km

1053.1
89.8
131.5
159.1

Intrinsic νe , ν̄eWrong-sign signal

NC

CC-νμ ,ν̄μ

Total

15.4
1.7
2.0
2.4

Neutrino mode
269.3
28.3
33.8
39.1

125.0
12.5
21.4
39.1

7.1
1.7
2.4
3.7

1842.9
132.2
182.3
224.8

164.3
15.5
19.8
23.9

Antineutrino mode
338.3
39.4
46.3
54.3

153.5
14.3
23.4
39.5

4.2
0.8
1.1
1.7

1713.4
159.8
222.1
278.5

∼1/10 the rates at the 295 km baseline due to the 1/L2 dependence of the ﬂux. In the 1Rμ samples,the ﬁrst and second oscillation maxima can be observed at 2 GeV and 0.7 GeV, respectively.
The variations of the 1Re spectra in neutrino mode and antineutrino mode for different δCP values
at different detector locations are shown in Fig. 15. Similarly, the asymmetries of predicted 1Re
spectra between neutrino mode and antineutrino mode as a function of δCP are shown in Fig. 16.
For the detectors in Korea, the magnitude of the potential neutrino/antineutrino asymmetry is larger
and this effect can partially compensate for the larger statistical uncertainties at the 3.7 times longer
baseline. The purely statistical separations between the maximally CP-violating and CP-conserving
hypotheses are listed in Table 5, where it is assumed that the mass ordering is known. The 2.0◦ off-axis
slice has the strongest statistical separation between CP-violating and CP-conserving hypotheses.
Here, the detectors at 1100 km do not match the signiﬁcance for CP violation discovery of the 295 km
detectors as suggested in Sect. 3.1. The lower signiﬁcance is due to a few factors. First, the 1100 km
baseline means that the second oscillation maximum is at a higher energy than the ﬁrst oscillation
maximum at the 295 km baseline, and the neutrino ﬂux is decreased by a factor of 14 at 1100 km
compared with 295 km. The width of the second oscillation maximum is also narrower than the ﬁrst
oscillation maximum, so for a 2.0◦ off-axis beam, a larger fraction of events do not have energies very
close to the second oscillation maximum. The introduction of the matter effect also decreases the CP
violation signiﬁcance as it introduces degeneracies between the mass ordering and δCP . Despite thelower statistical signiﬁcance at the 1100 km baseline, the overall signiﬁcance with a second detector
in Korea is higher when systematic uncertainties are accounted for, as is shown in the sensitivity
studies presented later in this section.
The impact of the matter effect and sensitivity to mass ordering is illustrated in Fig. 17. Here, adouble difference is presented. First, the difference in observed neutrino-mode and antineutrino-mode
1Re candidates is calculated as a function of reconstructed energy. This difference is calculated forboth the normal and inverted hierarchies, and the difference between hierarchies is taken. It canbe seen that the neutrino–antineutrino difference varies differently with reconstructed energy forthe normal and inverted hierarchies. For the normal mass ordering, the neutrinos are enhanced in
the < 0.8 GeV and > 1.1 GeV regions and diminished in the 0.8–1.0 GeV region relative to theinverted mass ordering. This relative difference is nearly independent of the true value of δCP , asillustrated in Fig. 17. The 1.5◦ off-axis angle conﬁguration allows for a signiﬁcant observation of
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Fig. 14. Predicted 1Rμ candidate rates for neutrino mode (left) and antineutrino mode (right) with the detector
at a 1.5◦ (top), 2.0◦ (middle), or 2.5◦ (bottom) off-axis angle. The oscillation parameters are set to δCP = 0,m232 = 2.5 × 10−3 eV2 (normal mass ordering), sin2 θ23 = 0.5, sin2 θ13 = 0.0219.

this spectral dependence of the asymmetry in the 0.8–1.0 GeV and > 1.1 GeV regions. The 2.0◦
off-axis angle conﬁguration has little sensitivity to the > 1.1 GeV region, and the 2.5◦ off-axis
conﬁguration is only sensitive to the < 0.8 GeV region. Figure 17 illustrates the mass ordering
sensitivity for the neutrino/antineutrino mode difference for ﬁxed bins of reconstructed energy, but
additional sensitivity arises from the energy-dependent enhancements and deﬁcits observed in eachmode independently.
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Table 4. The expected number of νμ and ν̄μ 1Rμ candidate events. Normal mass ordering with sin2 θ23 = 0.5,
m232 = 2.5 × 10−3 eV2 , and sin2 θ13 = 0.0219 are assumed.
Detector location

SignalWrong-sign signal

OAA, L
2.5◦ , 295 km
2.5◦ , 1100 km
2.0◦ , 1100 km
1.5◦ , 1100 km

9062.51275.02047.23652.0

571.2
32.7
42.8
55.4

OAA, L
2.5◦ , 295 km
2.5◦ , 1100 km
2.0◦ , 1100 km
1.5◦ , 1100 km

8636.11119.5
1888.53579.24905.9
300.6
390.0
490.8

NC

CC-νe ,ν̄e

Total

Neutrino mode
813.6
58.5
107.7
210.4

29.5
1.9
2.5
2.9

10476.9
1368.1
2200.23920.7

Antineutrino mode
860.8
61.9
102.6
185.1

23.6
2.0
2.4
2.8

14426.5
1484.02384.44257.9While the CP-even and CP-odd interference terms in the electron (anti)neutrino appearance probability are enhanced at the 1100 km baseline due to the 21 dependence, no such enhancement ispresent in the muon (anti)neutrino survival probability. Hence, the statistical constraint from the 1Rμsamples on m232 and sin2 2θ23 will be stronger for the detector at L = 295 km due to the larger
statistics. The Korean detector, however, has the unique feature of measuring the oscillation patternover two periods, conﬁrming the oscillatory behavior of the neutrino transitions. Figure 18 shows
the ratio of the expected spectrum after oscillations to the expected spectrum without oscillations.
For all three Korean detector locations, the oscillation pattern over two periods may be observed.
While the measurement in Hyper-K provides higher statistics, only one period of oscillations can beobserved.

4.2.

Systematic errors

Due to the statistically large samples available in the Hyper-K experiment, systematic errors arelikely to represent the ultimate limit on oscillation parameter measurement precision. An advantage
of a Korean detector is to enhance the contribution of the δCP -dependent interference terms at the costof fewer statistics, achieving similar sensitivity in a statistics-limited measurement. To evaluate theimpact of the Korean detector on the Hyper-K sensitivities, it is necessary to implement a systematic
error model that takes into account what are expected to be the dominant systematic errors forHyper-K. The systematic error model should also account for any new systematic errors introducedby having a detector in Korea. The systematic errors considered for the sensitivity studies presented
in this paper are:◦ σνe /σνμ and σν̄e /σν̄μ : The interaction cross sections for νe and ν̄e are not currently precisely
measured with near-detector data, although they may be more precisely measured in the HyperK era. When extrapolating the measured νμ and ν̄μ rates from the near detectors to predictthe νe and ν̄e appearance rates at the far detector, it is necessary to assign an uncertainty on
the interaction cross section ratios σνe /σνμ and σν̄e /σν̄μ . Here, the T2K approach based on thework of Day and McFarland [43] is taken. Separate normalization parameters are assigned tovary σνe and σν̄e . The correlation between these parameters is assigned assuming there is a 2%
systematic effect that is uncorrelated between neutrinos and antineutrinos and an additional 2%systematic effect with anticorrelation between neutrinos and antineutrinos.
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Fig. 15. The predicted 1Re spectra in neutrino mode (left) and antineutrino mode (right) for different valuesof δCP . The error bars represent statistical errors only.

◦ Energy scale at the far detectors: The energy scale at Super-K is calibrated using samplesof Michel electrons, π 0 s, and stopping cosmic muons. In T2K oscillation analyses, the energy
scale error is found to be 2.4% [39]. Here, a 2.4% energy scale uncertainty is applied to thereconstructed energy for events in Hyper-K and the Korean detector. Independent parameterswith no correlation are used for Hyper-K and the Korean detector. It is assumed that there is
100% correlation between the 1Rμ and 1Re samples.
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Fig. 16. The event rate asymmetry between neutrino mode and antineutrino mode for variations of δCP atdifferent detector site locations. The error bars represent statistical errors only.

Table 5. The statistical separation of the predicted maximally CP-violating spectra from the predicted CPconserving spectrum. Here the signiﬁcance is calculated for both CP-conserving hypotheses, and the smallest
signiﬁcance is shown. The mass ordering is assumed to be known.
Detector location

Signiﬁcance (σ )NH

OAA, L
2.5◦ , 295 km
2.5◦ , 1100 km
2.0◦ , 1100 km
1.5◦ , 1100 km

δCP = π/2
11.6
6.1
7.9
6.9

IH
δCP = 3π/2
11.0
4.9
5.9
5.3

δCP = π/2
11.8
6.5
7.1
5.9

δCP = 3π/2
10.9
4.9
6.3
5.7

◦ Matter density: For the results presented here, a constant matter density of 3.0 g cm−3 isassumed for the path to the Korean detector. An uncertainty of 6% is assigned based on previous
estimates [37].
◦ The NCπ + background: NCπ + interactions are a signiﬁcant background in the 1Rμ samples.
Based on the approach taken by T2K [39], a 30% error is applied here.
◦ The intrinsic νe (ν̄e ) and NCπ 0 backgrounds: The backgrounds for the 1Re samples are theintrinsic νe (ν̄e ) in the beam and NCπ 0 interactions mistaken for an electron. It is expected that
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Fig. 17. The difference of the observed neutrino–antineutrino difference in the 1Re samples for normal massordering relative to the expected differences for inverted mass ordering. The error bars are the propagatedstatistical errors for the neutrino-mode and antineutrino-mode 1Re samples.

these backgrounds will be measured by an intermediate water-Cherenkov detector with similarνe (ν̄e ) and total ﬂuxes to the far detector ﬂuxes. The ﬂuxes are similar since the oscillation effecton νe (ν̄e ) is ∼5%, and oscillations do not affect the neutral current event rate. Studies of thismeasurement with the NuPRISM detector show an expected statistical error of 3%. A total error
of 5% is considered to account for uncertainties in the different efﬁciency and ﬂuxes between
the near and far detectors. It is assumed that there is 100% correlation between Hyper-K and
the Korean detector, but no correlation is assumed between the neutrino and antineutrino beammodes.
◦ The CC non-quasielastic fraction: The fraction of non-quasielastic interactions in the candidates’ samples affects the predicted normalization and reconstructed energy distribution. In
T2K near-detector ﬁts, the normalization of the non-quasielastic 2p–2h component of the crosssection is ﬁtted with a 20% error [40]. The 2p–2h interactions are sometimes called multinucleon interactions, and they consist of interactions on correlated pairs of nucleons rather
than a single nucleon. T2K models these interactions based on the work of Nieves et al.
[41,42]. Here, a 20% error is applied to the normalization of the non-quasielastic interactions, which includes 2p–2h events, as well as events where a pion is produced but is absorbed
before exiting the nucleus. An anticorrelated parameter is applied to the quasielastic interactions, and its error is chosen such that the normalization of the unoscillated event rate is
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Fig. 18. The ratio of the predicted 1Rμ spectrum with oscillations to the predicted 1Rμ spectrum without
oscillations. Here, the neutrino-mode and antineutrino-mode data have been summed. The bin width varies
from 25 MeV at low energy to 100 MeV at high energy, and the errors on each bin represent the statistical error
for that bin.

