submitted to Physical Review Letters

arXiv:1308.0465v1 [hep-ex] 2 Aug 2013

Measurement of Neutrino Oscillation Parameters from Muon Neutrino Disappearancewith an Off-axis Beam
K. Abe,49 N. Abgrall,14 H. Aihara,48, ∗ T. Akiri,11 C. Andreopoulos,47 S. Aoki,26 A. Ariga,2 T. Ariga,2S. Assylbekov,9 D. Autiero,31 M. Barbi,41 G.J. Barker,57 G. Barr,37 M. Bass,9 M. Batkiewicz,15 F. Bay,13
S.W. Bentham,28 V. Berardi,20 B.E. Berger,9 S. Berkman,4 I. Bertram,28 S. Bhadra,61 F.d.M. Blaszczyk,30
A. Blondel,14 C. Bojechko,54 S.B. Boyd,57 D. Brailsford,19 A. Bravar,14 C. Bronner,27 N. Buchanan,9R.G. Calland,29 J. Caravaca Rodrı́guez,17 S.L. Cartwright,45 R. Castillo,17 M.G. Catanesi,20 A. Cervera,18
D. Cherdack,9 G. Christodoulou,29 A. Clifton,9 J. Coleman,29 S.J. Coleman,8 G. Collazuol,22 K. Connolly,58
L. Cremonesi,40 A. Curioni,13 A. Dabrowska,15 I. Danko,39 R. Das,9 S. Davis,58 P. de Perio,52 G. De Rosa,21
T. Dealtry,47, 37 S.R. Dennis,57, 47 C. Densham,47 F. Di Lodovico,40 S. Di Luise,13 O. Drapier,12 T. Duboyski,40
F. Dufour,14 J. Dumarchez,38 S. Dytman,39 M. Dziewiecki,56 S. Emery,6 A. Ereditato,2 L. Escudero,18 A.J. Finch,28
E. Frank,2 M. Friend,16, † Y. Fujii,16, † Y. Fukuda,32 A.P. Furmanski,57 V. Galymov,6 A. Gaudin,54 S. Giffin,41
C. Giganti,38 K. Gilje,34 T. Golan,60 J.J. Gomez-Cadenas,18 M. Gonin,12 N. Grant,28 D. Gudin,24 D.R. Hadley,57
A. Haesler,14 M.D. Haigh,57 P. Hamilton,19 D. Hansen,39 T. Hara,26 M. Hartz,25, 53 T. Hasegawa,16, † N.C. Hastings,41
Y. Hayato,49 C. Hearty,4, ‡ R.L. Helmer,53 M. Hierholzer,2 J. Hignight,34 A. Hillairet,54 A. Himmel,11 T. Hiraki,27
S. Hirota,27 J. Holeczek,46 S. Horikawa,13 K. Huang,27 A.K. Ichikawa,27 K. Ieki,27 M. Ieva,17 M. Ikeda,27 J. Imber,34
J. Insler,30 T.J. Irvine,50 T. Ishida,16, † T. Ishii,16, † S.J. Ives,19 K. Iyogi,49 A. Izmaylov,18, 24 A. Jacob,37
B. Jamieson,59 R.A. Johnson,8 J.H. Jo,34 P. Jonsson,19 K.K. Joo,7 C.K. Jung,25, 34 A.C. Kaboth,19 T. Kajita,50, ∗H. Kakuno,51 J. Kameda,49 Y. Kanazawa,48 D. Karlen,54, 53 I. Karpikov,24 E. Kearns,3, ∗ M. Khabibullin,24
A. Khotjantsev,24 D. Kielczewska,55 T. Kikawa,27 A. Kilinski,33 J. Kim,4 S.B. Kim,44 J. Kisiel,46 P. Kitching,1
T. Kobayashi,16, † G. Kogan,19 A. Kolaceke,41 A. Konaka,53 L.L. Kormos,28 A. Korzenev,14 K. Koseki,16, †Y. Koshio,35, ∗ I. Kreslo,2 W. Kropp,5 H. Kubo,27 Y. Kudenko,24 S. Kumaratunga,53 R. Kurjata,56 T. Kutter,30
J. Lagoda,33 K. Laihem,43 M. Laveder,22 M. Lawe,45 M. Lazos,29 K.P. Lee,50 C. Licciardi,41 I.T. Lim,7
