Prog. Theor. Exp. Phys. 2015, 053C02 (35 pages)
DOI: 10.1093/ptep/ptv061

Physics potential of a long-baseline neutrino
oscillation experiment using a J-PARC neutrino
beam and Hyper-Kamiokande†Also at: J-PARC, Tokai, Japan.
‡ Also at: Moscow Institute of Physics and Technology and National Research Nuclear University “MEPhI”, Moscow, Russia.
§ Also at: Institute of Particle Physics, Canada.
¶ Also at: BMCC/CUNY, Science Department, New York, NY, USA.
© The Author(s) 2015. 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.
Funded by SCOAP3

Downloaded from http://ptep.oxfordjournals.org/ at Kokusai Hoken Keikakugaku (UNIV OF TOKYO) on May 24, 2015

Hyper-Kamiokande Proto-Collaboration
K. Abe57,59 , H. Aihara60,59 , C. Andreopoulos29 , I. Anghel23 , A. Ariga1 , T. Ariga1 ,R. Asfandiyarov15 , M. Askins4 , J. J. Back65 , P. Ballett11 , M. Barbi43 , G. J. Barker65 ,G. Barr41 , F. Bay14 , P. Beltrame13 , V. Berardi18 , M. Bergevin4 , S. Berkman3 , T. Berry47 ,S. Bhadra70 , F. d. M. Blaszczyk31 , A. Blondel15 , S. Bolognesi7 , S. B. Boyd65 , A. Bravar15 ,C. Bronner59 , F. S. Cafagna18 , G. Carminati5 , S. L. Cartwright49 , M. G. Catanesi18 ,K. Choi35 , J. H. Choi9 , G. Collazuol20 , G. Cowan13 , L. Cremonesi46 , G. Davies23 ,G. De Rosa19 , C. Densham53 , J. Detwiler66 , D. Dewhurst41 , F. Di Lodovico46 ,S. Di Luise14 , O. Drapier12 , S. Emery7 , A. Ereditato1 , P. Fernández32 , T. Feusels3 ,A. Finch28 , M. Fitton53 , M. Friend24,† , Y. Fujii24,† , Y. Fukuda34 , D. Fukuda39 ,V. Galymov7 , K. Ganezer6 , M. Gonin12 , P. Gumplinger62 , D. R. Hadley65 , L. Haegel15 ,A. Haesler15 , Y. Haga57 , B. Hartfiel6 , M. Hartz59,62 , Y. Hayato57,59 , M. Hierholzer1 ,J. Hill6 , A. Himmel10 , S. Hirota26 , S. Horiuchi68 , K. Huang26 , A. K. Ichikawa26 ,T. Iijima35,36 , M. Ikeda57 , J. Imber52 , K. Inoue55,59 , J. Insler31 , R. A. Intonti18 , T. Irvine58 ,T. Ishida24,† , H. Ishino39 , M. Ishitsuka61 , Y. Itow37,36 , A. Izmaylov22 , B. Jamieson67 ,H. I. Jang51 , M. Jiang26 , K. K. Joo8 , C. K. Jung52,59 , A. Kaboth17 , T. Kajita58,59 ,J. Kameda57,59 , Y. Karadhzov15 , T. Katori46 , E. Kearns2,59 , M. Khabibullin22 ,A. Khotjantsev22 , J. Y. Kim8 , S. B. Kim50 , Y. Kishimoto57,59 , T. Kobayashi24,† ,M. Koga55,59 , A. Konaka62 , L. L. Kormos28 , A. Korzenev15 , Y. Koshio39,59 , W. R. Kropp5 ,Y. Kudenko22,‡ , T. Kutter31 , M. Kuze61 , L. Labarga32 , J. Lagoda38 , M. Laveder20 ,M. Lawe49 , J. G. Learned16 , I. T. Lim8 , T. Lindner62 , A. Longhin27 , L. Ludovici21 ,W. Ma17 , L. Magaletti18 , K. Mahn33 , M. Malek17 , C. Mariani68 , L. Marti59 , J. F. Martin63 ,C. Martin15 , P. P. J. Martins46 , E. Mazzucato7 , N. McCauley29 , K. S. McFarland45 ,C. McGrew52 , M. Mezzetto20 , H. Minakata48 , A. Minamino26 , S. Mine5 , O. Mineev22 ,M. Miura57,59 , J. Monroe47 , T. Mori39 , S. Moriyama57,59 , T. Mueller12 , F. Muheim13 ,M. Nakahata57,59 , K. Nakamura59,24,† , T. Nakaya26,59 , S. Nakayama57,59 , M. Needham13 ,T. Nicholls53 , M. Nirkko1 , Y. Nishimura58 , E. Noah15 , J. Nowak28 , H. Nunokawa44 ,H. M. O’Keeffe28 , Y. Okajima61 , K. Okumura58,59 , S. M. Oser3 , E. O’Sullivan10 ,T. Ovsiannikova22 , R. A. Owen46 , Y. Oyama24,† , J. Pérez32 , M. Y. Pac9 , V. Palladino19 ,J. L. Palomino52 , V. Paolone42 , D. Payne29 , O. Perevozchikov31 , J. D. Perkin49 , C. Pistillo1 ,S. Playfer13 , M. Posiadala-Zezula64 , J.-M. Poutissou62 , B. Quilain12 , M. Quinto18 ,E. Radicioni18 , P. N. Ratoff28 , M. Ravonel15 , M. A. Rayner15 , A. Redij1 , F. Retiere62 ,C. Riccio19 , E. Richard58 , E. Rondio38 , H. J. Rose29 , M. Ross-Lonergan11 , C. Rott54 ,S. D. Rountree68 , A. Rubbia14 , R. Sacco46 , M. Sakuda39 , M. C. Sanchez23 ,E. Scantamburlo15 , K. Scholberg10,59 , M. Scott62 , Y. Seiya40 , T. Sekiguchi24,† ,H. Sekiya57,59 , A. Shaikhiev22 , I. Shimizu55 , M. Shiozawa57,59 , S. Short46 ,PTEP 2015, 053C02

K. Abe et al.

G. Sinnis30 , M. B. Smy5,59 , J. Sobczyk69 , H. W. Sobel5,59 , T. Stewart53 , J. L. Stone2,59 ,Y. Suda60 , Y. Suzuki59 , A. T. Suzuki25 , R. Svoboda4 , R. Tacik43 , A. Takeda57 , A. Taketa56 ,Y. Takeuchi25,59 , H. A. Tanaka3,§ , H. K. M. Tanaka56 , H. Tanaka57,59 , R. Terri46 ,L. F. Thompson49 , M. Thorpe53 , S. Tobayama3 , N. Tolich66 ,T. Tomura57,59 , C. Touramanis29 , T. Tsukamoto24,† , M. Tzanov31 , Y. Uchida17 ,M. R. Vagins59,5 , G. Vasseur7 , R. B. Vogelaar68 , C. W. Walter10,59 , D. Wark41,53 ,M. O. Wascko17 , A. Weber41,53 , R. Wendell57,59 , R. J. Wilkes66 , M. J. Wilking52 ,J. R. Wilson46 , T. Xin23 , K. Yamamoto40 , C. Yanagisawa52,¶ , T. Yano25 ,S. Yen62 , N. Yershov22 , M. Yokoyama60,59,∗ , and M. Zito7
University of Bern, Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics(LHEP), Bern, Switzerland
2
Boston University, Department of Physics, Boston, MA, USA
3
University of British Columbia, Department of Physics and Astronomy, Vancouver, BC, Canada
4
University of California, Davis, Department of Physics, Davis, CA, USA
5
University of California, Irvine, Department of Physics and Astronomy, Irvine, CA, USA
6
California State University, Department of Physics, Carson, CA, USA
7
IRFU, CEA Saclay, Gif-sur-Yvette, France
8
Chonnam National University, Department of Physics, Gwangju, Korea
9
Dongshin University, Department of Physics, Naju, Korea
10
Duke University, Department of Physics, Durham, NC, USA
11
University of Durham, Science Laboratories, Durham, UK
12
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
13
University of Edinburgh, School of Physics and Astronomy, Edinburgh, UK
14
ETH Zurich, Institute for Particle Physics, Zurich, Switzerland
15
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
16
University of Hawaii, Department of Physics and Astronomy, Honolulu, HI, USA
17
Imperial College London, Department of Physics, London, UK
18
INFN Sezione di Bari and Università e Politecnico di Bari, Dipartimento Interuniversitario di Fisica,
Bari, Italy
19
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy
20
INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy
21
INFN Sezione di Roma, Roma, Italy
22
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
23
Iowa State University, Department of Physics and Astronomy, Ames, IA, USA
24High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
25
Kobe University, Department of Physics, Kobe, Japan
26
Kyoto University, Department of Physics, Kyoto, Japan
27
Laboratori Nazionali di Frascati, Frascati, Italy
28
Lancaster University, Physics Department, Lancaster, UK
29
University of Liverpool, Department of Physics, Liverpool, UK
30
Los Alamos National Laboratory, NM, USA
31
Louisiana State University, Department of Physics and Astronomy, Baton Rouge, LA, USA
32
University Autonoma Madrid, Department of Theoretical Physics, Madrid, Spain
33
Michigan State University, Department of Physics and Astronomy, East Lansing, MI, USA
34
Miyagi University of Education, Department of Physics, Sendai, Japan
35
Nagoya University, Graduate School of Science, Nagoya, Japan
36
Nagoya University, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe,
Nagoya, Japan
37
Nagoya University, Solar-Terrestrial Environment Laboratory, Nagoya, Japan38
National Centre for Nuclear Research, Warsaw, Poland
39
Okayama University, Department of Physics, Okayama, Japan40
Osaka City University, Department of Physics, Osaka, Japan
41
Oxford University, Department of Physics, Oxford, UK