conserved for variations of these parameters. This approach models the effect of the near-detector
constraint.
◦ Near to far extrapolation: The T2K oscillation analysis [39] accounts for an uncertainty fromthe ﬂux and cross section model parameters that are constrained by the near-detector data. Thiserror includes the near-detector measurement error and extrapolation uncertainties in the ﬂux
and cross section models that arise due to different neutrino ﬂuxes and detector acceptances at
the near and far detectors. To model this uncertainty, the T2K errors are applied as an overall
uncertainty on the charged current event rate. In principle, the extrapolation error includes theeffect of the previously described uncertainty on the non-quasielastic fraction. To avoid double
counting the error on the non-quasielastic fraction, the T2K errors are corrected by subtracting in
quadrature the normalization uncertainty that is explicitly calculated from the non-quasielastic
uncertainty.
◦ Far detector modeling: In addition to the energy scale uncertainty, there are uncertainties
related to the modeling of efﬁciencies in the far detector. This uncertainty is estimated basedon the uncertainty evaluated for T2K. Since the far detector efﬁciency model is tuned using
atmospheric neutrino control samples, it is assumed that the uncertainty will be reduced with
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the larger sample of atmospheric neutrinos available in Hyper-K. For the studies presented√
here, the assumption is that 50% of the error is reduced by a factor of 1/ 8.3, where 8.3
is the ﬁducial mass ratio between Hyper-K and Super-K. The remaining 50% of the error
remains unchanged under the assumption that perfect agreement between the detector modeland control samples may not be achieved and systematic errors may be applied to cover any
disagreement. For this error source, there are no correlations between Hyper-K and the Korean
detector.
For the purpose of this document, the above systematic error model is used in place of the model
adopted for the Hyper-K design report. This is done because the systematic errors used in the HyperK design report are based on the T2K systematic error estimate for a 2.5◦ off-axis angle ﬂux anda 1Re sample with a Erec < 1.25 GeV cut applied. The T2K systematic error model has not yet
been applied to the other off-axis angle positions and 1Re samples with the reconstructed energy cut
removed.
The effects of systematic errors propagated to the normalization uncertainties on the 1Rμ and 1Re
samples are summarized in Table 6. The normalization uncertainties for individual samples are in
the 4%–5% range. These uncertainties are slightly more conservative than those presented in theHyper-K design report, which included a total systematic error between 3% and 4% depending on thesample. The uncertainties for the more on-axis detector locations appear marginally smaller because
the broader spectrum tends to average over shape uncertainties more. The uncertainties as a fractionof the total predicted event rate and as a function of reconstructed energy are shown in Fig. 19. Here,the most prominent feature is the large uncertainty in the 1–3 GeV region of the 1Rμ samples forthe detector at L = 1100 km. This energy range is the location of the ﬁrst oscillation maximum
and the large uncertainty arises from energy scale and non-quasielastic fraction uncertainties thatcan cause feed-down or feed-up (in the case of energy scale) into the region of the oscillation
maximum.
The relationship between systematic uncertainties and the physics sensitivity with a Korean detector
can be better understood by investigating a speciﬁc measurement, the precision measurement of δCP
when δCP is near a maximally CP-violating value of π/2 or 3π/2. Near these values, the derivative ofsin(δCP ) approaches zero, degrading the sensitivity to the CP-odd term in the oscillation probability.
Here, the CP-even term, which depends on cos(δCP ), may contribute to the precision measurementof the phase. Figure 20 shows the changes to the spectra for a change in a δCP by +13◦ from an
initial value of π/2 for the Hyper-K detector. Here, 13◦ is chosen since it is expected to be theultimate precision of Hyper-K after a 10 yr×1.3 MW exposure with two tanks. It can be seen that thechange to δCP by 13◦ largely affects the spectrum through the cos(δCP ) term, causing a downward
shift in energy with little change to the overall normalization. Figure 20 also shows the effect ofan energy scale shift by −0.5% for comparison. The energy scale shift has a similar effect on the
spectrum, indicating that even a 0.5% uncertainty on the energy scale can degrade the δCP precisionnear maximally CP-violating values.
The Korean detector is constraining δCP with a signiﬁcant number of events at the second and third
oscillation maxima. Near the second oscillation maximum, the effect of the CP-odd interferenceterm in the oscillation probability is three times larger, and for the same shift in δCP , the CP-odd
effect may be observable. Figure 21 shows the spectrum ratios for the Korean detector at 1100 km
baseline and 1.5◦ off-axis. Here, the effect of both the CP-even terms can be seen in the increased
rate from 1.3 GeV and above for both neutrino and antineutrino modes. The CP-odd term causes an
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Table 6. Percentage error on the normalization of the predicted 1Rμ and 1Re samples in neutrino and antineutrino mode for each systematic error source. The error on the ratio of neutrino mode to antineutrino mode isalso shown for 1Re since this uncertainty is relevant for the detection of a CP asymmetry.
Error source

Percent error (%)ν 1Rμν̄ 1Rμν 1Re

ν̄ 1Re(ν 1Re)/(ν̄ 1Re)◦σνe /σνμ , σν̄e /σν̄μEnergy scale
Matter density
NCπ + backgroundνe & NCπ 0 backgroundCC non-QE fraction
Extrapolation
Far detector model
Total

OAA=2.5 , L = 1100 km
0.00
0.00
0.02
0.02
0.04
0.08
1.28
1.25
0.00
0.00
2.76
1.88
2.70
2.60
2.64
2.64
4.69
4.16

2.10
0.01
0.43
0.00
1.32
1.98
2.44
2.08
4.54

1.68
0.01
0.09
0.00
1.41
1.29
3.06
2.08
4.47

3.12
0.01
0.53
0.00
1.88
2.35
1.95
0.00
4.86

σνe /σνμ , σν̄e /σν̄μEnergy scale
Matter density
NCπ + backgroundνe & NCπ 0 backgroundCC non-QE fraction
Extrapolation
Far detector model
Total

OAA=2.0◦ , L = 1100 km
0.00
0.00
0.02
0.01
0.02
0.06
1.47
1.29
0.00
0.00
0.87
0.82
2.68
2.68
2.64
2.64
3.89
3.83

2.01
0.01
0.55
0.00
1.26
1.24
2.38
2.08
4.18

1.67
0.01
0.12
0.00
1.29
0.76
3.00
2.08
4.27

3.07
0.01
0.67
0.00
1.76
1.51
1.92
0.00
4.39

σνe /σνμ , σν̄e /σν̄μEnergy scale
Matter density
NCπ + backgroundνe & NCπ 0 backgroundCC non-QE fraction
Extrapolation
Far detector model
Total

OAA=1.5◦ , L = 1100 km
0.00
0.00
0.01
0.01
0.01
0.06
1.61
1.30
0.00
0.00
0.44
0.30
2.67
2.60
2.64
2.64
3.83
3.81

1.72
0.01
0.24
0.00
1.42
0.52
2.23
2.08
3.84

1.41
0.01
0.28
0.00
1.37
0.37
2.88
2.08
4.11

2.67
0.01
0.53
0.00
1.93
0.75
1.84
0.00
3.91

σνe /σνμ , σν̄e /σν̄μEnergy scale
Matter density
NCπ + backgroundνe & NCπ 0 backgroundCC non-QE fraction
Extrapolation
Far detector model
Total

OAA=2.5◦ , L = 295 km
0.01
0.00
0.04
0.03
—
—
2.33
1.79
0.00
0.00
1.68
1.72
2.60
2.56
2.64
2.64
4.13
4.15

2.44
0.42
—
0.00
0.94
2.07
2.51
2.08
4.71

1.82
0.63
—
0.00
1.22
1.00
3.05
2.08
4.47

3.53
0.21
—
0.00
1.51
2.25
1.96
0.00
4.90

OAA=2.5◦ , L = 295 km (Hyper-K design report)
3.6
3.6
3.2
3.9

—

Total

asymmetry in the normalization of the neutrino-mode and antineutrino-mode samples below 1 GeV.
These effects cannot be reproduced with a small variation of the energy scale parameter, as is thecase for Hyper-K. This study shows that the constraint on δCP near δCP = π/2, 3π/2 is sensitive
to different systematic errors for Hyper-K and the Korean detector. It also shows that the fractional
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Fig. 19. The fractional systematic errors per bin on the predicted spectra binned in reconstructed energy.

change to the spectrum from the δCP variation is larger for the detector at a longer baseline, suggestingthat the measurement is less likely to be systematics limited. The full impact of the Korean detector
on the δCP precision will be shown in the following section, where the physics sensitivities arepresented.
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Fig. 20. The ratios to nominal predicted spectra (δCP = π/2) for a δCP shift of +13◦ and an energy scale shiftof −0.5%. The ratios are shown for the 1Re samples in neutrino mode (top) and antineutrino mode (bottom).
The ratios are calculated for the Hyper-K detector at 295 km and 2.5◦ off-axis.

4.3.

Impact of the Korean detector on physics results

For the physics sensitivity studies presented here, it is assumed that one or two 187 kt detectors will
be operated for ten years (10 × 107 s) at 1.3 MW beam power, corresponding to 27 × 1021 protons
on target. For the initial studies, ﬁve conﬁgurations are considered:◦ JD×1: A single detector is located in Japan at the Tochibora site with a baseline of 295 km andan off-axis angle of 2.5◦ .
◦ JD×2: Two detectors are located in Japan at the Tochibora site with a baseline of 295 km andan off-axis angle of 2.5◦ .
◦ JD+KD at 2.5◦ : One detector is located in Japan at a baseline of 295 km and an off-axis angleof 2.5◦ , while the second is located in Korea at a baseline of 1100 km and an off-axis angleof 2.5◦ .
◦ JD+KD at 2.0◦ : One detector is located in Japan at a baseline of 295 km and an off-axis angleof 2.5◦ , while the second is located in Korea at a baseline of 1100 km and an off-axis angleof 2.0◦ .
◦ JD+KD at 1.5◦ : One detector is located in Japan at a baseline of 295 km and an off-axis angleof 2.5◦ , while the second is located in Korea at a baseline of 1100 km and an off-axis angleof 1.5◦ .
Later in this section, the sensitivities for the Mt. Bisul site (L = 1084 km and OAA=1.3◦ ) and the
Mt. Bohyun site (L = 1043 km and OAA=2.3◦ ) will also be presented.
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Fig. 21. The ratios to nominal predicted spectra (δCP = π/2) for a δCP shift of +13◦ and an energy scale shiftof −0.5%. The ratios are shown for the 1Re samples in neutrino mode (top) and antineutrino mode (bottom).
The ratios are calculated for the Korean detector at 1100 km and 1.5◦ off-axis.