T. Lindner,53 C. Lister,57 R.P. Litchfield,57, 27 A. Longhin,22 G.D. Lopez,34 L. Ludovici,23 M. Macaire,6L. Magaletti,20 K. Mahn,53 M. Malek,19 S. Manly,42 A.D. Marino,8 J. Marteau,31 J.F. Martin,52 T. Maruyama,16, †J. Marzec,56 P. Masliah,19 E.L. Mathie,41 V. Matveev,24 K. Mavrokoridis,29 E. Mazzucato,6 N. McCauley,29
K.S. McFarland,42 C. McGrew,34 C. Metelko,29 P. Mijakowski,33 C.A. Miller,53 A. Minamino,27 O. Mineev,24
S. Mine,5 A. Missert,8 M. Miura,49 L. Monfregola,18 S. Moriyama,49, ∗ Th.A. Mueller,12 A. Murakami,27
M. Murdoch,29 S. Murphy,13 J. Myslik,54 T. Nagasaki,27 T. Nakadaira,16, † M. Nakahata,49, ∗ T. Nakai,36
K. Nakamura,25, 16, † S. Nakayama,49, ∗ T. Nakaya,27, ∗ K. Nakayoshi,16, † C. Nielsen,4 M. Nirkko,2 K. Nishikawa,16, †Y. Nishimura,50 H.M. O’Keeffe,37 R. Ohta,16, † K. Okumura,50, ∗ T. Okusawa,36 W. Oryszczak,55 S.M. Oser,4M. Otani,27 R.A. Owen,40 Y. Oyama,16, † M.Y. Pac,10 V. Palladino,21 V. Paolone,39 D. Payne,29 G.F. Pearce,47
O. Perevozchikov,30 J.D. Perkin,45 Y. Petrov,4 E.S. Pinzon Guerra,61 C. Pistillo,2 P. Plonski,56 E. Poplawska,40
B. Popov,38, § M. Posiadala,55 J.-M. Poutissou,53 R. Poutissou,53 P. Przewlocki,33 B. Quilain,12 E. Radicioni,20
P.N. Ratoff,28 M. Ravonel,14 M.A.M. Rayner,14 A. Redij,2 M. Reeves,28 E. Reinherz-Aronis,9 F. Retiere,53
A. Robert,38 P.A. Rodrigues,42 E. Rondio,33 S. Roth,43 A. Rubbia,13 D. Ruterbories,9 R. Sacco,40 K. Sakashita,16, †F. Sánchez,17 E. Scantamburlo,14 K. Scholberg,11, ∗ J. Schwehr,9 M. Scott,53 Y. Seiya,36 T. Sekiguchi,16, †H. Sekiya,49, ∗ D. Sgalaberna,13 M. Shiozawa,49, ∗ S. Short,19 Y. Shustrov,24 P. Sinclair,19 B. Smith,19 R.J. Smith,37
M. Smy,5 J.T. Sobczyk,60 H. Sobel,5, ∗ M. Sorel,18 L. Southwell,28 P. Stamoulis,18 J. Steinmann,43 B. Still,40
Y. Suda,48 A. Suzuki,26 K. Suzuki,27 S.Y. Suzuki,16, † Y. Suzuki,49, ∗ T. Szeglowski,46 R. Tacik,41, 53 M. Tada,16, †S. Takahashi,27 A. Takeda,49 Y. Takeuchi,26, ∗ H.A. Tanaka,4, ‡ M.M. Tanaka,16, † I.J. Taylor,34 D. Terhorst,43
R. Terri,40 L.F. Thompson,45 A. Thorley,29 S. Tobayama,4 W. Toki,9 T. Tomura,49, ∗ Y. Totsuka,¶ C. Touramanis,29
T. Tsukamoto,16, † M. Tzanov,30 Y. Uchida,19 K. Ueno,49 A. Vacheret,37 M. Vagins,25, 5 G. Vasseur,6 T. Wachala,9A.V. Waldron,37 C.W. Walter,11, ∗ D. Wark,47, 19 M.O. Wascko,19 A. Weber,47, 37 R. Wendell,49, ∗ R.J. Wilkes,58
M.J. Wilking,53 C. Wilkinson,45 Z. Williamson,37 J.R. Wilson,40 R.J. Wilson,9 T. Wongjirad,11 Y. Yamada,16, †K. Yamamoto,36 C. Yanagisawa,34, ∗∗ S. Yen,53 N. Yershov,24 M. Yokoyama,48, ∗ T. Yuan,8 A. Zalewska,15
J. Zalipska,33 L. Zambelli,38 K. Zaremba,56 M. Ziembicki,56 E.D. Zimmerman,8 M. Zito,6 and J. Żmuda60(The T2K Collaboration)
1