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1

PTEP 2015, 053C02

K. Abe et al.

42

University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA, USA
University of Regina, Department of Physics, Regina, SK, Canada
44
Pontifı́cia Universidade Católica do Rio de Janeiro, Departamento de Fı́sica, Rio de Janeiro,
Brazil45
University of Rochester, Department of Physics and Astronomy, Rochester, NY, USA
46
Queen Mary University of London, School of Physics and Astronomy, London, UK
47
Royal Holloway University of London, Department of Physics, Egham, Surrey, UK
48
Universidade de São Paulo, Instituto de Fı́sica, São Paulo, Brazil
49
University of Sheffield, Department of Physics and Astronomy, Sheffield, UK
50
Seoul National University, Department of Physics, Seoul, Korea
51
Seoyeong University, Department of Fire Safety, Gwangju, Korea
52
State University of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook,
NY, USA
53
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, UK
54
Sungkyunkwan University, Department of Physics, Suwon, Korea
55
Research Center for Neutrino Science, Tohoku University, Sendai, Japan
56
University of Tokyo, Earthquake Research Institute, Tokyo, Japan
57
University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan58
University of Tokyo, Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos,
Kashiwa, Japan
59
University of Tokyo, Kavli Institute for the Physics and Mathematics of the Universe (WPI),
Todai Institutes for Advanced Study, Kashiwa, Chiba, Japan
60
University of Tokyo, Department of Physics, Tokyo, Japan
61
Tokyo Institute of Technology, Department of Physics, Tokyo, Japan
62
TRIUMF, Vancouver, BC, Canada
63
University of Toronto, Department of Physics, Toronto, ON, Canada
64
University of Warsaw, Faculty of Physics, Warsaw, Poland
65
University of Warwick, Department of Physics, Coventry, UK
66
University of Washington, Department of Physics, Seattle, WA, USA
67
University of Winnipeg, Department of Physics, Winnipeg, MB, Canada
68
Virginia Tech, Center for Neutrino Physics, Blacksburg, VA, USA
69
Wroclaw University, Faculty of Physics and Astronomy, Wroclaw, Poland
70
York University, Department of Physics and Astronomy, Toronto, ON, Canada∗
E-mail: masashi@phys.s.u-tokyo.ac.jp43...............................................................................
Hyper-Kamiokande will be a next-generation underground water Cherenkov detector with a
total (fiducial) mass of 0.99 (0.56) million metric tons, approximately 20 (25) times larger
than that of Super-Kamiokande. One of the main goals of Hyper-Kamiokande is the study
of C P asymmetry in the lepton sector using accelerator neutrino and anti-neutrino beams.
In this paper, the physics potential of a long-baseline neutrino experiment using the HyperKamiokande detector and a neutrino beam from the J-PARC proton synchrotron is presented. The
analysis uses the framework and systematic uncertainties derived from the ongoing T2K experiment. With a total exposure of 7.5 MW ×107 s integrated proton beam power (corresponding
to 1.56 × 1022 protons on target with a 30 GeV proton beam) to a 2.5◦ off-axis neutrino beam,
it is expected that the leptonic C P phase δC P can be determined to better than 19 degrees for
all possible values of δC P , and C P violation can be established with a statistical significanceof more than 3 σ (5 σ ) for 76% (58%) of the δC P parameter space. Using both νe appearance and νμ disappearance data, the expected 1 σ uncertainty of sin2 θ23 is 0.015(0.006) forsin2 θ23 = 0.5(0.45).

...............................................................................
Subject Index

C03, C04, C32

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Received February 19, 2015; Revised March 29, 2015; Accepted March 29, 2015; Published May 19 , 2015

PTEP 2015, 053C02

1.

K. Abe et al.

Introduction

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The discovery of neutrino oscillations by the Super-Kamiokande (Super-K) experiment in 1998 [1]opened a new window to explore physics beyond the Standard Model (BSM). Evidence of neutrino
oscillations is one of the most convincing experimental proofs known today for the existence of
BSM physics at work. The mixing parameters of neutrinos were found to be remarkably different
from those of quarks, which suggests the presence of an unknown flavor symmetry waiting to be
explored. The extremely small masses of neutrinos compared with those of their charged partners
lead to the preferred scenario of a seesaw mechanism [2–5], in which small neutrino masses are areflection of the ultra-high-energy scale of BSM physics.
Furthermore, a theoretical framework called leptogenesis points to the intriguing possibility thatC P asymmetries related to flavor mixing among the three generations of neutrinos may have played
an important role in creating the observed matter–antimatter asymmetry in the universe [6]. This
makes a study of the full picture of neutrino masses and mixings and the measurement of the C P
asymmetry in the neutrino sector among the most important and urgent subjects in today’s elementary
particle physics world.
C P asymmetry in the neutrino sector arising from the presence of the phase that corresponds
to the Kobayashi–Maskawa phase [7] in the quark sector can only be seen if all the three mixing angles governing neutrino oscillations differ from zero. The Super-K detector has successfullymeasured all three angles. The angle θ23 was first measured in atmospheric neutrino observations [1], θ12 was constrained in solar neutrino observations [8] (together with another water
Cherenkov detector SNO [9]), and the evidence of nonzero θ13 was found by T2K [10], whichused Super-K as the far detector. In 2013, T2K established νμ → νe oscillation with 7.3 σ significance, leading the way towards C P violation measurements in neutrinos [11] in combination
with precise measurements of θ13 by reactor neutrino experiments [12–14]. The highly successful Super-K program indicates that Hyper-Kamiokande (Hyper-K) is well placed to discover C P
violation.
In this paper, the physics potential of a long-baseline neutrino experiment using the HyperKamiokande detector and a neutrino beam from the J-PARC proton synchrotron is presented.
The Hyper-K detector is designed as a next-generation underground water Cherenkov detector thatserves as a far detector of a long-baseline neutrino oscillation experiment for the J-PARC neutrino
beam and as a detector capable of observing proton decays, atmospheric and solar neutrinos, andneutrinos from other astrophysical origins. The baseline design of Hyper-K is based on the wellproven technologies employed and tested at Super-K. Hyper-K consists of two cylindrical tanks lying
side-by-side, the outer dimensions of each tank being 48 (W) × 54 (H) × 250 (L) m3 . The total(fiducial) mass of the detector is 0.99 (0.56) million metric tons, which is about 20 (25) times larger
than that of Super-K. A proposed location for Hyper-K is about 8 km south of Super-K (and 295 km
away from J-PARC) and 1750 meters water equivalent (or 648 m of rock) deep. The inner detector
region is viewed by 99 000 20 inch PMTs, corresponding to a PMT density of 20% photocathodecoverage (the same as the second phase of Super-K). A schematic view of the Hyper-K detector is
illustrated in Fig. 1.
In addition to the long-baseline neutrino oscillation experiment that is the main focus of this paper,
Hyper-K will provide a rich program in a wide range of science [15]. The scope of the project includes
observation of atmospheric and solar neutrinos, proton decays, and neutrinos from other astrophysicalorigins. The physics potential of Hyper-K is summarized in Table 1.

PTEP 2015, 053C02

K. Abe et al.

Table 1. Physics targets and expected sensitivities of the Hyper-Kamiokande experiment, based on
the study shown in Ref. [15] except for the long-baseline experiment that is described in this paper.
Improvement is expected with further optimization of the detector design and development of reconstruction/analysis tools. Also, only selected values are listed; e.g., other channels will be accessible for nucleon
decays.
Physics target

Sensitivity

Conditions

Neutrino study w/ J-PARC ν− C P phase precision<19− C P V discovery coverage

76% (3 σ ), 58% (5 σ )− sin2 θ23±0.015

7.5 MW × 107 s@ sin2 2θ13 = 0.1, mass hierarchy
known@ sin2 2θ13 = 0.1, mass hierarchy
known
1 σ @ sin2 θ23 = 0.5

Atmospheric neutrino study− MH determination− θ23 octant determination>3 σ CL>3 σ CL

10 yr observation@ sin2 θ23 > 0.4@ sin2 θ23 < 0.46 or sin2 θ23 > 0.56

Nucleon decay searches− p → e+ + π 0− p → ν̄ + K +Astrophysical neutrino sources− 8 B ν from Sun− Supernova burst ν− Supernova relic ν− WIMP annihilation at Sun(σ S D : WIMP–proton spindependent cross section)◦

10 yr data
1.3 × 1035 yr (90% CL UL)
5.7 × 1034 yr (3 σ discovery)
3.2 × 1034 yr (90% CL UL)
1.2 × 1034 yr (3 σ discovery)
200 ν/day
170 000–260 000 ν
30–50 ν830 ν/10 yr
σ S D = 10−39 cm2σ S D = 10−40 cm2

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7.0 MeV threshold (total energy)
w/ osc.
@ Galactic center (10 kpc)
@ M31 (Andromeda galaxy)
5 yr observation@ MWIMP = 10 GeV, χ χ →bb̄ dominant@ MWIMP = 100 GeV, χ χ →W + W − dominant

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Fig. 1. Schematic view of the Hyper-Kamiokande detector.

PTEP 2015, 053C02

K. Abe et al.

2. Neutrino oscillations and CP violation
2.1. Neutrino oscillations in the three-flavor framework
Throughout this paper, unless stated otherwise, we consider the standard three-flavor neutrino framework. The 3×3 unitary matrix U that describes the mixing of neutrinos [16] (that is often referred
to as the Maki–Nakagawa–Sakata–Pontecorvo (MNSP) or Maki–Nakagawa–Sakata (MNS) [16,17]
matrix) relates the flavor and mass eigenstates of neutrinos:
να =

3


Uαi νi ,(α = e, μ, τ ),

(1)

i=1

where ci j ≡ cos θi j , si j ≡ sin θi j , and δC P —often called the Dirac C P phase—is the Kobayashi–
Maskawa-type C P phase [7] in the lepton sector. On the other hand, the two phases, α21 andα31 —often called Majorana C P phases—exist only if neutrinos are of Majorana type [19–21].
While the Majorana C P phases cannot be observed in neutrino oscillation, they can be probed by
lepton-number-violating processes such as neutrinoless double beta decay.
In vacuum, the oscillation probability of να → νβ (α, β = e, μ, τ ) for ultrarelativistic neutrinos isgiven byP(να → νβ ) =

3


m2

2

i
∗
Uαi
Uβi e−i 2Eν L

i=1= δαβ − 4



∗
 Uαi
Uα j Uβi Uβ∗j

2

sin

i> j

+2



∗
 Uαi
Uα j Uβi Uβ∗j sin

i> j

m i2j
2E ν

m i2j
4E ν
L ,

L

(3)

where E ν is the neutrino energy, L is the baseline, and m i2j ≡ m i2 − m 2j (i, j = 1, 2, 3) are themass-squared differences with m i and m j being the neutrino masses. For the C P conjugate channel,ν̄α → ν̄β , the same expression in Eq. (3) holds, but the matrix U is replaced by its complex conjugate(or equivalently δC P → −δC P in Eq. (2)), resulting in the third term in Eq. (3) switching sign. For
neutrinos traveling inside matter, coherent forward scattering induces an asymmetry between theoscillation probabilities of neutrinos and anti-neutrinos supplementary to the intrinsic C P violation.
The magnitude of the C P violation in neutrino oscillation can be characterized by the differencein probabilities between neutrino and anti-neutrino channels, which, in vacuum, is given by [22,23]




(4)
Pαβ ≡ P να → νβ − P ν̄α → ν̄β = 16Jαβ sin 21 sin 32 sin 31 ,6/35

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where να (α = e, μ, τ ) and νi (i = 1, 2, 3) denote, respectively, flavor and mass eigenstates of neutrinos. Using the standard parametrization, which can be found, e.g., in Ref. [18], U can be expressed
as
⎞
⎞⎛
⎞⎛
⎛
0 s13 e−iδC P
c13
c12 s12 0
1
0
0
⎟
⎟⎜
⎟⎜
⎜
U = ⎝0 c23 s23 ⎠ ⎝0
10⎠ ⎝−s12 c12 0⎠0
0 1
0 −s23 c23−s13 eiδC P 0
c13
⎛
⎞
1
0
0
⎜
⎟
α
i 21
×⎜
(2)
0 ⎟
⎝0 e 2
⎠
α31
0
0
ei 2

PTEP 2015, 053C02

andK. Abe et al.