The initial physics sensitivity studies focus on three measurements: the determination of the massordering, the discovery of CP violation through the exclusion of the sin(δCP ) = 0 hypothesis, and theprecision measurement of δCP . In all cases, the sensitivities are evaluated on pseudo-data generated
with the following true oscillation parameter values:◦ |m232 | = 2.5 × 10−3 eV2◦ sin2 θ23 = 0.5◦ sin2 θ13 = 0.0219◦ m221 = 7.53 × 10−5 eV2◦ sin2 θ12 = 0.304.
The pseudo-data are also generated for multiple values of δCP and both mass orderings, and thesensitivities are presented as a function of the true value of δCP and the mass ordering. In the ﬁts
to the pseudo-data, m232 , sin2 θ23 , and δCP are free parameters with no prior constraints. sin2 θ13 ,sin2 θ12 , and m221 also vary in the ﬁts, but they have prior Gaussian constraints with 1 σ uncertainties
of 0.0012, 0.041, and 0.18 × 10−5 eV2 , respectively. The prior uncertainties on these parameters aretaken from the 2015 edition of the PDG Review of Particle Physics [38]. The systematic parametersdescribed in the previous section are also allowed to vary as nuisance parameters in the ﬁt within
their prior constraints. In all cases, the sensitivities are evaluated on the ﬁt to the so-called Asimovset, where the prediction for each sample is made for the nominal values of the oscillation parametersand systematic parameters, and no statistical variations are applied. All four samples (neutrino-mode
1Re, 1Rμ and antineutrino-mode 1Re, 1Rμ) are used to construct a binned likelihood, and the33/65
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product of the pseudo-data likelihood is taken with the Gaussian priors for constrained oscillation
parameters and systematic parameters to construct the full likelihood, L. To simplify the notation,
we write −2log(L) as χ 2 .
The test statistic used for the mass ordering determination is:
2 = χ2 − χ2 .
χMH
(5)
WH
CH
2 and χ 2 are the best-ﬁt −2log(L) for the wrong and correct mass hierarchies, respectively.
Here, χWH
CH
In the Gaussian limit, the test parameter can be interpreted as the signiﬁcance of the mass ordering
determination. Here, sensitivities are shown for the Hyper-K accelerator neutrinos only and do notaccount for the additional constraint from Hyper-K atmospheric neutrinos.
The test statistic used for the CP violation discovery potential is:


2
2 (δ
2
2
χCPV
= min[χBF(6)CP = 0), χBF (δCP = π)] − χBF .
2 (δ2Here, χBF
CP = 0) and χBF (δCP = π) are the best-ﬁt −2log(L) where δCP is ﬁxed to one of the
2 is the best-ﬁt
CP-conserving values. The minimum of these two is used for the test statistic. χBF
minimum of −2log(L) where δCP is allowed to vary. Two cases are treated for the CP violation
studies. In the ﬁrst case, the mass ordering is assumed to be known based on external measurements
and the measurement using the Hyper-K atmospheric neutrinos. In the second case, the constraints
from external measurements and Hyper-K atmospheric neutrinos are not used, in order to estimate thesensitivity from the accelerator neutrinos alone. When the mass ordering is determined with Hyper-K
accelerator neutrinos alone, the sign of m232 is allowed to vary in the minimization procedure. The
test parameter can be interpreted as the signiﬁcance to exclude the CP-conserving hypotheses.
For the evaluation of the δCP measurement precision the ﬁtted value of δCP is scanned and the−2log(L) is minimized at each value of δCP , i.e. the proﬁling method. The δCP values that correspondto a one-unit change in −2log(L) relative to the minimum are taken as the bounds for the 68%
conﬁdence interval. The plotted 1 σ error is the width of the 68% conﬁdence interval divided by two.
The signiﬁcances to reject the wrong mass ordering are shown in Fig. 22, and the fraction ofδCP values for which a given signiﬁcance is achieved is shown in Fig. 23. As is expected basedon Fig. 17, the signiﬁcance is largest for the conﬁguration with the Korean detector at 1.5◦ offaxis since the more on-axis position gives more events in the 1–2 GeV range where the matter
effect is large. For this conﬁguration, the signiﬁcance to reject the wrong mass ordering is greaterthan 6 σ for most values of δCP , and greater than 5 σ for all values of δCP . The signiﬁcance of thewrong mass ordering rejection degrades as the Korean detector is moved to more off-axis locations.
However, even the conﬁguration with the 2.5◦ off-axis Korean detector has 3 σ rejection sensitivity
for most values of δCP , and improved sensitivity over the conﬁguration with one (both) detector(s)in Japan for all (most) values of δCP . Based on this study, it is clear that the sensitivity may be
improved further by adding events above 1 GeV in reconstructed energy. This may be achieved bymoving to a more on-axis position (see Mt. Bisul) or by including multi-ring event reconstructionthat allows the inclusion of higher-energy events with one or more detected pions. Multi-ring event
reconstruction will be the topic of a future study. Based on this study of the conﬁgurations witha detector in Korea, the accelerator neutrinos can provide an alternative measurement of the massordering that is complementary to the measurement using atmospheric neutrinos. By combining thetwo measurements, an even stronger constraint can be obtained, and better sensitivity can be achieved
earlier in the lifetime of Hyper-K.

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Fig. 22. The signiﬁcance for the wrong mass ordering rejection as a function of the true value of δCP and thetrue mass ordering (top=normal, bottom=inverted).

Fig. 23. The fraction of δCP values (averaging over the true mass ordering) for which the wrong hierarchy canbe rejected with a given signiﬁcance or greater.

The plots showing the signiﬁcance to reject the CP-conserving hypotheses are in Fig. 24, and Fig. 25
shows the fraction of δCP values for which a given signiﬁcance can be achieved. The fractions oftrue δCP values for which 3 σ and 5 σ sensitivity are achieved are listed in Table 7. When the massordering is already known, all four two-detector conﬁgurations have similar sensitivity, but the best
sensitivity is available when the Korean detector is placed at 2.0◦ off-axis. It should be mentioned thatin this study, it is assumed that the mass ordering is determined by external experiments and Hyper-K
atmospheric neutrinos with a signiﬁcance greater than the CP conservation rejection signiﬁcancebeing studied. Compared to a single detector in Japan, the conﬁguration with a second detector in
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Fig. 24. The signiﬁcance for CP conservation rejection as a function of the true value of δCP and the true
mass ordering (left=normal, right=inverted). The top row shows the signiﬁcance when the mass ordering isdetermined independently from the accelerator neutrinos, while the bottom row shows the signiﬁcance whenthe mass ordering is determined only by accelerator neutrinos observed in the Hyper-K detectors.

Korea at 2.0◦ off-axis has 3 σ (5 σ ) sensitivity for an additional 7%–8% (13%–14%) of δCP values
depending on the mass ordering. When the mass ordering is only determined by the accelerator
neutrinos, the conﬁguration with the Korean detector at 1.5◦ off-axis gives the largest fraction oftrue δCP values for which a 5 σ discovery is possible. This is true because this conﬁguration has
the best sensitivity to determine the mass ordering, breaking the mass ordering–δCP degeneracy.
For the case with the 1.5◦ off-axis conﬁguration, the dependence of the CP violation discovery
sensitivity on the relative fraction of antineutrino-mode to neutrino-mode operation has been evaluate
for ratios ranging from 3 : 1 (default) to 1 : 3. The fraction of δCP values with a 5 σ discovery
changes by only 0.01 depending on the relative fraction of antineutrino-mode and neutrino-mode
operation.
The evolution of the CP violation discovery potential with exposure is summarized in Fig. 26. At a
20 yr×1.3 MW exposure, the presence of the Korean detector can increase the fraction of δCP values
for which a 5 σ discovery is possible by up to 8%. This is a 27% reduction in the number of δCPvalues for which a 5 σ discovery of CP violation would not be possible.
The δCP measurement precision is shown in Fig. 27, and Fig. 28 shows the fraction of δCP values
for which a given level of precision can be achieved. The conﬁgurations with the Korean detector
give the best δCP precision on average. Near the CP-conserving values, the conﬁgurations with the
2.0◦ and 1.5◦ off-axis Korean detectors have similar precision. However, near the maximally CPviolating values of δCP the 1.5◦ off-axis conﬁguration has 1.5◦ better precision for δCP than the 2.0◦
off-axis conﬁguration. The conﬁguration with the 1.5◦ off-axis Korean detector also improves on
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Fig. 25. The fraction of δCP values (averaging over the true mass ordering) for which the CP-conserving
values can be rejected with a given signiﬁcance or greater. The top ﬁgure shows the signiﬁcance when themass ordering is determined independently from the accelerator neutrinos, while the bottom ﬁgure shows thesigniﬁcance when the mass ordering is determined only by accelerator neutrinos observed in the Hyper-K
detectors.
Table 7. The fraction of true δCP values for which CP violation can be discovered at 3 σ or 5 σ .

JD×1
JD×2
JD+KD at 2.5◦
JD+KD at 2.0◦
JD+KD at 1.5◦

True NH, known
3σ
5σ
0.70
0.47
0.74
0.55
0.76
0.58
0.78
0.61
0.77
0.59

True IH, known
3σ
5σ
0.71
0.48
0.74
0.55
0.76
0.59
0.78
0.61
0.77
0.59

True NH, unknown
3σ
5σ
0.43
0.23
0.52
0.27
0.76
0.48
0.77
0.55
0.77
0.59

True IH, unknown
3σ
5σ
0.41
0.24
0.50
0.28
0.72
0.30
0.79
0.51
0.77
0.59

the precision of the conﬁguration with two detectors in Japan by 3◦ near the maximally CP-violating
values of δCP . The precision for the conﬁguration with two detectors in Japan is 3◦ better than what
is presented in the Hyper-K design report. An improved sensitivity is expected since the Hyper-K
design report assumes a staged approach with the second detector starting operation after six years,
while these studies assume that both detectors start operation simultaneously.
The evolution of the δCP precision with exposure is summarized in Fig. 29. For the worst-case
uncertainty, when δCP is near the maximally CP-violating values, the relative advantage of the detector
in Korea remains constant with exposure. It should be noted that these conclusions depend on thesystematic errors that are assumed, and may change if different levels of systematic uncertainty canbe achieved.
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Fig. 26. The fraction of δCP values (averaging over the true mass ordering) with at least a 5 σ signiﬁcanceto reject the CP-conserving values of δCP . The top ﬁgure shows the signiﬁcance when the mass ordering isdetermined independently from the accelerator neutrinos, while the bottom ﬁgure shows the signiﬁcance whenthe mass ordering is determined only by accelerator neutrinos observed in the Hyper-K detectors.