∗
∗
Uβ1
Uβ2 = ±JC P ,Jαβ ≡  Uα1Uα22
JC P ≡ s12 c12 s23 c23 s13 c13
sin δC P(5)with positive (negative) sign for (anti-)cyclic permutation of the flavor indices e, μ, and τ . The
parameter JC P is the lepton analogue of the C P-invariant factor for quarks, the unique and phaseconvention-independent measure for C P violation [24]. Using the current best-fitted values of
mixing parameters [25], we get JC P  0.034 sin δC P , orPαβ  ±0.55 sin δC P sin

21 sin31 .

32 sin(6)

2.2.

Physics case with νμ → νe oscillation

The oscillation probability from νμ to νe in accelerator experiments is expressed, to the first order ofthe matter effect, as follows [43]:2 2 2P(νμ → νe ) = 4c13
s13 s23 · sin2 31

2+ 8c13s12 s13 s23 c12 c23 cos δC P − s12 s13 s23 · cos

32 · sin2− 8c13c12 c23 s12 s13 s23 sin δC P · sin

21

32 · sin

31 · sin

31 · sin

2 2
2 2
2 2 2
+ 4s12
c13 c12c23 + s12
s23 s13 − 2c12 c23 s12 s23 s13 cos δC P · sin2
2 2 2
− 8c13s13 s23 ·2 2 2+ 8c13s13 s23aL2
1 − 2s13
· cos
4E ν
a
2
1 − 2s13· sin2m 231
7/35

32 · sin
31 ,

21

21

31

(7)

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Thus, large C P violation effects are possible in the neutrino oscillation.
In general, it is considered that the C P violation in the neutrino sector that can be observed in the
low-energy regime, namely, in neutrino oscillation, does not directly imply the C P violation required
at high energy for successful leptogenesis in the early universe. It has been discussed, however, thatthey could be related to each other, and the C P-violating phase in the MNS matrix could also be
responsible for the generation of the observed baryon asymmetry through leptogenesis in some scenarios. For example, in Refs. [26,27], in the context of the seesaw mechanism, it has been pointed out
that, assuming the hierarchical mass spectrum for right-handed Majorana neutrinos with the lightest
mass being 5×1012 GeV, the observed baryon asymmetry could be generated through leptogenesis
if | sin θ13 sin δC P |  0.1, which is compatible with the current neutrino data. Hence, measurementof C P asymmetry in neutrino oscillations may provide a clue for understanding the origin of thematter–antimatter asymmetry of the universe.
Since there are only three neutrinos, only two mass-squared differences, e.g., m 221 and m 231 ,are independent. Therefore, for a given energy and baseline, there are six independent parameters,
namely, three mixing angles, one C P phase, and two mass-squared differences, to describe neutrino
oscillations. Among these six parameters, θ12 and m 221 have been measured by solar [9,28,29]
and reactor [30–32] neutrino experiments. The parameters θ23 and | m 232 | (only its absolute value)
have been measured by atmospheric [33,34] and accelerator [35–38] neutrino experiments. Reactor
experiments have also started to measure the atmospheric mass-squared difference, | m 231 |, though
the uncertainty is still large [12]. Recently, (θ13 ) has also been measured by accelerator [10,11,39,40]
and reactor experiments [12–14,41,42]. The relatively large value of θ13 opens a window to explore
the C P phase (δC P ) and the mass hierarchy (the sign of m 231 ) using neutrino oscillation.

PTEP 2015, 053C02

K. Abe et al.





2 2
2 2
P νμ → νμ  1 − 4c13
s23 1 − c13s23 sin2
 1 − sin2 2θ23 sin2m 232 L/4E ν

m 232 L/4E ν ,(for c13  1)

(8)
(9)

there is an octant ambiguity: either θ23 ≤ 45◦ (in the first octant) or θ23 > 45◦ (in the second octant).
By combining the measurement of P(νμ → νe ), the θ23 octant can be determined.

2.3. Anticipated neutrino physics landscape in the 2020s and uniquenessof this experiment
Before Hyper-K commences data taking in ∼2025, we expect that a number of ongoing and planned
neutrino experiments as well as cosmological observations will advance our understanding of neutrino physics. In addition to accelerator and reactor experiments, Super-K will provide precise
measurements of neutrino oscillation parameters from atmospheric neutrino observations, and will
look for the mass hierarchy and the octant of θ23 . Cosmological observations will provide the information on neutrino masses. An observation of neutrinoless double β decay in the next 10 years would
be evidence that the neutrino is a Majorana particle with the inverted mass hierarchy. Following thisprogress, we definitely need a new experiment to discover C P violation in neutrinos, and to unambiguously establish the mass hierarchy and θ23 octant. For these purposes, we propose the Hyper-K
experiment with the J-PARC neutrino beam.
The Hyper-K experiment will have several unique advantages.
◦ The experiment will have high statistics of neutrino events thanks to the large fiducial mass andthe high-power J-PARC neutrino beam.
◦ The relatively short baseline among the proposed long-baseline experiments results in a small
ambiguity from the matter effect.
◦ The experiment will operate in the same beamline as T2K with the same off-axis configuration.
The features of the neutrino beam and the operation of the high-power beam are well understood.
◦ The systematic errors are already well understood based on Super-K and T2K, allowing reliable
extrapolations.
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√






where i j is m i2j L/4E ν , and a = 2 2G F n e E ν = 7.56 × 10−5 eV2 × ρ g/cm3 × E ν GeV .
The corresponding probability for a ν μ → ν e transition is obtained by replacing δC P → −δC P anda → −a. The third term, containing sin δC P , is the C P-violating term that flips sign between ν andν̄ and thus introduces C P asymmetry if sin δC P is nonzero. The last two terms are due to the matter
effect. Those terms that contain a change their sign depending on the mass hierarchy. As seen fromthe definition of a, the amount of asymmetry due to the matter effect is proportional to the neutrinoenergy at a fixed value of L/E ν . A direct test of C P violation, in a model-independent way, is possible
by measuring both neutrino and anti-neutrino appearance probabilities. If the mass hierarchy is notknown, the sensitivity of C P violation is affected by the presence of the matter effect. However,
the mass hierarchy could be determined by the atmospheric neutrino measurement in Hyper-K andseveral measurements by other experiments.
The currently measured value of θ23 is consistent with maximal mixing, θ23 ≈ π/4 [38,44,45].
It is of great interest to determine if sin2 2θ23 is maximal or not, and, if not, if θ23 is less or greaterthan π/4, as it could constrain models of neutrino mass generation [46–51]. When we measure θ23with the survival probability P νμ → νμ , which is proportional to sin2 2θ23 to first order,

PTEP 2015, 053C02

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With these features, Hyper-K will be one of the most sensitive experiments to probe neutrino C P
violation, as we present in this paper.

3. Experimental setup
3.1. J-PARC accelerator and neutrino beamline

3.2.

Near detectors

The accelerator neutrino event rate observed at Hyper-K depends on the oscillation probability, neutrino flux, neutrino interaction cross section, detection efficiency, and the detector fiducial mass ofHyper-K. To extract estimates of the oscillation parameters from data, one must model the neutrino
flux, cross section, and detection efficiency with sufficient precision. In the case of the neutrino cross
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An intense and high-quality neutrino beam is key to the success of a long-baseline neutrino oscillation
experiment. J-PARC (Japan Proton Accelerator Research Complex) is one of the world’s leading
facilities in neutrino physics, currently providing a beam for the T2K experiment. We will utilize thefull potential of this existing facility with future increase of the beam power to the designed value of
750 kW and beyond.
The J-PARC accelerator cascade [52] consists of a normal-conducting LINAC as an injection system, a rapid cycling synchrotron (RCS), and a main ring synchrotron (MR). In the fast extraction
mode operation, MR has achieved 1.24 × 1014 protons per pulse (ppp) beam intensity, which is aworld record for extracted ppp for any synchrotron. The corresponding beam power is 240 kW. The
upgrade scenario of the J-PARC accelerator [53] is being implemented to reach the designed powerof 750 kW in forthcoming years, with a typical planned parameter set as listed in Table 2. This will
double the current repetition rate by (i) replacing the magnet power supplies, (ii) replacing the RF system, and (iii) upgrading injection/extraction devices. The designed power of 750 kW will be achieved
well before Hyper-K starts data taking. Furthermore, conceptual studies on how to realize 1–2 MWbeam powers and even beyond, such as by raising the RCS top energy, enlarging the MR aperture, orinserting an “emittance-damping” ring between the RCS and MR, are now underway [54].
Figure 2 shows an overview of the neutrino experimental facility [55,56]. The primary beamline
guides the extracted proton beam to a production target/pion-focusing horn system in a target station. The pions decay into muons and neutrinos during their flight in a 110 m-long decay volume.
A graphite beam dump is installed at the end of the decay volume, and muon monitors downstreamof the beam dump monitor the muon profile. A near neutrino detector complex is situated 280 m
downstream of the target to monitor neutrinos at production. To generate a narrow-band neutrino
beam, the beamline utilizes an off-axis beam configuration [57], with the capability of varying theoff-axis angle in a range from 2.0◦ to 2.5◦ . The latter value has been used for the T2K experimentand is also assumed for the proposed project. The centerline of the beamline extends 295 km to thewest, passing midway between Tochibora (Hyper-K candidate site) and Mozumi (where Super-K is
located), so that both sites have identical off-axis angles.
Based on the considerable experience gained on the path to achieving 240 kW beam power operation, improvement plans to realize 750 kW operation, such as improving the activated air confinementin the target station and expanding the facilities for the treatment of activated water, are being implemented and/or proposed. Table 3 gives a summary of the acceptable beam power and/or achievableparameters for each beamline component [58], after the proposed improvements in forthcoming
years.

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Table 2. Planned parameters of the J-PARC main ring for fast
extraction. Numbers in parentheses are those achieved up to May
2013.
Parameter

Value
1567.530
2.0 × 1014 (1.24 × 1014 )2.5 × 1013 (1.57 × 1013 )
9
8
∼5
∼50
560 (280)
1.28 (2.48)
750 (240)

Fig. 2. The neutrino experimental facility (neutrino beamline) at J-PARC.

section, the model must describe the exclusive differential cross section that includes the dependence on the incident neutrino energy, E ν , the kinematics of the outgoing lepton, pl and θl , and thekinematics of final-state hadrons and photons. In our case, the neutrino energy is inferred from thelepton kinematics, while the modeling of reconstruction efficiencies depends on the hadronic final
state as well.
The neutrino flux and cross-section models can be constrained by data collected at near detectors,
situated close enough to the neutrino production point so that oscillation effects are negligible. Our
approach to using near-detector data will build on the experience of T2K while considering new neardetectors that may address important uncertainties in the neutrino flux or cross-section modeling.
The conceptual design of the near detectors is being developed based on the physics sensitivity
studies described in Sect. 4. In this section, we present basic considerations on the near-detector
requirements and conceptual designs. More concrete requirements and a detector design will bepresented in the future.
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Circumference (m)Kinetic energy (GeV)
Beam intensity (ppp)(ppb)
Harmonic number
Number of bunches per spill
Spill width (μs)
Bunch full width at extraction (ns)Maximum RF voltage (kV)
Repetition period (s)Beam power (kW)PTEP 2015, 053C02

K. Abe et al.

Table 3. Acceptable beam power and achievable parameters for each beamline
component [58]. Limitations as of May 2013 are also given in parentheses.
Component

Beam power/parameter

TargetBeam window
Horn

3.3 × 1014 ppp
3.3 × 1014 ppp

Decay volume
Hadron absorber/beam dump
Water cooling facilities
Radiation shielding
Radioactive air leakage to the target station ground floor
Radioactive cooling water treatment

2 MW
1–2 MW (400 kW)
1–2 MW (300 kW)
320 kA (250 kA)
1 Hz (0.4 Hz)
4 MW
3 MW
∼2 MW (750 kW)
4 MW (750 kW)∼2 MW (500 kW)∼2 MW (600 kW)

We assume the use of T2K near detectors [55], INGRID and ND280, possibly with an upgrade.
The INGRID detector [59] consists of 16 iron-scintillator modules configured in a cross patterncentered on the beam axis 280 m downstream of the T2K target. The rate of interactions in each
module is measured and a profile is constructed to constrain the neutrino beam direction. The ND280
off-axis detector is located 280 m downstream of the T2K target as well, but at an angle of 2.5
degrees away from the beam direction. It consists of the P0D π 0 detector [60], time projection chambers (TPCs) [61], fine-grain scintillator bar detectors (FGDs) [62] and surrounding electromagnetic
calorimeters (ECALs) [63]. The detectors are immersed in a 0.2 T magnetic field and the magnetic
yoke is instrumented with plastic scintillator panels for muon range detection [64]. The magnetic field
allows for momentum measurement and sign selection of charged particles. The magnetization of
ND280 is particularly important for operation in anti-neutrino mode where the neutrino backgroundis large. In that case, ND280 is able to separate the “right-sign” μ+ from the “wrong-sign” μ− . The
P0D and FGDs act as the neutrino targets, while the TPCs provide measurements of momentum andionizing energy loss for particle identification. The P0D and one of the FGDs include passive waterlayers that allow for neutrino interaction rate measurements on the same target as Super-K. ND280
has been employed to measure the rates of charged-current (CC) νμ and νe interactions, as well as
neutral-current (NC) π 0 interactions.
The T2K Collaboration is in the process of discussing various upgrade possibilities at the ND280
site [65]. These include the deployment of heavy water (D2 O) within the passive water targets in
FGD2 that would allow the extraction of neutrino interaction properties on the quasi-free neutron indeuterium via a subtraction with data taken with light water H2 O. The use of a water-based liquid
scintillator (WbLS) developed at BNL [66] is being explored in the context of a tracking detector
with comparable or finer granularity than the FGD to allow the detailed reconstruction of the hadronicsystem emerging from the neutrino interactions or a larger detector with coarser segmentation thatwould allow high-statistics studies. Either would significantly enhance the study of neutrino interactions on water by reducing the reliance on subtraction and enhancing the reconstruction capabilities
relative to the currently deployed passive targets. Finally, a high-pressure TPC that can contain various noble gases (He, Ne, Ar) to serve both as the target and tracking medium is being studied. Sucha detector would allow the ultimate resolution of the particles emitted from the target nucleus while
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Cooling for conductors
Stripline cooling
Hydrogen production
Horn current
Power supply repetition

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(1) The detector should be large enough to contain muons up to the momentum of interest formeasurements at the far detector, and to provide sufficient radiation length for detection of
gamma rays.
(2) The detector should be far enough from the neutrino production point so that there is minimal
pile-up of interactions in the same beam timing bunch.
These requirements lead to designs for kiloton-size detectors located at intermediate distances,
1–2 km from the target, for the J-PARC neutrino beam.
The main disadvantage of the WC detector is the inability to separate positively and negatively
charged leptons, and hence anti-neutrino and neutrino interactions. This ability is especially important for a C P asymmetry measurement where the wrong sign contribution to the neutrino flux should
be well understood. Hence, the WC detector will most likely be used in conjunction with a magnetized tracking detector such as ND280. Recent developments in the addition of gadolinium (Gd) [69]and water-based liquid scintillator (WbLS) compounds [66] to water do raise the possibility of separating neutrino and anti-neutrino interactions by detecting the presence of neutrons or protons in the
final state.
Two conceptual designs for possible intermediate WC detectors have been studied. Unoscillated
Spectrum (TITUS) is a 2 kiloton WC detector located about 2 km from the target at the same offaxis angle as the far detector. At this baseline the detector sees fluxes for the neutral-current and νebackgrounds that are nearly identical to the Hyper-K fluxes. The detector geometry and the presenceof a muon range detector are optimized to detect the high-momentum tail of the muon spectrum.
The use of Gd in TITUS to separate neutrino and anti-neutrino interactions is being studied. The
νPRISM detector is located 1 km from the target and is 50 m tall, covering a range of off-axis angles
from 1–4 degrees. The νPRISM detector sees a range of neutrino spectra, peaking at energies from
0.4 to 1.0 GeV depending on the off-axis angle. The purpose of νPRISM is to use these spectra tobetter probe the relationship between the incident neutrino energy and final-state lepton kinematics,
a part of the interaction model with larger uncertainties arising from nuclear effects.

3.3.

Hyper-Kamiokande

Hyper-Kamiokande is to be the third-generation water Cherenkov detector in Kamioka, designed fora wide variety of neutrino studies and nucleon decay searches. Its total (fiducial) water mass of one(0.56) million tons would be approximately 20 (25) times larger than that of Super-Kamiokande.
Table 4 summarizes the baseline design parameters of the Hyper-K detector.
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allowing a study of the A-dependence of the cross sections and final-state interactions to rigorously
test models employed in neutrino event generators.
Since many of the uncertainties on the modeling of neutrino interactions arise from uncertainties
on nuclear effects, the ideal near detector should include the same nuclear targets as the far detector.
In T2K near detectors, the P0D [60] and FGD [62] detectors include passive water layers; however,extracting water-only cross sections requires complicated analyses that subtract out the interactions
on other materials in the detectors. An alternative approach is to build a water Cherenkov (WC) neardetector to measure the cross section on H2 O directly and with no need for a subtraction analysis.
This approach was taken by K2K [35] and was proposed for T2K [67]. The MiniBooNE experimenthas also employed a mineral-oil Cherenkov detector at a short baseline to great success [68]. A WC
near-detector design is largely guided by two requirements:

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Table 4. Parameters of the Hyper-Kamiokande baseline design.
Detector type
Candidate site

Ring-imaging
water Cherenkov detector
Address

Detector geometry

Total water mass
Inner detector (fiducial) mass
Outer detector mass

0.99 megaton
0.74 (0.56) megaton
0.2 megaton

Photo-sensors

Inner detector
Outer detector

99 000 20 inch φ PMTs
20% photo-coverage
25 000 8 inch φ PMTs

Light attenuation length
Rn concentration>100 m @ 400 nm<1 mBq/m3

Lat.
Long.
Alt.
Overburden

Water quality†

World geographical coordination system.

In the baseline design, the Hyper-K detector is composed of two separate caverns, as shown in
Fig. 1, each having an egg-shaped cross section 48 meters wide, 54 meters tall, and 250 meters long,as shown in Figs. 3 and 4. The welded polyethylene tanks are filled up to a depth of 48 m withultra-pure water: the total water mass equals 0.99 million tons.
Each tank will be optically separated by segmentation walls located every 49.5 m to form 5 (in total
10) compartments, as shown in Fig. 4, such that event triggering and event reconstruction can be
performed in each compartment separately and independently. Because the compartment dimensionof 50 m is comparable with that of Super-K (36 m) and is shorter than the typical light attenuation
length in water achieved by the Super-K water filtration system (>100 m @ 400 nm), we expect thatthe detector performance of Hyper-K for beam and atmospheric neutrinos will be effectively thesame as that of Super-K.
The water in each compartment is further optically separated into three regions. The inner region
has a barrel shape of 42 m in height and width, and 48.5 m in length, and is viewed by an inwardfacing array of 20 inch diameter photomultiplier tubes (PMTs). The entire array consists of 99 000
Hamamatsu R3600 PMTs, uniformly surrounding the region and giving a photocathode coverageof 20%. The PMT type, size, and number density are subject to optimization. We have also beendeveloping new photosensors as possible alternative options to the R3600, such as a PMT with a
box-and-line dynode and a hybrid photo-detector (HPD), both with a high-quantum-efficiency photocathode. An outer region completely surrounds the 5 (in total 10) inner regions and is equippedwith 25 000 8 inch diameter PMTs. This region is 2 m thick at the top, bottom, and barrel sides,
except at both ends of each cavern, where the outer region is larger than 2 m due to rock engineering
considerations. A primary function of the outer detector is to reject entering cosmic-ray muon backgrounds and to help in identifying nucleon decays and neutrino interactions occurring in the inner
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Cosmic-ray muon flux
Off-axis angle for the J-PARC ν
Distance from the J-PARC

Tochibora mine
Kamioka town, Gifu, JAPAN36◦ 21 20.105 N†
137◦ 18 49.137 E†
508 m
648 m rock(1750 m water equivalent)∼8 × 10−7 s−1 cm−22.5◦ (same as Super-K)
295 km (same as Super-K)

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detector. The middle region or dead space is an uninstrumented, 0.9 m thick shell between the innerand outer detector volumes where the stainless steel PMT support structure is located. The bordersof both the inner and outer regions are lined with opaque sheets. This dead space, along with theouter region, acts as a shield against radioactivity from the surrounding rock. The total water massof the inner region is 0.74 million tons and the total fiducial mass is 10 times 0.056 = 0.56 million
tons. The fiducial volume is defined as the region formed by a virtual boundary located 2 m awayfrom the inner PMT plane.
The estimated cosmic-ray muon rate around the Hyper-K detector candidate site is ∼8 × 10−7−1s cm−2 , which is roughly 5 times larger than the flux at Super-K’s location (∼1.5 ×
10−7 s−1 cm−2 ). The expected deadtime due to these muons is less than 1% and is negligible forlong-baseline experiments, as well as nucleon decay searches and atmospheric neutrino studies.
Water is the target material and signal-sensitive medium of the detector, and thus its quality directly
affects the physics sensitivity. In Super-Kamiokande the water purification system has been continually modified and improved over the course of two decades. As a result, the transparency is
now kept above 100 m and is very stable, and the radon concentration in the tank is held below
1 mBq/m3 . Following this success, the Hyper-Kamiokande water system has been designed based on
the current Super-Kamiokande water system with scaling-up of the process speeds to 1200 m3 /hour
for water circulation and 400 m3 /hour for radon free air generation. With these systems, the water
quality in Hyper-Kamiokande is expected to be the same as that in Super-Kamiokande. Adding dissolved gadolinium sulfate for efficient tagging of neutrons has been studied as an option to enhance
the Hyper-K physics capability. The feasibility of adding Gd to Super-K [69] is now being studied with the EGADS (Evaluating Gadolinium’s Action on Detector Systems) project in Kamioka.
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Fig. 3. Cross-section view of the Hyper-Kamiokande detector.