4.3.1. Sensitivity studies for the Mt. Bisul and Mt. Bohyun sites
The potential Mt. Bisul site is located at a baseline of 1084 km and an off-axis angle of 1.3◦ . The
primary effect of the off-axis angle change from 1.5◦ to 1.3◦ is to decrease the (anti)neutrino ﬂux
at 700 MeV by ∼10% while increasing the ﬂux above 1.2 GeV by ∼50%. With these ﬂux changes,
it is expected that the Mt. Bisul location should provide better sensitivity to determine the massordering, while the CP violation discovery potential may be slightly degraded. The Mt. Bohyunsite is located at a baseline of 1043 km and an off-axis angle of 2.3◦ . With a lower energy ﬂux that
more directly probes the second oscillation maximum, it is expected that Mt. Bohyun should havea slightly improved CP violation discovery sensitivity compared to the Mt. Bisul site, but will haveless sensitivity to the mass ordering.
For the sensitivities presented here, the combinations of the detector in Japan with a detector at
Mt. Bisul or Mt. Bohyun are shown. For comparison, the sensitivity with two detectors in Japan isshown. Here, the sensitivities are shown as a function of true δCP and the band of sensitivities shows
the variation of the sensitivity for the range of true sin2 θ23 values between 0.4 and 0.6.
The wrong mass ordering rejection signiﬁcances including the Mt. Bisul and Mt. Bohyun conﬁgurations are shown in Fig. 30. The wrong mass ordering rejection signiﬁcance is largest for the
Mt. Bisul conﬁguration for all true values of the mass ordering and δCP , and is above 6 σ for almost
all true values of the oscillation parameters. The mass ordering rejection sensitivity with the Mt.
Bohyun site is above 3 σ for almost all true values of the oscillation parameters and higher than the
conﬁguration with two detectors in Japan for most values.
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Fraction of δcp

Fig. 27. The 1 σ precision of the δCP measurement as a function of the true δCP value. Here, it is assumed that
there is no prior knowledge of the mass ordering.
1
0.8
0.6
0.4

JD×1
JD×2
JD+KD at 2.5°
JD+KD at 2.0°
JD+KD at 1.5°

0.2
0

0

5

10

15

20

25
σδ (°)
cp

Fig. 28. The fraction of δCP values (averaging over the true mass ordering) for which a given precision or
better on δCP can be achieved.

The CP conservation rejection signiﬁcances including the Mt. Bisul and Mt. Bohyun conﬁgurations
are shown in Fig. 31. There is little change to the fraction of δCP values with 3 σ or 5 σ rejection
compared to the conﬁguration with the Korean detector at 1.5◦ and 2.5◦ off-axis. For the scenarios
where the mass ordering is determined by the accelerator neutrinos only, better CP conservation
rejection with Mt. Bisul is achieved for some values of δCP where the improved wrong mass ordering
rejection impacts the CP violation measurement.
The δCP precision is shown in Fig. 32. Near the maximally CP-violating values, the Mt. Bisul
site has the best precision, indicating that the measurement is in part due to the spectrum distortionin the > 1 GeV region arising from the cos(δCP )-dependent term. Near the CP-conserving values,
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Fig. 29. The evolution of the δCP measurement precision with exposure. The “Minimum” and “Maximum”
errors are the uncertainties at the true δCP and mass ordering values with the best and worst measurement
resolution, respectively.

Fig. 30. The signiﬁcance for the wrong mass ordering rejection as a function of the true value of δCP and the true
mass ordering (top=normal, bottom=inverted). Results are shown for the Mt. Bisul and Mt. Bohyun sites. The
bands represent the dependence of the sensitivity on the true value of sin2 θ23 in the range 0.4 < sin2 θ23 < 0.6.

the conﬁgurations with the Mt. Bisul and Mt. Bohyun sites give nearly identical precision. Bothconﬁgurations with a detector in Korea show improved precision compared to the conﬁguration withtwo detectors in Japan for almost all true values of the oscillation parameters.
4.3.2. Atmospheric parameters and octant sensitivity
The Korean detector has enhanced sensitivity for the CP violation and CP phase measurements dueto the L/E dependence in the δCP -dependent interference terms of the electron (anti)neutrino appearance probability. No such enhancement is present in the leading terms of the muon (anti)neutrino
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Fig. 31. The signiﬁcance for CP conservation rejection as a function of the true value of δCP and the true massordering (left=normal, right=inverted). The top row shows the signiﬁcance when the mass ordering is determined using external data and Hyper-K atmospheric neutrinos, while the bottom row shows the signiﬁcancewhen the mass ordering is determined only by accelerator neutrinos observed in the Hyper-K detectors. Results
are shown for the Mt. Bisul and Mt. Bohyun sites. The bands represent the dependence of the sensitivity on
the true value of sin2 θ23 in the range 0.4 < sin2 θ23 < 0.6.

survival probability or the electron (anti)neutrino appearance probability. Since the leading terms inthese probabilities provide the constraints on m232 and sin2 θ23 we may expect no advantage for a
conﬁguration with one detector in Japan and one in Korea over a conﬁguration with two detectors inJapan. In fact, there may be a reduced sensitivity with one detector in Korea due to the lower statistics
at the longer baseline. We have studied the sensitivity to m232 and sin2 θ23 as well as the θ23 octant
determination in conﬁgurations that include detectors in Japan and Korea or detectors only in Japan.
Figure 33 shows the 2 σ sensitivities for the m232 and sin2 θ23 parameter determination for different
true values of these parameters. There is a reduction in the sensitivity when a conﬁguration with aJapanese and Korean detector is used relative to a conﬁguration with two Japanese detectors, but the
reduction in sensitivity is not large. Figure 34 shows the signiﬁcance of the octant determination as
a function of the true value of sin2 θ23 for different detector conﬁgurations. The addition of a second
detector in Japan or Korea does little to improve the octant sensitivity.
From the sensitivity studies presented here, we conclude that a conﬁguration with one detector inJapan and the second in Korea has similar but slightly worse sensitivity for atmospheric parameter
determination than a conﬁguration with two detectors in Japan. The measurement program for these
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Fig. 32. The 1 σ precision of the δCP measurement as a function of the true δCP value. Results are shown for
the Mt. Bisul and Mt. Bohyun sites. The bands represent the dependence of the sensitivity on the true value ofsin2 θ23 in the range 0.4 < sin2 θ23 < 0.6.

parameters will not be signiﬁcantly degraded in a conﬁguration where the second detector is in
Korea.

5.

Sensitivities with long-baseline and atmospheric neutrinos

In addition to neutrino data from the J-PARC beam, Hyper-K will collect atmospheric neutrino data,
which will add sensitivity to its oscillation measurements. These neutrinos are produced in decaysof particles emerging from the interaction of primary cosmic rays with nuclei in the atmosphere.
Indeed, the production mechanism is identical to that of beam neutrinos, with the notable exceptionthat the lack of an absorber results in a signiﬁcant fraction of νe and ν̄e in the ﬂux. Up to ∼10 GeV,
the ratio of muon- to electron-type neutrinos is roughly 2 : 1, with the fraction of muon neutrinos
increasing at higher energies. Since the primary cosmic ray ﬂux spans several orders of magnitude
and is roughly isotropic about the Earth, the resulting atmospheric neutrino spectrum covers anequally wide range of energies and a given detector can expect to observe neutrinos with a variety ofpathlengths from O(10) km, for neutrinos produced overhead, to ∼10,000 km, for those producedon the opposite side of the planet. Importantly, these events will be accumulated at both detectors
in Japan and Korea in similar proportion, modulo differences in the atmospheric densities and the
local geomagnetic ﬁelds.
Though atmospheric neutrinos lack the precise timing and directional information afforded by thebeam, they offer a high-statistics sample, roughly 150 × 103 events/Mton-year, with large matter
effects. These matter effects provide mass hierarchy sensitivity in a manner analogous to the beam
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Fig. 33. Two-σ sensitivity curves for the atmospheric parameter determination at true values ofm232 = 2.67 × 10−3 eV2 and sin2 θ23 = 0.4 (top), m232 = 2.67 × 10−3 eV2 and sin2 θ23 = 0.6 (middle),
m232 = 2.51 × 10−3 eV2 and sin2 θ23 = 0.514 (bottom).

neutrinos, but more enhanced oscillations. Neutrinos traversing the core of the Earth pass througha matter proﬁle whose density varies from 1 to 13 g cm−3 , which induces a parametric oscillation
resonance for energies between 2 and 10 GeV. For neutrinos experiencing this effect the νμ → νe(appearance channel) oscillation probability can be as large as 50% (Fig. 35). This effect depends on
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Fig. 34. The signiﬁcance of the octant determination as a function of the true value of sin2 θ23 for different
detector conﬁgurations.

Fig. 35. Atmospheric neutrino oscillation probabilities as a function of energy and cosine of the neutrino zenith
angle (−1 corresponds to upward-going). The left (right) plot shows the νμ → νe (ν̄μ → ν̄e ) probability. In
this plot the normal mass hierarchy is assumed. For an inverted hierarchy the features in the neutrino plot moveto the antineutrino plot and vice versa.

both the sign of the mass hierarchy and whether the neutrino is a particle or antiparticle; for a normal(inverted) mass hierarchy only neutrinos (antineutrinos) undergo these oscillations. Sensitivity to
the mass hierarchy is obtained by studying the upward-going electron neutrino event rate in thisenergy region. It should be noted that this sample will provide a test of the mass hierarchy largely
independent of the beam measurement.
Resonant oscillations in the Earth also depend on the value of sin2 θ23 . Not only does it affect theappearance of electron neutrinos described above, but it also impacts the upward-going muon rate.
Atmospheric neutrino sensitivity to the mixing parameters m232 and θ23 is driven primarily by theoscillation of νμ → ντ ,e seen in this sample, and these matter effects provide additional power todiscriminate the octant of θ23 .
At energies below a few GeV atmospheric neutrinos carry additional sensitivity to δCP , again
through an appearance channel. However, with no precise knowledge of the incoming neutrino
direction and poor correlation between the outgoing lepton from an interaction and its parent neutrino
direction at these energies, the atmospheric neutrino sensitivity is weaker than that from the beam
sample.
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Fig. 36. Sensitivity to the normal mass hierarchy for components of a combined measurement of beam andatmospheric neutrinos for a ten-year exposure. Here, JD refers to a single Hyper-K detector in Kamioka, Japan,
and JD×2 refers to two such detectors operating simultaneously. The horizontal axis shows the assumed valueof sin2 θ23 , and the width of the bands shows the variation in sensitivity with δCP .

5.1.