PTEP 2015, 053C02

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array

array

array

array

K. Abe et al.

Fig. 4. Profile of the Hyper-K detector. Top: the detector segmentation. Bottom: PMT arrays and the support structure for the inner and outer detectors. Eachquasi-cylindrical tank lying horizontally is segmented by intermediate walls into five compartments.

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K. Abe et al.
100
90
80

Count

70
60
50
40
30
20

0
–1000 –800 –600 –400 –200

0

200

400

600

800 1000

Likelihood

Fig. 5. PID likelihood functions for electrons (blue solid histogram) and μ (red dashed histogram) with
500 MeV/c momentum. A negative (positive) value indicates an electron-like (μ-like) particle.
Table 5. Comparison of the performance of SK-II (20% photo-coverage), SK-IV (40% photo-coverage), andthe expected performance of the Hyper-Kamiokande baseline design (20% photo-coverage) with preliminary
Hyper-K simulation and reconstruction.
SK-II
Particle type ( p = 500 MeV/c)
Vertex resolution
Particle identification
Momentum resolution

SK-IV

Hyper-K

e

μ

e

μ

e

μ

28 cm
98.5%
5.6%

23 cm
99.0%
3.6%

25 cm
98.8%
4.4%

17 cm
99.5%
2.3%

27 cm
>99.9%
4.0%

30 cm
99.2%
2.6%

We have been careful to keep the possibility of gadolinium loading in mind when designing theoverall Hyper-Kamiokande water system.
We have evaluated the expected performance of the Hyper-K detector using the MC simulation and reconstruction tools under development. We have been developing a detector simulation
dedicated to Hyper-K based on “WCSim” [70], which is an open-source water Cherenkov detector simulator based on the GEANT4 library [71,72]. A new reconstruction algorithm developed forSuper-K/T2K [11], named “fiTQun,” has been adopted for the Hyper-K analysis. It uses a maximum likelihood fit with charge and time probability density functions constructed for every PMT
hit assuming several sets of physics variables (such as vertex, direction, momentum, and particletype) [11,73].
As an example of the evaluation, electrons and muons with 500 MeV/c are generated with a fixed
vertex (at the center of the tank) and direction (toward the barrel of the tank) in the Hyper-K detector
simulation. Figure 5 shows the likelihood function for the particle identification. A negative (positive) value indicates an electron-like (μ-like) particle. It demonstrates a clear separation of electrons
and muons. The obtained performance of Hyper-Kamiokande is compared with the performance of
SK-II (20% photo coverage, old electronics) and SK-IV (40% photo coverage, new electronics) in
Table 5. The vertex resolution for muon events will be improved to the same level as Super-K withan update of the reconstruction program. From the preliminary studies, the performance of Hyper-K
is similar to or possibly better than SK-II or SK-IV with the new algorithm. In the physics sensitivity study described in Sect. 4, a Super-K full MC simulation with the SK-IV configuration is used
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because it includes the simulation of new electronics and is tuned with real data, while giving asimilar performance to Hyper-K, as demonstrated above.

4. Physics sensitivities
4.1. Overview= −0.28 sin δ + 0.07.

(11)

The effect of the C P-violating term can be as large as 28%, while the matter effect is much smaller.
The uncertainty of Earth density between Tokai and Kamioka is estimated to be at most 6%[74]. Because the matter effect contribution to the total appearance probability is less than 10%
for a 295 km baseline, the uncertainty from matter density is estimated to be less than 0.6% and isneglected in this analysis.
Due to the relatively short baseline and thus lower neutrino energy at the oscillation maximum, thecontribution of the matter effect is smaller for the J-PARC to Hyper-Kamiokande experiment compared to other proposed experiments, like LBNE in the United States [75] or LBNO in Europe [76].
Thus the C P asymmetry measurement with the J-PARC to Hyper-K long-baseline experiment hasless uncertainty related to the matter effect, while other experiments with >1000 km baseline havemuch better sensitivity to the mass hierarchy with accelerator neutrino beams1 . The sensitivities for

1

Note that Hyper-K has sensitivity to the mass hierarchy using atmospheric neutrinos, as shown in Table 1.
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As discussed in Sect. 2.2, a comparison of muon-type to electron-type transition probabilities
between neutrinos and anti-neutrinos is one of the most promising methods to observe the lepton
C P asymmetry. Recent observation of a nonzero, rather large value of θ13 [10,14,41,42] makes thisexciting possibility more realistic.
Figure 6 shows the νμ → νe and ν μ → ν e oscillation probabilities as a function of the true neutrinoenergy for a baseline of 295 km. The Earth matter density of 2.6 g/cm3 is used in this analysis. The
cases for δC P = 0, 12 π , π , and − 12 π are overlaid. Also shown are the cases of normal mass hierarchy( m 232 > 0) with solid lines and inverted mass hierarchy ( m 232 < 0) with dashed lines. The oscillation probabilities depend on the value of δC P , and, by comparing the neutrinos and anti-neutrinos,
one can see the effect of C P violation.
There are sets of different mass hierarchy and values of δC P that give similar oscillation probabilities. This is known as the degeneracy due to unknown mass hierarchy and may introduce an ambiguity
if we do not know the true mass hierarchy. Because there are a number of experiments planned todetermine mass hierarchy in the near future, it is expected that the mass hierarchy will be determinedby the time Hyper-K starts to take data. If not, Hyper-K itself has a sensitivity to the mass hierarchy
by the atmospheric neutrino measurements, as shown in Table 1. Furthermore, a combined analysisof the accelerator and atmospheric neutrino data in Hyper-K will enhance the sensitivity, as shown in
Sect. 4.7. Thus, the mass hierarchy is assumed to be known in this analysis, unless otherwise stated.
Figure 7 shows the contribution from each term of the νμ → νe oscillation probability formula,Eq. (7), for L = 295 km, sin2 2θ13 = 0.1, sin2 2θ23 = 1.0, δC P = π/2, and normal mass hierarchy.
For E ν  0.6 GeV, which gives sin 32  sin 31  1,


a




2 s2 s22−16JC P sin 21 + 16c13
13 23 m 2 1 − 2s13
P νμ → νe − P ν̄μ → ν̄e
31




(10)
2 s2 s2P νμ → νe + P ν̄μ → ν̄e
8c13
13 23

PTEP 2015, 053C02

K. Abe et al.
neutrino

0.1

0.1

anti-neutrino

L = 295 km, sin2 2θ13 = 0.1

0.06

L = 295 km, sin 2 2θ 13 = 0.1

0.08

δ=0
δ = 1/2p
δ=p
δ = –1/2p

P (νm →νe)

P (νm →νe)

0.08

0.04
0.02

δ=0
δ = 1/2p
δ=p
δ = –1/2p

0.06
0.04
0.02

0
0

1

0
0

2

Eν (GeV)1

2Eν (GeV)Solar

Leading (θ 13)

P (νm →νe)

0.05
Total

Matter0

CPC
CPV
L = 295 km
sin22θ 13 = 0.1

–0.05
0

1
E ν (GeV)

2

Fig. 7. Oscillation probability of νμ → νe as a function of the neutrino energy with a baseline of 295 km.
sin2 2θ13 = 0.1, δC P = 12 π , and normal hierarchy are assumed. The contribution from each term of theoscillation probability formula is shown separately.

C P violation and mass hierarchy can be further enhanced by combining measurements with different
baselines.
The analysis method is based on a framework developed for the sensitivity study by T2K reported
in Ref. [77]. A binned likelihood analysis based on the reconstructed neutrino energy distribution
is performed using both νe (ν e ) appearance and νμ (ν μ ) disappearance samples simultaneously. In
addition to sin2 2θ13 and δC P , sin2 θ23 and m 232 are also included as free parameters in the fit. Table 6
shows the nominal oscillation parameters used in the study presented in this paper, and the treatment
during the fitting. Systematic uncertainties are estimated based on the experience and prospects of
the T2K experiment, and implemented as a covariance matrix that takes into account the correlationof uncertainties.
An integrated beam power of 7.5 MW × 107 s is assumed in this study. It corresponds to
1.56 × 1022 protons on target with a 30 GeV J-PARC beam. We have studied the sensitivity to C P
violation with various assumptions of neutrino mode and anti-neutrino mode beam running time ratio
for both normal and inverted mass hierarchy cases. The dependence of the sensitivity on the ν:ν ratio
is found to be not significant between ν:ν = 1:1 to 1:5. In this paper, the ν:ν ratio is set to be 1:3
so that the expected number of events is approximately the same for the neutrino and anti-neutrino
modes.
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Fig. 6. Oscillation probabilities as a function of the neutrino energy for νμ → νe (left) and ν μ → ν e (right)
transitions with L = 295 km and sin2 2θ13 = 0.1. Black, red, green, and blue lines correspond to δC P = 0, 12 π ,π , and − 12 π , respectively. Solid (dashed) line represents the case for a normal (inverted) mass hierarchy.