Combination of beam and atmospheric neutrino data

As described above, atmospheric neutrinos provide complementary sensitivity to the same oscillation
physics as the beam neutrino samples. Though there are common systematic error effects between
the two samples from the cross section and detector modeling, the disparate energy regimes and ﬂux
systematics allow for a nearly independent study of oscillations. More importantly, the atmospheric
neutrino data are accumulated continuously and independently of the beam, such that the combinationof the two samples provides improved sensitivity on shorter time scales. In this section we present
a combined analysis of beam and atmospheric neutrino data assuming a Hyper-K detector in Japan(JD) and at the Mt. Bisul site (off-axis angle 1.3◦ ) and compare with sensitivities assuming two
detectors in Japan (JD×2). The treatment of the atmospheric neutrino samples and their systematic
errors follows that of Super-Kamiokande, with no assumed improvements (cf. the discussion in
Ref. [44]).
Figure 36 shows the sensitivity to the mass hierarchy for the combined analysis using the sametest statistic as Eq. 5. Afterten years of running, the expected ability to reject the wrong mass
2hierarchy is better than χ = 7. Atmospheric neutrinos by themselves provide sensitivity better
than χ 2 > 3 for all currently allowed values of sin2 θ23 and have comparable sensitivity to
the beam measurement at the Korean detector for the largest values of this parameter. Though the
combined JD and Mt. Bisul beam measurement has better sensitivity than the atmospheric neutrino
measurement alone, when all of the samples are combined the sensitivity improves further. The
power of this improvement manifests as an earlier realization of the hierarchy,
 as shown in the left
panel of Fig. 37. Within two years of operation the sensitivity will exceed χ 2 > 4.
Sensitivity to sin2 θ23 for the combined analysis and its components appears in Fig. 38. Here, thetest statistic reﬂects the ability to reject the incorrect octant as
Toctant =
2 − χ 2 ,
χWO
CO

(7)

2 and χ 2 represent the minimum likelihood value taken over the wrong and correctwhere χWO
COoctants, respectively. The minimum for the ﬁrst (second) octant is taken over values of the likelihoodin the range of parameters sin2 θ23 < 0.5 (> 0.5). If θ23 differs from maximal mixing by 2◦ or more,

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Fig. 37. Sensitivity as a function of year to the mass hierarchy (left) and the fraction of δCP phase space forwhich CP violation (sin δCP = 0) can be determined at 3 σ or better. Red lines show a combined beam andatmospheric neutrino measurement with one Hyper-K detector in Kamioka, Japan (JD) and one at the Mt.
Bisul site in Korea. Cyan lines show the same analysis assuming two detectors in Kamioka (JD×2), and graylines assume only one detector in Kamioka (JD×1). Different symbols show the assumed value of sin2 θ23 .

the octant will be resolved at better that three units of the test statistic. As shown in the ﬁgure, thismarks a considerable improvement over the beam-only measurement.
While atmospheric neutrinos themselves have less sensitivity to δCP than the beam measurement,
they provide additional constraints on extreme values of the parameter as shown in Fig. 39. Typically,
the atmospheric neutrino constraint covers about 50% of the parameter space, such that one of the
CP-conserving points sin δCP = 0 is weakly allowed regardless of the parameter’s true value. For
this reason, the constraint on CP violation shown in Fig. 40 is weaker than that from the beam andprovides only a slight improvement in sensitivity. The test statistic used in this ﬁgure is the sameas in Eq. 6. However, as with the other oscillation measurements the power of the combined beam
and atmospheric measurement comes in the early realization of this sensitivity (cf. the right panel ofFig. 37).

6. Additional beneﬁts
In addition to the long-baseline program with multiple baselines, there are potential beneﬁts to theHyper-K physics program by placing a second detector in Korea. There are two main beneﬁts thatarise from the second Hyper-K detector in Korea. First, the candidate sites for a Korean detector are
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Fig. 38. Sensitivity to the θ23 octant (right) assuming the normal mass hierarchy for components of a combined
measurement of beam and atmospheric neutrinos for a ten-year exposure. The plot has been produced in thesame manner as Fig. 36.

Fig. 39. Sensitivity to δCP = 0 for components of a combined measurement of beam and atmospheric neutrinos
for a ten-year exposure. Here, JD refers to a single Hyper-K detector in Kamioka, Japan.

Fig. 40. Sensitivity to CP violation (sin δCP = 0) for components of a combined measurement of beam andatmospheric neutrinos for a ten-year exposure. Here, JD refers to a single Hyper-K detector in Kamioka, Japan,
and JD×2 refers to two such detectors operating simultaneously. The horizontal axis shows the assumed true
value of δCP .

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Table 8. Position and altitude for simulated locations.

LatitudeLongitude
Altitude (820 m overburden)
Altitude (1000 m overburden)

Mt. Bisul

Mt. Bohyun◦

36◦ 09 47 N
128◦ 58 26 E
304 m
124 m





35 43 00 N
128◦ 31 28 E
264 m
84 m

deeper than their Japanese counterparts, providing a greater overburden to reduce the ﬂux of cosmic
ray muons. This translates into a reduced rate of spallation-induced isotopes that are backgrounds tolower-energy physics, such as solar and supernova neutrino studies. Second, the large geographicalseparation between the Japanese and Korean detectors provides two horizons for studying supernova
neutrinos. For a supernova burst, the likelihood of observing neutrinos below at least one of thehorizons is increased, allowing broader study of the Earth-matter effect on these events. This section
explores the potential beneﬁts to the Hyper-K physics program beyond studies of PMNS mixing
provided by a Korean detector.

6.1.

Solar and supernova neutrino physics

Observations of low-energy neutrinos, such as those from the Sun (E < 10 MeV) or the diffuse
supernovae ﬂux (E < 30 MeV), are complicated by backgrounds from natural sources. Amongthese cosmic-ray-muon-induced spallation products, which decay to produce photons or electronsof similar energies, are a background that can be readily mitigated with the larger overburden afforded
by a detector in Korea. The rate of such spallation backgrounds at each of the candidate sites has
been estimated with simulations based on their local tomographies.

6.1.1. Estimate of muon spallation background
The muon ﬂux and average energy at each site are estimated using the muon simulation code MUSIC[47,48], a three-dimensional Monte Carlo (MC) tool dedicated to muon transportation in matter.
Elevation data for the areas around Mt. Bisul and Mt. Bohyun have been extracted from the “ALOS
World 3D-30m” database published by JAXA [50] for input to the simulation. The latitude, longitude,
and altitude of each of the simulated locations are summarized in Table 8. For both Mt. Bisul
and Mt. Bohyun, simulations assuming 820 m and 1000 m overburdens have been performed using
muons that are generated at the surface following the parameterization in Ref. [49]. The rock typeis assumed to be the same as the Super-K site (Inishi rock) with a density of 2.70 g cm−3 . Table 9summarizes the calculated muon ﬂux () and average energy (E μ ) at the Mt. Bisul, Mt. Bohyun,
Hyper-K (Tochibora), and Super-K sites. Based on the uncertainty of the exact rock composition,
the uncertainty of the muon ﬂux is assumed to be ±20%.
Figure 41 shows the calculated muon energy spectra for Hyper-K (Tochibora, 650 m overburden),
Mt. Bisul (1000 m overburden), Mt. Bisul (1000 m overburden), and Super-K. The corresponding
ﬂuxes as a function of zenith and azimuthal angles are shown in Fig. 42. Note that the absolute ﬂux andshape of the Super-K data are reproduced well by the simulation. Further, with 1000 m overburdens,
the Korean sites are expected to have similar muon ﬂuxes and energies as those observed at Super-K.
For the shallower 820 m overburden the ﬂux is expected to increase by more than a factor of two
according to Table 9). Using this information the muon ﬂux ratio at Mt. Bisul relative to Super-K,
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Table 9. Calculated muon ﬂux () and average energy (E μ ) at Mt. Bisul, Mt. Bohyun, Hyper-K, andSuper-K.
Detector site (overburden) (10−7 cm−2 s−1 )E μ (GeV)

Mt. Bisul (820 m)
Mt. Bohyun (820 m)
Mt. Bisul (1000 m)
Mt. Bohyun (1000 m)
Hyper-K (Tochibora, 650 m)
Super-K

3.81
3.57
1.59
1.50
7.55
1.54

233
234
256
257
203
258

Fig. 41. Calculated muon energy spectra for Hyper-K (Tochibora), Mt. Bisul (1000 m overburden), Mt. Bohyun(1000 m overburden), and Super-K, based on the MUSIC simulation.

(HKKBisul )/(Super-K), is estimated to be 1.03 ± 0.21 (2.47 ± 0.49) assuming a 1000 m (820 m)
overburden.
Based on these calculated muon ﬂuxes, isotope production rates due to muon spallation havebeen calculated using FLUKA [45,46] version 2011.2b. The isotope yield per muon track length, Y ,depends on the muon energy, which increases with larger overburdens. As a result, the isotope yield
per muon becomes larger for deeper experimental sites. For the 1000 m overburden case the averagemuon energy is similar to that of Super-K, and thus the ratio of their isotope yields per muon are
similar: 1.03 ± 0.21. The same ratio calculated for the Hyper-K (Tochibora) site is about 0.8 [25].
Interpolating from these two, the isotope yield per muon for the 820 m overburden is estimated tobe 0.9, and similarly the isotope production rate for 820 m overburdens becomes about 2.22 ± 0.44
larger than that at Super-K. In contrast, the Tochibora site is estimated to be about 4 ± 1 times larger.
For similar overburdens the isotope yield is not expected to differ largely between the two Koreansites. Accordingly, the yield is expected to be between two to four times smaller than at the Tochibora
site in Japan.
6.1.2. Potential beneﬁts
Lower spallation backgrounds at a Korean detector will result in improved sensitivity to solar neutrinos. The day–night asymmetry in the rate of solar neutrinos due to Mikheyev–Smirnov–Wolfenstein(MSW) matter effects in the Earth [51–53] is expected to be larger for the higher-energy region of
the 8 B neutrino spectrum, where spallation is the dominant background source. Neutrinos from the
Hep reaction chain fall in a similar energy region, and as they are produced in a different region of the
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Fig. 42. Muon ﬂux as a function of the cosine of the zenith angle, cos θ, (upper) and azimuth angle φ (lower)for Hyper-K (Tochibora), Mt. Bisul (1000 m overburden), Mt. Bohyun (1000 m overburden), and Super-K.
Here, zero degrees represents the eastern direction. The blue lines show the data from Super-K, while the redlines show the MC prediction from the MUSIC simulation of the Tochibora (solid), Mt. Bisul (dashed), and
Mt. Bohyun (dotted) sites.

solar interior they can potentially provide new information on solar physics. With lower spallation
backgrounds, the short-time variability of the temperature in the solar core could be monitored more
precisely with these neutrinos. Further, lower backgrounds in the higher-energy sample can improve
resolution of the solar neutrino spectrum shape, whose lower-energy region is a sensitive probe ofmatter effects, both standard and otherwise, in the Sun.
Spallation backgrounds can be rejected based on their correlation with preceding muons. For solar
neutrino analysis, the effect of spallation reduction is estimated, keeping the signal efﬁciency to80%. The remaining spallation fraction is estimated, based on a study using Super-K data, to be
1.2% (2.3%) for the 1000 m (820 m) overburden. This can be compared to 3.9% estimated for theHyper-K Tochibora site.
The search for the diffuse ﬂux of neutrinos produced by all supernova explosions since thebeginning of the universe, the supernova relic neutrino (SRN) ﬂux, similarly beneﬁts from larger
overburdens. For the SRN analysis, because the signal ﬂux is expected to be only a few tens/cm2 /thesmall signal ﬂux, a more stringent event selection requiring a negligible spallation background contribution is used. In this case, the signal efﬁciency is 79% (56%) for neutrinos reconstructed withenergies between 17.5 and 20 MeV and 90% (75%) between 20 and 26 MeV for the 1000 m (820 m)
overburden site. These can be compared to 29% and 54%, respectively, for Hyper-K at Tochibora.
Above 26 MeV the spallation background decreases exponentially, but the signal is overwhelmed bybackgrounds from atmospheric neutrinos. In this way, reduced spallation backgrounds will enhance
the SRN detection capability, particularly below 20 MeV. After ten years of operation, the numberof events and the signiﬁcance of non-zero observation of SRN are 100 (90) events and 5.2 σ (4.8 σ ),respectively, for the 1000 m (820 m) overburden site in Korea assuming the SRN ﬂux of Ref. [55].
Hyper-K at Tochibora is expected to observe 70 events with a corresponding signiﬁcance of 4.2 σ .
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It is worth noting that the ability to observe neutrons via high-photon-yield photosensors or
gadolinium doping will provide other physics opportunities for a Korean detector. Among these,
the observation of neutrinos from nuclear reactors in Korea via their inverse beta decay reactions
becomes possible. Similarly, such neutron tagging is expected to provide highly efﬁcient suppressionof atmospheric neutrino backgrounds to searches for proton decay. Detailed studies of the expected
sensitivity of such measurements is planned for a future document.

6.2.

Neutrino geophysics

The inner Earth’s chemical composition is one of the most important properties of our planet. While
the matter density is well known through seismic measurements [67], the chemical composition
is much less understood [54]. Neutrino oscillations depend on the electron density of the medium
traversed by the neutrinos [51,52], and hence the electron density distribution of the Earth can bereconstructed from the neutrino energy spectrum. Accordingly, the chemical composition of the
Earth can be constrained for a given mass density distribution [56,57]. Hyper-K is expected to be theﬁrst experiment that could experimentally conﬁrm that the Earth’s core is composed of iron, rulingout lead or water scenarios at the 3 σ level [25]. The measurement relies on precisely measuring
atmospheric muon neutrino disappearance and electron neutrino appearance in the energy range
between 1 and 8 GeV as a function of the zenith angle. This measurement is limited by the reduced
neutrino ﬂux at these energies, such that a detector in Korea will double the statistics available.
If a supernova occurs such that the neutrinos travel through the Earth before reaching the detector,
i.e. below the detector’s local horizon, they will be subject to energy-dependent matter effects.
This would manifest as a distortion of the energy spectrum of neutrinos or antineutrinos dependingon the mass hierarchy, which can be observed under favorable conditions [58,60]. Having two
geographically separated detector locations increases the likelihood of the Earth shadowing theneutrino ﬂux reaching one of the detectors. In addition, comparing the energy spectra in two detectorsthat observe different shadowing scenarios (see Fig. 43) may make it easier to disentangle matter
effects from supernova burst neutrino properties.

6.3.

Dark matter searches

Hyper-K can search for physics beyond the standard model in the form of self-annihilating dark matter
captured in the Sun or the Earth, or from the Galactic dark matter halo. Super-K has demonstrated thisphysics potential through the world’s best constraints on spin-dependent scattering of dark matterwith matter [61]. Hyper-K can improve upon Super-K’s results and is expected to provide the bestindirect dark matter search sensitivities for masses below 100 GeV. As the background to a neutrinosignal from dark matter annihilation in the Sun comes from atmospheric neutrinos, a beneﬁt from asecond site could come from reduced systematic uncertainties associated with atmospheric neutrino
ﬂuxes. A neutrino signal originating from the decays of the dark matter annihilation products in the
Sun is also accompanied by a high-multiplicity stopped meson decay low-energy neutrino signal
from hadronic showers of the annihilation products in the center of the Sun [62–64]. The expectedsignal consists of neutrinos of a few tens of MeV from muon decays at rest in the Sun, as well as
neutrino line signals at 29.8 MeV and 235.5 MeV from two-body charged pion and kaon decays atrest. The possible addition of gadolinium in water [65] would reduce (invisible muon) backgrounds
signiﬁcantly for this signal, which can very efﬁciently be detected through the inverse beta decay
reaction [62].
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Fig. 43. Due to the distance between the Korean (KD) and Japanese (JD) detector locations, both detectors
could observe a supernova neutrino burst with different Earth shadowing. In scenario 1 (solid black arrows),
one detector would observe an unshadowed ﬂux, while neutrinos detected in the other detector would travel
through the Earth for up to 1800 km. In scenario 2 (dashed purple arrows), one detector would be shadowed by
the Earth’s mantle (yellow) only, while the other detector would be shadowed by the mantle and the outer core
(blue). While the resulting difference in path length is small, up to 4400 km of the path of neutrinos reaching
one detector would go through the outer core instead of the mantle. Since the matter density of the outer coreis much larger than that of the mantle, the matter effect along these two paths would be markedly different.
Using an online tool for calculating Earth crossing probabilities for different detector locations, we ﬁnd thatthe combined probability of these two scenarios is 6.4% [59]. (The difference between Mt. Bohyun and Mt.
Bisul is < 0.1%.)

6.4.

Modiﬁcations to neutrino propagation

T2HKK can also be a powerful probe of non-standard physics affecting neutrino propagation, in particular effects observable as modiﬁcations to the standard PMNS survival or appearance probability.
In Ref. [66], various types of non-standard physics scenarios for a beam experiment with detectors
in both Korea and Japan were considered, including models of quantum decoherence, violations ofLorentz symmetry with and without charge, parity, and time invariance, and non-standard neutrino
interactions with matter. In most cases, conﬁgurations with a large detector in both countries havesigniﬁcantly improved sensitivity to such types of new physics, relative to having the equivalentdetector mass in just one of them. Not only do the two baselines provide a more complete measure of
the neutrino spectrum, and hence distortions arising from new physics, but they also provide distanceL/E ranges to constrain scenarios with non-oscillating (or with oscillating admixtures) L/E effects.
See Tables I and II and Fig. 6 of Ref. [66] for more details. As one example, the expected sensitivity
to an enhanced matter effect caused by non-standard interactions is presented in the next section.

6.5.

Potential for improvement with a CC1π event selection

For Korean detector sites with a smaller off-axis angle, a harder (anti)neutrino spectrum is present.
The (anti)neutrinos above 1 GeV probe the ﬁrst oscillation maximum and the region between theﬁrst and second oscillation maxima. These (anti)neutrinos are important for determining the massordering, and measuring δCP if the phase is near π/2 and 3π/2. The quasi-elastic scattering crosssection is nearly constant above 1 GeV, while the rate of other processes that include pion production
increases. Higher statistics in the >1 GeV region may be achieved by including candidate eventswith evidence of pion production in addition to the charged lepton. These additional candidate events
may include events where a Michel electron from a pion decay chain is detected, or where a pion is
directly detected by the reconstruction of a second visible ring in the detector. The inclusion of thesepion production events will be the subject of future studies.
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7.

K. Abe et al.

Sensitivity of T2HKK to non-standard interactions

In this section we discuss the capability of the T2HKK experiment to put constraints on non-standard
interactions (NSI) in neutrino propagation. We present our results for only the 1.5◦ off-axis and normal
mass ordering. However, at the end we will comment on the results for other off-axis conﬁgurationsof T2HKK and also for inverted ordering. The discussions in this section are based on Refs. [68,69].

7.1.

Non-standard interactions

In the presence of ﬂavor-changing neutral currents the standard neutrino–matter interaction potential is modiﬁed, allowing for neutrino ﬂavor change via neutral current interactions with matter[51,70–73]. The presence of such NSI effects can be studied in neutrino oscillation experiments,
especially in long-baseline and atmospheric neutrino oscillation experiments where the neutrinos
experience the Earth matter effect of long distances. Theoretically this kind of interaction can arise
from the following four-fermion interaction:√ ff  P 

μ 
LNSI
=
−2
2
ε
G
ν
γ
ν
f
γ
f
(8)
F
αL
μ
βL
P
eff
P ,
αβ
ff  P

where fP and fP are fermions with chirality P, εαβ is a dimensionless constant, and GF is the Fermi
coupling constant. If these kinds of interactions exist in nature, then the MSW matter potential looks
like:
⎛
⎞
ε
ε
1
+
ε
ee
eμ
eτ
√
⎜
⎟
A ≡ 2GF Ne ⎝ εμe(9)εμμ εμτ ⎠,ετ eετ μ ετ τwhere εαβ is deﬁned byεαβ ≡ Nf f
ε ,
Ne αβ

(10)

f =e,u,dwith Nf (f = e, u, d) representing the number density of the fermions f . Here we deﬁne the NSI
f
ffL
ffR
parameters as εαβ = εαβ + εαβ . The present 90% conﬁdence level bounds on the NSI parameterscoming from non-oscillation experiments are compiled in Refs. [76,77]. Using the formula

εαβ 

 

eP
εαβ

2

+



uP
3εαβ

2

+



dP
3εαβ


2  1/2(11)

P

for neutral Earth-like matter with an equal number of neutrons and protons, Ref. [77] gives thefollowing bounds on εαβ :⎛⎜⎝|εee | < 4 × 100|εeμ | < 3 × 10−1|εμμ | < 7 × 10−2f⎞|εeτ | < 3 × 100⎟|εμτ | < 3 × 10−1 ⎠.
|ετ τ | < 2 × 101(12)

The bounds on the NSI parameters εαβ from oscillation experiments are given in Table 2 of Ref. [73]for f = d. From Eq. (12) it is clear that the bounds on εee , εeτ , and ετ τ are at least one order of
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Table 10. Systematic uncertainties assumed for the sample normalization (in percentages) for a single detector
at the T2HKK and T2HK experimental conﬁgurations. The “T2HK” column corresponds to the systematic
errors of the Kamioka detector (for T2HK the numbers are same for both the detectors), and the “T2HKK at
1.5◦ ” column corresponds to the systematic error of the Korean detector. (For the T2HKK setup, the systematic
error of the Kamioka detector is given by the “T2HK” column and the systematic error of the Korean detector
is given by the “T2HKK at 1.5◦ ” column).
Setup
νe eventsν̄e events
νμ eventsν̄μ events

T2HKK at 1.5◦

T2HK

3.84
4.11
3.83
3.81

4.71
4.47
4.13
4.15

magnitude weaker compared to the other NSI parameters. Thus, in order to keep the number ofparameter combinations to a manageable level, this section uses the following ansatz:
⎛
⎞
0
ε
1
+
ε
ee
eτ
√
⎜
⎟
A = 2GF Ne ⎝(13)00 0 ⎠.
∗εeτ
0 ετ τ
Therefore, the NSI parameters of interests are εee , |εeτ |, ετ τ , and arg(εeτ ) = φ31 . In the limitm221 → 0 it is known [88–90] that the oscillation probability depends only on δCP + φ31 , and wetherefore expect similar dependence on φ31 as on δCP .
For the simulation of the T2HKK experiment, we have taken the experimental conﬁguration fromthe detector setup in Sect. 2 and consider the highest energy (or least off-axis) conﬁguration at 1.5◦ .
We also compare our results with the T2HK setup, that is the JD×2 conﬁguration. We assume a3 : 1 ratio of antineutrino and neutrino running. For this analysis we incorporate systematics by themethod of pulls and considered four pull variables including a signal normalization, a backgroundnormalization, a signal tilt, and a background tilt. Namely, the numbers of signal (Sj ) and background(Bj ) events are scaled as Sj → Sj [1 + σs ξs + σstilt ξstilt (Ej − Emin )/(Emax − Emin )], Bj → Bj [1 + σb ξb +σbtilt ξbtilt (Ej −Emin )/(Emax −Emin )], where σs , σb , σstilt , σbtilt (ξs , ξb , ξstilt , ξbtilt ) are the systematic errors (the pullvariables) for a signal normalization, a background normalization, a signal tilt, and a backgroundtilt, respectively; Emax and Emin are the maximum and minimum energies; and Ej is the energy of
the jth bin. Hence, we understand that the normalization errors affect the scaling of the events,
whereas the tilt errors affect their energy dependence. Throughout the analysis we have ﬁxed thetilt error to 10%. A total normalization error for each detector location and event sample is used aslisted in Table 10; the magnitudes of these errors are taken from Table 6. The same normalization
error for signal and background are used, and all systematics are considered to be uncorrelated.
Unlike the PMNS-driven oscillation sensitivities described in the previous sections, this analysis has
been performed using the GLoBES [82,83] package with the MonteCUBES [84] NSI probability
engine.