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Table 6. Oscillation parameters used for the sensitivity analysis and treatment in the fitting. The nominal values are used forthe figures and numbers in this section, unless otherwise stated.
Parameter
2

Treatment

0.10
0
0.50
2.4 × 10−3 eV2Normal or Inverted
0.8704
7.6 × 10−5 eV2

FittedFittedFittedFitted
Fixed
Fixed
Fixed

Hyper-K Flux for Anti-neutrino Mode

106

νm
νm
νe
νe

5

10

104
103
102
0

1

2

3

4

5
6
Eν [GeV]

7

8

9

10

Flux [/(50 MeV⋅ cm2⋅ 1e21 POT)]

Flux [/(50 MeV⋅ cm2⋅ 1e21 POT)]

Hyper-K Flux for Neutrino Mode
106

νm
νm
νe
νe

5

10

104
103
102
0

1

2

3

4

5
6
Eν [GeV]

7

8

9

10

Fig. 8. The predicted Hyper-K neutrino fluxes from the J-PARC beam without oscillations. The neutrino
enhanced beam is shown on the left and the anti-neutrino enhanced beam is shown on the right.

4.2.

Neutrino flux

The neutrino flux is estimated by the T2K Collaboration [78] by simulating the J-PARC neutrino
beamline while tuning the modeling of hadronic interactions using data from NA61/SHINE [79,80] and other experiments measuring hadronic interactions on nuclei. To date, NA61/SHINE has
provided measurements of pion and kaon production multiplicities for proton interactions on a 0.04
interaction length graphite target, as well as the inelastic cross section for protons on carbon. Since“thin" target data are used, the secondary interactions of hadrons inside and outside the target aremodeled using other data or scaling the NA61/SHINE data to different center-of-mass energies ortarget nuclei. NA61/SHINE also took data with a replica of the 90 cm-long T2K target, which will
reduce the uncertainties related to the secondary interactions inside the target.
For the studies presented in this document, the T2K flux simulation has been used with the horncurrents raised from 250 kA to 320 kA. The flux is estimated for both polarities of the horn fields,corresponding to neutrino enhanced and anti-neutrino enhanced fluxes. The calculated fluxes at
Hyper-K, without oscillations, are shown in Fig. 8.
The sources of uncertainty in the T2K flux calculation include:◦ Uncertainties on the primary production of pions and kaons in proton-on-carbon collisions.
◦ Uncertainties on the secondary hadronic interactions of particles in the target or beamline
materials after the initial hadronic scatter.
◦ Uncertainties on the properties of the proton beam incident on the target, including the absolutecurrent and the beam profile.
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δC P
sin2 θ23m 232
Mass hierarchysin2 2θ12m 221

Nominal value

PTEP 2015, 053C02

K. Abe et al.

Hyper-K Flux Uncertainty for Neutrino Mode

Hyper-K Flux Uncertainty for Anti-neutrino Mode

0.25

0.25

νm
νm
νe
νe

0.15

0.2

Fractional Error

Fractional Error

0.2

0.1
0.05

0.15

νm
νm
νe
νe

0.1
0.05

0

1

2

3

4

5

Eν (GeV)

0

0

1

2

3

4

5

Eν (GeV)Fig. 9. The predicted uncertainty on the neutrino flux calculation assuming that replica target hadronproduction data are available.

◦ Uncertainties on the alignment of beamline components, including the target and magnetic
horns.
◦ Uncertainties on the modeling of the horn fields, including the absolute field strength andasymmetries in the field.
The uncertainties on the hadronic interaction modeling are the largest contribution to the flux uncertainty and may be reduced by using the hadron production data with a replica of the T2K target.
A preliminary analysis using a subset of the replica target data from NA61/SHINE has shown thatit can be used to predict the T2K flux [81]. Since it is expected that replica target data will beavailable for future long-baseline neutrino experiments, the Hyper-K flux uncertainty is estimatedassuming the expected uncertainties on the measurement of particle multiplicities from the replicatarget. Hence, uncertainties related to the modeling of hadronic interactions inside the target are nolonger relevant; however, uncertainties for interactions outside the target are considered. The uncertainties on the measured replica target multiplicities are estimated by applying the same uncertainties
that NA61/SHINE has reported for the thin target multiplicity measurements.
The total uncertainties on the flux as a function of the neutrino energy are shown in Fig. 9. In oscillation measurements, the predicted flux is used in combination with measurements of the neutrino
interaction rate from near detectors. Hence, it is useful to consider the uncertainty on the ratio of theflux at the far and near detectors:
φHK (E ν ).
(12)
δF/N (E ν ) = δ
φND (E ν )Here φHK (E ν ) and φND (E ν ) are the predicted fluxes at Hyper-K and the near detector, respectively.
T2K uses the ND280 off-axis detector located 280 m from the T2K target. At that distance, thebeamline appears as a line source of neutrinos, compared to a point source seen by Hyper-K, and the
far-to-near ratio is not flat. For near detectors placed further away, at, e.g., 1 or 2 km, the far-to-near
flux ratio becomes flatter and there is better cancellation of the flux uncertainties between the nearand far detectors. Figure 10 shows how the uncertainty on the far-to-near ratio evolves for baselinesof 280 m, 1 km, and 2 km. While this extrapolation uncertainty is reduced for near detectors further
from the production point, even the 280 m to Hyper-K uncertainty is less than 1% near the flux peakenergy of 600 MeV.
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0

PTEP 2015, 053C02

K. Abe et al.
ν Mode: νm

0.05
0.04

F/N Fractional Error

F/N Fractional Error

280 m
1 km
2 km

0.03
0.02
0.01

280 m

0.04

1 km
2 km

0.03
0.02
0.01

0

0
1

2
3
Eν (GeV)450ν Mode: νm

0.05

F/N Fractional Error

1 km
2 km

0.03
0.02

2
3
Eν (GeV)

4

5

4

5

ν Mode: νm

0.05

280 m

0.04

1

280 m

0.04

1 km
2 km

0.03
0.02
0.01

0.01

0

0
0

1

2

3
Eν (GeV)

4

5

0

1

2

3
Eν (GeV)Fig. 10. The uncertainty on the far-to-near flux ratio for near detectors at 280 m, 1 km, and 2 km. Left: neutrino
enhanced beam. Right: anti-neutrino enhanced beam. Top: the focused component of the beam. Bottom: thedefocused component of the beam.

4.3.

Expected observables at Hyper-K

Interactions of neutrinos in the Hyper-K detector are simulated with the NEUT program library[82–84], which is used in both Super-K and T2K. The response of the detector is simulated using theSuper-K full Monte Carlo simulation based on the GEANT3 package [85]. The simulation is basedon the SK-IV configuration with upgraded electronics and DAQ system. Events are reconstructedwith the Super-K reconstruction software. As described in Sect. 3.3, the performance of the HyperK detector for neutrinos with the J-PARC beam energy is expected to be similar to that of Super-K.
Thus, the Super-K full simulation gives a realistic estimate of the Hyper-K performance.
The criteria for selecting νe and νμ candidate events are based on those developed for and established with the Super-K and T2K experiments. Fully contained (FC) events with a reconstructedvertex inside the fiducial volume (FV) and visible energy (E vis ) greater than 30 MeV are selected
as FCFV neutrino event candidates. In order to enhance charged-current quasi-elastic (CCQE,
νl + n → l − + p or ν l + p → l + + n) interaction, a single Cherenkov ring is required.
Assuming a CCQE interaction, the neutrino energy (E νrec ) is reconstructed from the energy ofthe final-state charged lepton (E  ) and the angle between the neutrino beam and the charged lepton
directions (θ ) as
2 − m − V 2 − m2
2
m
−
V
E
+
m
n

n
p



,
E νrec =2 m n − V − E  + p cos θ
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0

F/N Fractional Error

ν Mode: νm

0.05

PTEP 2015, 053C02

K. Abe et al.
Appearance ν mode
Total
Signal ν μ → ν e

300

Signal ν μ → ν eBeam ν e + ν e
Beam: ν μ + ν μ

250
200
150
100
50
0

0

0.2

0.4

0.6

0.8

1

Number of events/50 MeV

Number of events/50 MeV

Appearance ν mode
350

1.2

Total
Signal ν μ → ν e

300

Signal ν μ → ν e

250Beam ν e + ν e
Beam: ν μ + νμ

200
150
100
50
0

0

0.2

0.4

0.6

0.8

1

1.2

Fig. 11. Reconstructed neutrino energy distribution of the νe candidate events. Normal mass hierarchy withsin2 2θ13 = 0.1 and δC P = 0 are assumed.
Table 7. The expected number of νe candidate events. Normal mass hierarchy with sin2 2θ13 = 0.1 andδC P = 0 are assumed. Background (BG) is categorized by the flavor before oscillation.
Signalν modeν̄ modeBG

νμ → νeνμ → νe

νμ CC

ν μ CC

νe CC

ν e CCNC

BG total

Total

3016
396

28
2110

11
4

0
5

503
222

20
396

172
265

706
891

3750
3397

where m n , m p , m  are the masses of the neutron, proton, and charged lepton, respectively, p is the
charged lepton momentum, and V is the nuclear potential energy (27 MeV).
Then, to select νe /ν e candidate events, the following criteria are applied:◦ The reconstructed ring is identified as electron-like (e-like).
◦ The visible energy (E vis ) is greater than 100 MeV.
◦ There is no decay electron associated to the event.
◦ The reconstructed energy (E νrec ) is less than 1.25 GeV.
◦ In order to reduce the background from mis-reconstructed π 0 events, additional criteria using areconstruction algorithm recently developed for T2K (fiTQun; see Sect. 3.3) is applied. With aselection based on the reconstructed π 0 mass and the ratio of the best-fit likelihoods of the π 0and electron fits as used in T2K [11], the remaining π 0 background is reduced to about 30%
compared to the previous study [15].
Figure 11 shows the reconstructed neutrino energy distributions of νe events after all the selections.
The expected number of νe candidate events is shown in Table 7 for each signal and backgroundcomponent. In the neutrino mode, the dominant background component is intrinsic νe contamination in the beam. The mis-identified neutral-current π 0 production events are suppressed thanks to
the improved π 0 rejection. In the anti-neutrino mode, in addition to ν e and ν μ , the νe and νμ components have non-negligible contributions due to larger fluxes and cross sections compared to theircounterparts in the neutrino mode.
For the νμ /ν μ candidate events, the following criteria are applied:◦ The reconstructed ring is identified as muon-like (μ-like).
◦ The reconstructed muon momentum is greater than 200 MeV/c.
◦ There is at most one decay electron associated to the event.
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Reconstructed Energy Eνrec (GeV)

Reconstructed Energy Eνrec (GeV)PTEP 2015, 053C02

K. Abe et al.

1000

Disappearance ν mode

Number of events/50 MeV

Number of events/50 MeV

Disappearance ν mode

Total
νm
νm
νe + νe

800
600
400
200
0
0

2

4

6

8

10

1200

Total
νm
νm
νe + νe

1000
800
600
400
200
0
0

2

Reconstructed Energy E rec
ν

4

6

8

10

Reconstructed Energy E recνTable 8. The expected number of νμ candidate events.
ν modeν̄ mode

νμ CC

ν μ CC

νe CC

ν e CCNC

νμ → νeTotal

17 225
10 0661088
15 597

11
7

1
7

999
1281

49
6

19 37226 964

Figure 12 shows the reconstructed neutrino energy distributions of the selected νμ /ν μ events. Table 8shows the number of νμ candidate events for each signal and background component. For the neutrinomode, most of the events are due to νμ , while in the anti-neutrino mode the contribution from wrongsign νμ components is significant.
The reconstructed neutrino energy distributions of νe events for several values of δC P are shownin the top plots of Fig. 13. The effect of δC P is clearly seen using the reconstructed neutrino energy.
The bottom plots show the differences in reconstructed energy spectra from δC P = 0◦ for the cases
δ = 90◦ , −90◦ , and 180◦ . The error bars correspond to the statistical uncertainty. By using not only
the total number of events but also the reconstructed energy distribution, the sensitivity to δC P can be
improved, and one can discriminate all the values of δC P , including the difference between δC P = 0
and π . Figure 14 shows the reconstructed neutrino energy distributions of the νμ sample for several
values of δC P . As expected, the difference is very small for νμ events.