7.2.

Constraining NSI parameters

First we discuss the ability of the T2HKK experiment to constrain the magnitudes of the NSIparameters εee , |εeτ |, and ετ τ . For this purpose we assume that the values of these parameters are
zero and present our results as limits in the εee –|εeτ | plane. The assumed true value of φ31 is zero andit has been marginalized over in the presentation of the results. The PMNS oscillation parameters
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Fig. 44. Ability of T2HKK to constrain the magnitude of the NSI parameters at 3 σ for θ23 = 45◦ andδCP = 270◦ with the normal hierarchy. The red lines show the comparison for two detectors at the Kamiokasite. The other lines show the effect of the uncertainty on the value of the mass splittings.

δCP and θ23 are marginalized over as well, whereas θ13 , θ12 , m221 , and m231 have been kept ﬁxed
close to their globally preferred values [85–87] and are not varied unless otherwise mentioned.
In Fig. 44, we present the sensitivities with PMNS parameters held at their currently favoredvalues: θ23 = 45◦ and δCP = 270◦ . In the left, middle, and right panels the 3 σ allowed region is
given in the εee –|εeτ |, εee –ετ τ , and ετ τ –|εeτ | planes, respectively. In each panel the NSI parametersthat are not plotted have been marginalized over. Here, and elsewhere unless otherwise noted, themarginalization is made over the ranges −4 to +4 for εee , 0 to 2 for |εeτ |, and −1 to +1 for ετ τ . We
have additionally checked that the χ 2 minima do indeed always appear within these chosen ranges of
εαβ . The purple curve in each panel shows the allowed region when m221 and m231 are kept ﬁxed in
the test spectrum. The green dotted curves and blue dashed curves show the effect of marginalizing
over these parameters. It is clear that the uncertainty in m231 has no effect on the sensitivity, whereas
the allowed region increases slightly when we marginalize over m221 .
To demonstrate how the sensitivity is improved by using a Korean detector, we also show theequivalent result for the JD×2 conﬁguration in Fig. 44 (red curves). It can be seen that this conﬁguration provides signiﬁcantly weaker constraints. Indeed, in this case it is necessary to extend
the marginalization range of ετ τ out to ±4 since there is still a signiﬁcant posterior probability outside the original region. From all three panels, we note that the sensitivity of the KD+JD (T2HKK)
conﬁguration is far better than the equivalent JD×2 conﬁguration, let alone the baseline single-tank
design. This is essentially the same effect as seen in the standard PMNS oscillation model, with thelonger baselines and the higher energies both enhancing the matter effect.
Next, we study the capability of T2HKK to constrain the NSI parameters assuming different
values of θ23 and δCP . Figure 45 shows how changes in these parameters within their current allowed
regions affect T2HKK’s constraints in the εee –|εeτ | plane. The left, middle, and right panels showδCP = 90◦ , 180◦ , and 270◦ , respectively. In each panel, the purple, blue, and green curves correspondto θ23 = 41◦ , 45◦ , and 49◦ , respectively. From the ﬁgure we note that the sensitivity is best forδCP = 180◦ and worst for δCP = 270◦ . The sensitivity for θ23 = 45◦ is the weakest in comparison
to the other two tested values.
Even at O(1000) km, there will be over a thousand events in the data samples at a Korean detector,
such that the statistical error on the event rate is a few percent. As a result, systematic errors are
expected to play an important role, so we next study their impact on T2HKK’s ability to constrain
the magnitude of the NSI parameters. To do this, we again examine the same εee –|εeτ | space as inFig. 45, but for four different values of the systematic errors. In these plots a systematic error of N %implies a normalization error of N % applied to both signal and background events, both electron and
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Fig. 45. Ability of T2HKK to constrain the magnitude of the NSI parameters at 3 σ for different true valuesof θ23 and δCP with the normal hierarchy.

Fig. 46. Ability of T2HKK to constrain the magnitude of the NSI parameters at 3 σ for different values of the
PMNS parameters with the normal hierarchy. The columns correspond to (from left to right) θ23 = 41◦ , 45◦ ,and 49◦ , and the rows are for (from top to bottom) δCP = 90◦ , 180◦ , and 270◦ .

muon events, and both neutrinos and antineutrinos. The dependence can be seen in Fig. 46. Here,rows correspond to (from left to right) δCP = 90◦ , 180◦ , and 270◦ . In each row the ﬁrst, second, andthird panels correspond to θ23 = 41◦ , 45◦ , and 49◦ , respectively. In all cases, we can see that thelimits on the axes (i.e. with one of the two parameters held at zero) are not substantially affected
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Fig. 47. Ability of T2HKK to constrain the two CP phases at 90% conﬁdence level assuming the normal
hierarchy. The left, middle, and right panels correspond to θ23 = 41◦ , 45◦ , and 49◦ , respectively, and the
purple, blue, and green contours correspond to φ31 (true) = 90◦ , 180◦ , and 270◦ , respectively. The + signs ineach panel correspond to the true values of (δCP , φ31 ).

by systematic uncertainties, but that the ability to rule out correlated changes in |εee | and |εeτ | areimpacted by such a systematic uncertainty.

7.3.

Constraining the CP phases

Assuming the NSI parameters are non-zero, there is an additional source of CP violation from theargument of the off-diagonal εeτ parameter. This would produce observable effects similar to thosefrom the δCP parameter of the PMNS formalism, so we next consider constraints in the δCP –φ31 plane,
with varying true values of θ23 , δCP , and φ31 . Here, the values of εee , |εeτ |, and ετ τ are assumed tobe 0.8, 0.2, and 0.0, respectively. These three parameters, as well as θ23 , are marginalized over in theanalysis. As before, other PMNS parameters are held at their global best-ﬁt values. Figure 47 shows
the resulting allowed regions for T2HKK, with the left, middle, and right panels showing results
assuming θ23 = 41◦ , 45◦ , and 49◦ , respectively. The purple, blue, and green contours show the φ31(true) = 90◦ , 180◦ , and 270◦ cases, respectively. From the panels it is clear that the best sensitivity
comes when φ31 δCP , and that the overall sensitivity is not signiﬁcantly affected by the true valueof θ23 . On the other hand, for the (δCP , φ31 ) combinations (90◦ , 270◦ ) and (270◦ , 90◦ ) φ31 is entirely
unconstrained.
Sensitivity to constraining the CP phases beneﬁts explicitly from having two detectors at different
baselines in the T2HKK conﬁguration. To illustrate this, Fig. 48 shows the contribution of eachdetector separately assuming θ23 = 45◦ , δCP = 270◦ , and φ31 = 180◦ . The purple contour shows thecontribution from the detector in Kamioka, the blue contour shows that from the Korean detector, andthe red is their combined sensitivity. For comparison, the orange contour illustrates the expectation
for two detectors in Kamioka. That there is not much difference between the contours with one andtwo detectors in Kamioka illustrates that the increase in sensitivity seen in the T2HKK conﬁguration
comes mainly from its second baseline.
It is important to recognize that the combination of a detector in Kamioka, which has higher
statistics, with a detector in Korea, which has a larger baseline, resolves parameter degeneracies andtherefore allows for simultaneous measurement of the NSI and CP parameters. This is illustrated
by the green contour, which shows the capability a single detector in Kamioka assuming that the
NSI parameters εee , |εeτ |, and ετ τ are non-zero, but known. First, this demonstrates that a single
measurement at the ﬁrst PMNS oscillation maximum is seriously limited by degeneracies in theextended model that cannot be untangled. Secondly, although the green contour shows a precise
measurement, there is a degeneracy between the two available CP parameters shown by the correlated
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Fig. 48. Contribution of different detectors to constraints on the CP phases at 90% conﬁdence level assuming
θ23 = 45◦ , φ31 = 180◦ , and δCP = 270◦ with the normal hierarchy. See the text for a full explanation.

nature of the allowed region. The degeneracy is lifted by measurements at the Korean detector. Indeed,
the T2HKK conﬁguration, shown in red, yields a more precise measurement even though the NSIparameters are considered unknown in the analysis. In this sense an analysis that allows for the
possibility of deviations from the PMNS model can beneﬁt much more from the extra information
obtained using multiple baselines than it would from simply improving the available statistics for asingle-baseline measurement.
As before, we study how our systematic uncertainties affect our ability to constrain the CP phases.
Figure 49 shows the expected sensitivity under four systematic error assumptions, 1%, 3%, 5%, and
7%, using the same procedure as in Fig. 46. The ﬁrst, second, and third rows are for φ31 = 90◦ , 180◦ ,and 270◦ , respectively. In each row, the left, middle, and right panels correspond to θ23 = 41◦ , 45◦ ,and 49◦ , respectively. For δCP = 270◦ and φ31 = 90◦ , it is possible to have a small closed contour in
φ31 for small systematic error assumptions. As the systematic error is increased from 1%, it becomes
impossible to constrain φ31 regardless of the assumed value of θ23 . For φ31 = 180◦ the sensitivity
improves gradually when the systematic uncertainty is reduced from 7% to 1% for all values of θ23 .
For φ31 = 270◦ , the sensitivities evolve in a similar way to the φ31 = 90◦ case, but do not reach aclosed φ31 interval for δCP = 90◦ .
The above analyses have assumed a normal ordering and the 1.5◦ off-axis detector conﬁguration
at T2HKK, but here we discuss brieﬂy the cases of an inverted ordering and other off-axis angles.
For an inverted ordering we ﬁnd that the sensitivity to constrain the NSI parameters and the phases
is slightly weaker compared to the normal ordering. For example, T2HKK can constrain εee in theregion −3.2 < εee < 1.4 assuming the normal ordering, whereas the bound for inverted ordering is−3.2 < εee < 1.8 assuming θ23 = 45◦ , δCP = 270◦ .
Among the three T2HKK off-axis detector conﬁgurations, 1.5◦ , 2.0◦ , and 2.5◦ , we ﬁnd that the best
sensitivity is obtained for 1.5◦ . Indeed, the bounds on εee are −3.6 < εee < 1.8 and −4 < εee < 2.2
for 2.5◦ and 2.0◦ off-axis conﬁgurations of T2HKK, respectively, assuming the normal ordering,θ23 = 45◦ , and δCP = 270◦ . This is in line with naive expectation, since the NSI parameters induce
larger oscillation effects at higher energies. The 1.5◦ conﬁguration further beneﬁts from having
the largest number of events among the conﬁgurations and a comparatively broad ﬂux to provide
more access to the neutrino energy spectrum [68]. For similar reasons, the sensitivity of the 2.0◦
conﬁguration is better than that of the 2.5◦ one.
From the discussions above, we can conclude that the proposed long-baseline T2HKK experiment
would have good sensitivity to NSI in neutrino propagation and can be expected to place stronger
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Fig. 49. Ability of T2HKK to constrain the CP phases at 90% conﬁdence level with systematic uncertainties of
1%, 3%, 5%, and 7%, shown by the purple, blue, green, and red curves, respectively. The columns correspondto θ23 = 41◦ , 45◦ , and 49◦ . The rows are for φ31 = 90◦ , 180◦ , and 270◦ . The + signs correspond to the true
values of (δCP , φ31 ). The normal hierarchy is assumed.

bounds than with the two HK detectors in Kamioka (the T2HK setup). In addition, the sensitivity
to constrain the NSI amplitudes does not vary much with the assumed values of θ23 and δCP . The
achievable precision on the phases does depend upon the true values of δCP and φ31 , and for particular
combinations it can be much harder to determine the value of φ31 . However, the unique two-detector
conﬁguration of the T2HKK setup is more powerful than a single detector, and would be extremely
helpful in measuring the neutrino CP phases if NSI exist in nature. In studying the effect of systematics, it is found that T2HKK is not insensitive to the magnitude of the systematic errors, but that while
the overall measurement is improved by reduction of the systematic uncertainties, the systematics
are most important when considering sensitivity to speciﬁc degenerate parameter combinations.

8.

Summary and conclusion

The design of the future Hyper-K experiment is to build two identical water-Cherenkov detectors of
260 kt per detector in stages: one at the Tochibora mine in Japan at a 2.5◦ off-axis angle and a baselineof 295 km from the J-PARC neutrino target, and the other perhaps in Korea. The second detector
improves physics sensitivities, from beam neutrino physics to astroparticle physics, due to increased
statistics. In particular, searches for proton decay provide a strong motivation for having two detectors.
According to our sensitivity studies, by locating the second detector in Korea the physics sensitivities
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are further improved due to the longer baseline (∼1100 km) and the possibility of a larger overburden(1000 m) at the candidate sites. These sites cover a range of possible off-axis angles to the J-PARC
beam, between 1◦ and 3◦ , depending on the site. With the longer baseline in Korea both the ﬁrst andsecond oscillation maxima of the PMNS neutrino appearance probability are reachable. The longer
baseline of the Korean sites enhances the CP-violating component of the oscillation probability, andresolves parameter combinations between the neutrino mass ordering and CP-violating phase thatwould be nearly degenerate when measuring only at the Japanese site with beam neutrinos. Thisis a unique opportunity afforded by the J-PARC neutrino beam. By adding atmospheric neutrinos,
neutrino mass ordering determination is improved at both the Japan and Korean sites.
Assuming a relatively simplistic systematic uncertainty model based on T2K systematic error
evaluations [39], sensitivity studies of the long-baseline program of T2HKK have been performed.
These have compared different conﬁgurations of Hyper-K detector(s) in Japan and Korea for ten
years of operation without staging and with 1.3 MW beam power for ν : ν = 1 : 3. In general, theconﬁguration with one detector in Japan and one in Korea at a smaller off-axis angle gives better
sensitivity overall than two detectors in Japan. Based on this systematic error model, the beneﬁts
of a smaller off-axis angle seem to outweigh the extra uncertainties of using a higher beam energy.
Overall, the Mt. Bisul site, with its 1088 km baseline, 1.3◦ off-axis angle, and 1084 m overburden, isthe leading candidate location. Although the smaller off-axis angle introduces more π 0 -production
high-energy tail of the beam ﬂux, the large value of θ13 makes this less important and the sensitivity
to the CP phase is improved over the nominal Hyper-K design.
According to our sensitivity studies, the precision at which δCP can be measured improves from22◦ (17◦ ) for one detector (two detectors) in Japan, to at worst 14◦ for T2HKK assuming CP is
maximally violated. The coverage fraction for establishing CP violation at 5 σ improves from 47%(55%) to 60% if the mass ordering is known from independent measurements, and the improvement
is much larger otherwise. The signiﬁcance of a CP violation discovery is improved relative to having
two detectors in Japan for 0 < sin δCP < 1, though the improvement is marginal for values near 1
unless the mass ordering is still unknown at the time of the experiment. The signiﬁcance at which thewrong mass ordering can be rejected for any value of δCP improves from 0.7 σ (1 σ ) for the nominal
Hyper-K design (two detectors in Japan) to 5.5 σ at T2HKK using beam neutrino data alone. In
contrast, relative to two detectors in Japan the sensitivity of T2HKK to the atmospheric mixing
parameters is weaker due to the reduction in statistics over the longer baseline to Korea. The additionof atmospheric neutrinos improves the sensitivity overall, but is particularly useful for resolving theoctant degeneracy.
T2HKK is also expected to have improved sensitivity to non-standard interactions in neutrino
propagation. Indeed, according to our study the sensitivity to the NSI parameters, ee , eτ , and τ τ , isenhanced relative to Hyper-K conﬁgurations with only Japanese detectors, especially with the 1.5◦
off-axis site in Korea, due to the larger matter effects along its baseline.
With ∼1000 m overburdens, sensitivities to solar-neutrino and SRN physics are further enhanced
at the Korean candidate sites compared to the Tochibora mine (∼650 m overburden) due to a much
lower muon ﬂux and spallation background rate. Using a simple MC, the expected signiﬁcance of asupernova relic neutrino search for ten years of operation is 5.2 σ (4.2 σ ) with the Korean (Tochibora)sites.
In this paper we have demonstrated that the second detector in Korea provides enhanced sensitivity
to Hyper-K’s physics goals in broad physics programs.

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Acknowledgements
This work was supported by MEXT Grant-in-Aid for Scientiﬁc Research on InnovativeAreas titled “Uniﬁcation
and Development of the Neutrino Science Frontier,” under Grants Nos. 25105001, 25105004, and 25105009.
In addition, the participation of individual researchers has been further supported by funds from INFN (Istituto
Nazionale Fisica Nucleare), Italy; JSPS, Japan; the European Union ERC-207282, H2020 RISE-GA644294JENNIFER, and H2020 RISE-GA641540-SKPLUS; SSTF-BA1402-06, NRF grant Nos. 2009-0083526,
NRF-2015R1A2A1A05001869, NRF-2016R1D1A1A02936965, NRF-2016R1D1A3B02010606, and NRF2017R1A2B4012757 funded by the Korean government (MSIP); RSF, RFBR, and MES, Russia; JSPS andRFBR under the Japan–Russia Research Cooperative Program; the Brazilian National Council for Scientiﬁc
and Technological Development (CNPq); STFC, UK. Alfred P. Sloan Foundation; USA.
Funding
Open Access funding: SCOAP3 .

Appendix.

Construction details for bi-probability plots

Most common constructions of bi-probability plots show a single pair of ellipses, for a given valueof L and E and assumed oscillation parameters. This common practice is an over-simpliﬁcation;although long-baseline oscillation experiments have negligible variation in the baseline, the neutrinoenergy typically ranges over at least a factor of two, and often more. For the ﬁrst generation of νe appearance experiments (that is to say, T2K and NOνA) that use a narrow-band beam peaking near theenergy of the ﬁrst oscillation maximum this is tolerable, since the ﬁrst period of the oscillation runs
from half the peak energy up to inﬁnity. When considering these experiments there are two obvious“ﬁxes”: Either use one energy (typically the peak energy) as a stand-in for the entire spectrum of
measured neutrinos, or integrate the probability over the expected (without oscillations) spectrumof events.
The latter method corresponds to an (idealized) rate-only measurement, and provided backgrounds
are accounted for could be compared to the data in the form of number of neutrino and antineutrino
events. But this is not often done, as integrating over the full spectrum (much of which has lower
appearance probabilities) signiﬁcantly reduces the sensitivity of the experiment. On the other hand,the former method does not have any problems with averaging, but the number of events for which theellipses are a good approximation is a small fraction of the total. This makes it difﬁcult to summarize
the overall sensitivity of an experiment in a correct way.
For experiments where the event spectrum is broad compared to the oscillation (wide-band beams
such as DUNE, and second-maxima experiments such as T2HKK), approximating things as a single
pair of measurements is even less suitable. Part of the point of such experiments is that they can makemeasurements at independent energies and see the different δCP and mass ordering dependencies.
Plotting a continuum of ellipses is not practical, so to give a sense of how the energy affects themeasurement of δCP some representative energies have to be chosen. The plots in Sect. 3.1.1 use
three representative energies. This is still far from a complete summary of a real measurement, but
it provides a better illustration of what the conﬁguration can measure.

A.1.

Choice of representative energies

The energies used to summarize the interaction spectrum are chosen based on a procedure that takes
into account the interaction rates of neutrinos but is independent of the oscillation probabilities. First,
the interaction rate (i.e. ﬂux × cross section) spectrum is calculated, in the absence of oscillations. For
water-Cherenkov detectors such as Hyper-K and the proposed ESSnuSB the quasi-elastic spectrum is
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used as their analyses use primarily quasi-elastic events. For other experiments that can use any kindof neutrino interaction, the inclusive CC cross section is more appropriate. Note that for ESSnuSB
and any experiment that uses inclusive CC cross sections, the cross section grows roughly linearlywith energy, so the interaction rate spectrum is often substantially harder than the corresponding
ﬂux.
From the interaction-rate spectrum, the blue ellipses represent the peak energy, EP , the value
which is typically taken as representative in simpler bi-probability plots. This divides the interaction
spectrum in two, with a fraction f of events below (and a fraction 1 − f above) EP . The green ellipses
are drawn for the median energy of the lower f events, while the red are the median energy of theupper 1 − f events. In this way, 50% of the events lie between the energies represented by the green
and red ellipses. This method of identifying a peak and central 50% of the spectrum is also used inFig. 3, where a band covering the central 75% of events is deﬁned in a similar way.
The fact that measurements with a detector at Kamioka can be reasonably approximated as being“rate-only” is evident in Fig. 9. Although the ellipses differ in size and eccentricity, the separation
between the two mass orderings, and the dependence of the appearance probabilities on the value of δ,is similar for all three energies. The most important difference is only apparent on closer inspection:the δ = 0 CP-conserving point generates either higher or lower appearance probabilities than theδ = π point. Which point provides the larger appearance probability depends on both the massordering and whether the neutrino energy is above or below the energy of the oscillation maximum.
For other conﬁgurations (Figs. 10, 11, and 12) the location, size, and orientation of the ellipses isdramatically different.

A.2.

Statistical sensitivity

The gray ellipses give an indication of the statistical power of the measurement made in each√conﬁguration. They use a simpliﬁed background model to estimate a fractional error (S + B)/S
from the number of signal (S) and background (B) events expected in the central 25% of the events
around the peak energy (i.e. 1/4 of the total unoscillated ﬂux). The number of signal events isscaled according to the appearance probabilities at the center of the ellipse, while the background isassumed to be independent. Five ellipses are drawn, to show how the sensitivity will vary with theactual oscillation probability. This is a somewhat arbitrary measure—not least because the shape andlocation of the bi-probability ellipse can vary over even this narrower energy range—but it enables
some comparison between the statistical power of measurements with different baselines and ﬂuxes,
and using different run lengths.

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