4.4.

Analysis method

The sensitivity of a long-baseline experiment using Hyper-K and the J-PARC neutrino beam isstudied using a binned likelihood analysis based on the reconstructed neutrino energy distribution. Both νe appearance and νμ disappearance samples, in both neutrino and anti-neutrino runs,
are simultaneously fitted.
The χ 2 used in this study is defined asχ 2 = −2 ln L + P,
where ln L is the log likelihood of a Poisson distribution,− 2 ln L =− Nktest (1 + f i ) + Nktrue ln Nktest (1 + f i ) .
k

(14)

(15)



Here, Nktrue Nktest is the number of events in the kth reconstructed energy bin for the true (test) oscillation parameters. The index k runs over all reconstructed energy bins for muon and electron neutrino
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Fig. 12. Reconstructed neutrino energy distribution of the νμ candidate events.

PTEP 2015, 053C02

K. Abe et al.
Anti-neutrino mode: Appearance

Number of events/50 MeV

Number of events/50 MeV

Neutrino mode: Appearance
450
400
350
300
250
200
150
100
50
0
0

0.2

0.4

0.6

0.8

1

400
350

δ=0

300

δ = 90250

δ = –90
δ = 180

200
150
100
50
0
0

1.2

0.2

0.4

0.6

0.8

1

Difference of events/50 MeV

150
100
50
0
–50
–100
–150
0

0.2

0.4

0.6

0.8

1

1.2

E rec
ν (GeV)

1.2

150(δ = 90) – (δ = 0)(δ = –90) – (δ = 0)(δ = 180) – (δ = 0)

100
50
0
–50
–100
–150
0

0.2

0.4

Reconstructed Energy E rec
(GeV)
ν

0.6

0.8

1

1.2

Reconstructed Energy E rec(GeV)νFig. 13. Top: Reconstructed neutrino energy distribution for several values of δC P . sin2 2θ13 = 0.1 and normal
hierarchy is assumed. Bottom: Differences in the reconstructed neutrino energy distributions from the casewith δC P = 0◦ . The error bars represent the statistical uncertainties of each bin.
Anti-neutrino mode: Disappearance
Number of events/50 MeV

Number of events/50 MeV

Neutrino mode: Disappearance
δ=0

1000

δ = 90800

δ = –90
δ = 180

600
400
200
0
0

1

2

3

4

5

6

7

8

9

10

Reconstructed Energy E rec
(GeV)
ν

1200

δ=0

1000

δ = 90800

δ = –90
δ = 180

600
400
200
0
0

1

2

3

4

5

6

7

8

9

10

Reconstructed Energy E recν (GeV)

Fig. 14. Reconstructed neutrino energy distribution of νμ candidates for several values of δC P .

samples and for neutrino and anti-neutrino mode running. The parameters f i represent systematic
uncertainties. For anti-neutrino mode samples, an additional overall normalization parameter with
6% prior uncertainty is introduced to account for a possible uncertainty in the anti-neutrino interaction, which is less known experimentally in this energy region. This additional uncertainty is expected
to decrease as we accumulate and analyze more anti-neutrino data in T2K, but we conservativelyν
is multiplied to Nktest
assign the current estimate for this study. A normalization weight 1 + f normin the anti-neutrino mode samples.
The penalty term P in Eq. (14) constrains the systematic parameters f i with the normalized
covariance matrix C: 
f i C −1 i, j f j .
(16)
P=
i, j

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Difference of events/50 MeV

Reconstructed Energy E rec(GeV)νPTEP 2015, 053C02

K. Abe et al.

i) Flux and cross-section uncertainties constrained by the fit to current near-detector data: These
arise from systematics of the near detectors. The understanding of the detector will improvein the future, but this category of uncertainties is conservatively assumed to stay at the samelevel as currently estimated.
ii) Cross-section uncertainties that are not constrained by the fit to current near-detector data:
Errors in this category will be reduced as more categories of samples are added to the neardetector data fit, which constrains the cross-section models. We assume that the uncertainties
arising from different target nuclei between the near and far detectors will become negligible
by including the measurement with the water target in the near detector.
iii) Uncertainties on the far-detector efficiency and reconstruction modeling: Because most ofthem are estimated by using atmospheric neutrinos as a control sample, errors in this category
are expected to decrease with the statistics available with Hyper-K, which is more than an orderof magnitude larger than that currently used for T2K. Uncertainties arising from the energy
scale are kept the same because they are not estimated by the atmospheric neutrino sample.
The flux and cross-section uncertainties are assumed to be uncorrelated between the neutrino andanti-neutrino running, except for the uncertainty in the νe /νμ cross-section ratio, which is treatedas anti-correlated considering the theoretical uncertainties studied in Ref. [86]. Because some of
the uncertainties, such as those from the cross-section modeling or near-detector systematics, areexpected to be correlated and give more of a constraint, this is a conservative assumption. The fardetector uncertainty is treated as fully correlated between the neutrino and anti-neutrino running.
Figures 15 and 16 show the fractional systematic uncertainties for the appearance and disappearance reconstructed energy spectra in neutrino and anti-neutrino mode, respectively. Black lines
represent the prior uncertainties and bin widths of the systematic parameters f i , while colored lines
show the contribution from each uncertainty source. Figure 17 shows the correlation matrix of thesystematic uncertainties between the reconstructed neutrino energy bins of the four samples. The
systematic uncertainties (in %) of the number of expected events at the far detector are summarizedin Table 9.

4.5.

Expected sensitivity to CP violation

Figure 18 shows the 90% CL allowed regions on the sin2 2θ13 –δC P plane. The results for the true values of δC P = − 90◦ , 0, 90◦ , 180◦ are overlaid. The top (bottom) plot shows the case for the normal
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In order to reduce the number of the systematic parameters, several reconstructed energy bins thathave similar covariance values are merged for f i .
The size of the systematic uncertainty is evaluated based on the experience and prospects of theT2K experiment, as it provides the most realistic estimate as the baseline. We estimate the systematic uncertainties assuming the T2K neutrino beamline and near detectors, taking into accountimprovements expected with future T2K running and analysis improvements. For Hyper-K, a further
reduction of systematic uncertainties will be possible with upgrade of the beamline and near detectors, improvements in detector calibration and analysis techniques, and improved understanding of
neutrino interaction with more measurements. In particular, as described in Sect. 3.2, studies of neardetectors are ongoing with a goal of further reducing systematic uncertainties. The sensitivity update
is expected in the near future as the near-detector design studies advance.
There are three main categories of systematic uncertainties. We assume improvement from thecurrent T2K uncertainties for each category as follows.

K. Abe et al.

ve in neutrino mode
Total
Flux + ND
Cross-section model
Far detector

0.2

Frac. error

Frac. error

PTEP 2015, 053C02

0.1

vµ in neutrino mode

0.2

Total
Flux + ND
Cross-section model
Far detector

0.1

0
0

0
0

0. 5
1
Reconstructed energy [GeV]1
2
Reconstructed energy [GeV]

3

Total
Flux + ND
Cross-section model
Far detector

0.2

Frac. error

Frac. error

ve in anti-neutrino mode

0.1

vµ in anti-neutrino mode
0.2

Total
Flux + ND
Cross-section model
Far detector

0.1

0
0

0. 5

0

1

0

1

Reconstructed energy [GeV]2

3

Reconstructed energy [GeV]Parameter number

Fig. 16. Fractional error size for the appearance (left) and disappearance (right) samples in the anti-neutrino mode. Black: total uncertainty, red: flux and cross section constrained by the near detector, magenta:
near-detector non-constrained cross section, blue: far-detector error.
1

40

0.8

35

0.6
30
0.4
25

0.2
0

20

–0.2

15

–0.4
10
–0.6
5
0
0

–0.8
5

1Re

10

15

1Rµ

20

25

1Re

Neutrino mode

30

35
40
Parameter number

–1

1Rµ

Anti-neutrino mode

Fig. 17. Correlation matrix between reconstructed energy bins of the four samples due to the systematic
uncertainties. Bins 1–8, 9–20, 21–28, and 29–40 correspond to the neutrino-mode single-ring e-like, the neutrino-mode single-ring μ-like, the anti-neutrino-mode single-ring e-like, and the anti-neutrino-mode single-ring
μ-like samples, respectively.

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Fig. 15. Fractional error size for the appearance (left) and disappearance (right) samples in the neutrino mode.
Black: total uncertainty, red: flux and cross section constrained by the near detector, magenta: near-detector
non-constrained cross section, blue: far-detector error.

PTEP 2015, 053C02

K. Abe et al.

Table 9. Uncertainties (in %) for the expected number of events at Hyper-K from the systematic
uncertainties assumed in this study. ND: near detector.
Flux & ND-constrained
cross section

ND-independent
cross section

Far detector

Total

Appearance
Disappearance

3.0
2.8

1.2
1.5

0.7
1.0

3.3
3.3

ν modeAppearance
Disappearance

5.6
4.2

2.0
1.4

1.7
1.1

6.2
4.5

150

Normal mass hierarchy

100
50
0
–50
Hyper-K
Hyper-K + reactor

–100
–150
0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

δCP [degree]

sin22θ13
150

Inverted mass hierarchy

100
50
0
–50
Hyper-K
Hyper-K + reactor

–100
–150
0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

sin 2θ13
2

Fig. 18. The 90% CL allowed regions in the sin2 2θ13 –δC P plane. The results for the true values of
δC P = (−90◦ , 0, 90◦ , 180◦ ) are overlaid. Top: normal hierarchy case. Bottom: inverted hierarchy case. Red(blue) lines show the result with Hyper-K only (with a sin2 2θ13 constraint from reactor experiments).

(inverted) mass hierarchy. Also shown are the allowed regions when we include a constraint fromthe reactor experiments, sin2 2θ13 = 0.100 ± 0.005. With reactor constraints, although the contour
becomes narrower in the direction of sin2 2θ13 , the sensitivity to δC P does not significantly change
because δC P is constrained by the comparison of neutrino and anti-neutrino oscillation probabilities
by Hyper-K and not limited by the uncertainty of θ13 .
Figure 19 shows the expected significance to exclude sin δC P = 0 (the C P conserved case). The
significance is calculated asχ 2 , where χ 2 is the difference in χ 2 for the trial value of δC P
and for δC P = 0◦ or 180◦ (the smaller value of difference is taken). We have also studied the casewith a reactor constraint, but the result changes only slightly. Figure 20 shows the fraction of δC P for
which sin δC P = 0 is excluded with more than 3 σ and 5 σ significance as a function of the integrated
beam power. The ratio of integrated beam power for the neutrino and anti-neutrino modes is fixed to
1:3. Normal mass hierarchy is assumed. The results for the inverted hierarchy are almost the same.
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δCP [degree]ν modePTEP 2015, 053C02

K. Abe et al.

σ = √χ2

10

Normal mass hierarchy
8
6

5σ

4

3σ

2
0

–150

–100

–50

0

50

100

150

σ = √χ2

10

Inverted mass hierarchy
8
6

5σ

4

3σ

2
0

–150

–100

–50

0

50

100

150

δCP [degree]

Fraction of δ CP [%]Fig. 19. Expected significance to exclude sin δC P = 0. Top: normal hierarchy case. Bottom: inverted hierarchy
case.

100
90
80
70
60
50
40
30
20
10
0
0

5σ
3σ

2
4
6
8
Integrated beam power [MW 10 7sec]

10

Fig. 20. Fraction of δC P for which sin δC P = 0 can be excluded with more than 3 σ (red) and 5 σ (blue)
significance as a function of the integrated beam power for the normal hierarchy case. The ratio of the neutrino
and anti-neutrino modes is fixed to 1:3.

C P violation in the lepton sector can be observed with more than 3(5) σ significance for 76(58)%of the possible values of δC P .
Figure 21 shows the 68% CL uncertainty of δC P as a function of the integrated beam power. With
7.5 MW × 107 s of exposure (1.56 × 1022 protons on target), the value of δC P can be determined tobetter than 19◦ for all values of δC P .
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δCP [degree]K. Abe et al.

68% CL error of δCP [degree]

PTEP 2015, 053C02
50
45
40
35
30
25
20
15
10
5
0
0

δ= 0
δ = 9010

Fraction of δ CP [%]Fig. 21. Expected 68% CL uncertainty of δC P as a function of integrated beam power.
100
90
80
70
60
50
40
30
20
10
0

5σ

T2K 90% CL

3σ
0.35

0.4

0.45

0.5

0.55

0.6

0.65
sin2 θ 23

Δ m 232 [eV2]

Fig. 22. Fraction of δC P for which sin δC P = 0 can be excluded with more than 3 σ (red) and 5 σ (blue)
significance as a function of the true value of sin2 θ23 , for the normal hierarchy case. Vertical dashed lines
indicate 90% confidence intervals of sin2 θ23 from the T2K measurement in 2014 [38].
3.0 ×10–3

T2K 2014
Hyper-K
Hyper-K + reactor

2.8
2.6
2.4
2.2
0.4

0.45

0.5

0.55

0.6

0.65
sin2θ23

Fig. 23. The 90% CL allowed regions in the sin2 θ23 – m 232 plane. The true values are sin2 θ23 = 0.5 andm 232 = 2.4 × 10−3 eV2 (red point). The effect of systematic uncertainties is included. The red (blue) line
corresponds to the result with Hyper-K alone (with a reactor constraint on sin2 2θ13 ). The dotted line is the
90% CL contour from the T2K experiment [38] with the best-fit values indicated by a black point.

As a nominal value, we use sin2 θ23 = 0.5, but the sensitivity to C P violation depends on the valueof θ23 . Figure 22 shows the fraction of δC P for which sin δC P = 0 is excluded with more than 3 σ
and 5 σ significance as a function of the true value of sin2 θ23 with the current best knowledge of thepossible sin2 θ23 range from the T2K Collaboration [38].
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2
4
6
8
Integrated beam power [MW 107 sec]

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Δ m 232 [eV2]–3

2.6 ×10Hyper-K

2.55
2.5
2.45
2.4
2.35
2.3
2.25
2.2
0.35

0.4

0.45

0.5

0.55

0.6

0.65

Δ m 232 [eV2]–3

2.6 ×10Hyper-K + reactor

2.55
2.5
2.45
2.4
2.35
2.3
2.25
2.2
0.35

0.4

0.45

0.5

0.55

0.6

0.65

sin2θ23

Fig. 24. 90% CL allowed regions in the sin2 θ23 – m 232 plane. The true values are sin2 θ23 = 0.45 andm 232 = 2.4 × 10−3 eV2 . The effect of systematic uncertainties is included. Top: Hyper-K only. Bottom: Witha reactor constraint.
Table 10. Expected 1 σ uncertainty of m 232 and sin2 θ23 for true sin2 θ23 = 0.45, 0.50, 0.55. A reactor
constraint on sin2 2θ13 = 0.1 ± 0.005 is imposed. NH: normal hierarchy, IH: inverted hierarchy.
0.45

0.50

0.55

True sin2 θ23
Parameter

m 232 (eV2 )sin2 θ23m 232 (eV2 )sin2 θ23m 232 (eV2 )sin2 θ23

NH
IH

1.4 × 10−5
1.5 × 10−5

0.006
0.006

1.4 × 10−5
1.4 × 10−5

0.015
0.015

1.5 × 10−5
1.5 × 10−5

0.009
0.009

4.6.

Sensitivity tom 232 and sin2 θ23

The result shown above is obtained with sin2 θ23 and m 232 as free parameters as well as sin2 2θ13
and δC P , with nominal parameters shown in Table 6. The use of the νμ sample in addition to νeenables us to also precisely measure sin2 θ23 and m 232 . Figure 23 shows the 90% CL allowed
regions for the true value of sin2 θ23 = 0.5 together with the 90% CL contour by the T2K νμ disappearance measurement [38]. Hyper-K will be able to provide a precise measurement of sin2 θ23
and m 232 . Figure 24 shows the 90% CL allowed regions on the sin2 θ23 – m 232 plane, for the true
values of sin2 θ23 = 0.45 and m 232 = 2.4 × 10−3 eV2 . For the determination of θ23 , a νμ disappearance measurement provides a precise measurement of sin2 2θ23 . However, when θ23 = π4 , there are
two possible solutions (θ23 and π2 − θ23 ), which give the same sin2 2θ23 . This is known as the octant
degeneracy. As seen from Eq. (7), the νe appearance measurement can determine sin2 θ23 sin2 2θ13 .
In addition, the reactor experiments provide an almost pure measurement of sin2 2θ13 . Thus, the30/35

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δCP Uncertainty

25

20

15

3σ

10

2σ

5

T2K 90% CL
0

0.4

0.45

0.5

0.55

0.6

sin θ 232

δCP Uncertainty

Δ χ 2 Wrong Octant Rejection

30

25

20

15

T2K 90% CL

10

3σ

5

2σ

0

0.4

0.45

0.5

0.55

0.6

sin θ 23
2

Fig. 25. Atmospheric neutrino sensitivities for a 10 yr exposure of Hyper-K assuming that the mass hierarchy
is normal. Top: the χ 2 discrimination of the wrong hierarchy hypothesis as a function of the assumed true
value of sin2 θ23 . Bottom: the discrimination between the wrong octant for each value of sin2 θ23 . The uncertainty
from δC P is represented by the thickness of the band. Vertical dashed lines indicate 90% confidence intervalsof sin2 θ23 from the T2K measurement in 2014 [38].

combination of these complementary measurements is known to be able to resolve this degeneracy
if θ23 is sufficiently away from π4 [87–89]. As shown in Fig. 24, with a constraint on sin2 2θ13 fromthe reactor experiments, Hyper-K measurements can resolve the octant degeneracy and precisely
determine sin2 θ23 .
The expected precision of m 232 and sin2 θ23 for true sin2 θ23 = 0.45, 0.50, 0.55 with a reactor
constraint on sin2 2θ13 is summarized in Table 10.

4.7.

Combination with atmospheric neutrino data

Atmospheric neutrinos can provide independent and complementary information to the accelerator
beam program on the study of neutrino oscillation. For example, through the matter effect inside the
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30

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30
Atmospheric ν
Accelerator ν

25

Δ χ2

20

15

5

0
–150

–100

–50

0

50

100

150

δCP [degree]
30

25

Atm. + Acc.

Δ χ2

20

15

10

5

0
–150

–100

–50

0

50

100

150

δCP [degree]

Fig. 26. Combination of the accelerator and atmospheric data. Top: Expected χ 2 values for accelerator andatmospheric neutrino measurements assuming that the mass hierarchy is unknown. The true mass hierarchy isnormal hierarchy and the true value of δC P = 0. Bottom: By combining the two measurements, the sensitivity
can be enhanced. In this example study, χ 2 is simply added.

Earth, a large-statistics sample of atmospheric neutrinos by Hyper-K will have a good sensitivity to
the mass hierarchy and θ23 octant.
Assuming a 10 yr exposure, Hyper-K’s sensitivity to the mass hierarchy and the octant of θ23 byatmospheric neutrino data are shown in Fig. 25. Depending on the true value of θ23 , the sensitivity
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5.

Conclusion

The sensitivity to leptonic C P asymmetry of a long-baseline experiment using a neutrino beam
directed from J-PARC to the Hyper-Kamiokande detector has been studied based on a full simulationof beamline and detector. With an integrated beam power of 7.5 MW × 107 s, the value of δC P canbe determined to better than 19◦ for all values of δC P , and C P violation in the lepton sector can beobserved with more than 3 σ (5 σ ) significance for 76% (58%) of the possible values of δC P .
Using both νe appearance and νμ disappearance data, a precise measurement of sin2 θ23 will bepossible. The expected 1 σ uncertainty is 0.015(0.006) for sin2 θ23 = 0.5(0.45).
Acknowledgements
This work was supported by a MEXT Grant-in-Aid for Scientific Research on Innovative Areas Number
25105004, titled “Unification and Development of the Neutrino Science Frontier.” In addition, the participation of individual researchers has been further supported by funds from JSPS, Japan; the European Union
ERC-207282, H2020 RISE-GA644294-JENNIFER, and H2020 RISE-GA641540-SKPLUS; RSF, RFBR, and
MES, Russia; and JSPS and RFBR under the Japan–Russia Research Cooperative Program.
Funding
Open Access funding: SCOAP3 .

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