University of Alberta, Centre for Particle Physics, Department of Physics, Edmonton, Alberta, Canada
2
University of Bern, Albert Einstein Center for Fundamental Physics,
Laboratory for High Energy Physics (LHEP), Bern, Switzerland
3
Boston University, Department of Physics, Boston, Massachusetts, U.S.A.
4
University of British Columbia, Department of Physics and Astronomy, Vancouver, British Columbia, Canada

2
5

University of California, Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.
6
IRFU, CEA Saclay, Gif-sur-Yvette, France
7
Chonnam National University, Institute for Universe & Elementary Particles, Gwangju, Korea
8
University of Colorado at Boulder, Department of Physics, Boulder, Colorado, U.S.A.
9
Colorado State University, Department of Physics, Fort Collins, Colorado, U.S.A.
10
Dongshin University, Department of Physics, Naju, Korea
11
Duke University, Department of Physics, Durham, North Carolina, U.S.A.
12
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
13
ETH Zurich, Institute for Particle Physics, Zurich, Switzerland
14
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
15
H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland
16
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
17
Institut de Fisica d’Altes Energies (IFAE), Bellaterra (Barcelona), Spain
18
IFIC (CSIC & University of Valencia), Valencia, Spain
19
Imperial College London, Department of Physics, London, United Kingdom
20
INFN Sezione di Bari and Università e Politecnico di Bari, Dipartimento Interuniversitario di Fisica, Bari, Italy
21
INFN Sezione di Napoli and Università di Napoli, Dipartimento di Fisica, Napoli, Italy
22
INFN Sezione di Padova and Università di Padova, Dipartimento di Fisica, Padova, Italy
23
INFN Sezione di Roma and Università di Roma “La Sapienza”, Roma, Italy
24
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
25
Kavli Institute for the Physics and Mathematics of the Universe (WPI),
Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan
26
Kobe University, Kobe, Japan
27
Kyoto University, Department of Physics, Kyoto, Japan
28
Lancaster University, Physics Department, Lancaster, United Kingdom
29
University of Liverpool, Department of Physics, Liverpool, United Kingdom
30
Louisiana State University, Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.
31
Université de Lyon, Université Claude Bernard Lyon 1, IPN Lyon (IN2P3), Villeurbanne, France
32
Miyagi University of Education, Department of Physics, Sendai, Japan
33
National Centre for Nuclear Research, Warsaw, Poland
34
State University of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New York, U.S.A.
35
Okayama University, Department of Physics, Okayama, Japan
36
Osaka City University, Department of Physics, Osaka, Japan37
Oxford University, Department of Physics, Oxford, United Kingdom
38
UPMC, Université Paris Diderot, CNRS/IN2P3, Laboratoire dePhysique Nucléaire et de Hautes Energies (LPNHE), Paris, France
39
University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, Pennsylvania, U.S.A.
40
Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom
41
University of Regina, Department of Physics, Regina, Saskatchewan, Canada
42
University of Rochester, Department of Physics and Astronomy, Rochester, New York, U.S.A.
43
RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany
44
Seoul National University, Department of Physics and Astronomy, Seoul, Korea
45
University of Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom
46
University of Silesia, Institute of Physics, Katowice, Poland
47
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United Kingdom
48
University of Tokyo, Department of Physics, Tokyo, Japan
49
University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
50
University of Tokyo, Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, Kashiwa, Japan
51
Tokyo Metropolitan University, Department of Physics, Tokyo, Japan
52
University of Toronto, Department of Physics, Toronto, Ontario, Canada
53
TRIUMF, Vancouver, British Columbia, Canada
54
University of Victoria, Department of Physics and Astronomy, Victoria, British Columbia, Canada
55
University of Warsaw, Faculty of Physics, Warsaw, Poland
56
Warsaw University of Technology, Institute of Radioelectronics, Warsaw, Poland
57
University of Warwick, Department of Physics, Coventry, United Kingdom
58
University of Washington, Department of Physics, Seattle, Washington, U.S.A.
59
University of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada
60
Wroclaw University, Faculty of Physics and Astronomy, Wroclaw, Poland
61
York University, Department of Physics and Astronomy, Toronto, Ontario, Canada(Dated: August 5, 2013)
The T2K collaboration reports a precision measurement of muon neutrino disappearance with
an off-axis neutrino beam with a peak energy of 0.6 GeV. Near detector measurements are used
to constrain the neutrino flux and cross section parameters. The Super-Kamiokande far detector,

3which is 295 km downstream of the neutrino production target, collected data corresponding to3.01 × 1020 protons on target. In the absence of neutrino oscillations, 205 ± 17 (syst.) events are
expected to be detected and only 58 muon neutrino event candidates are observed. A fit to theneutrino rate and energy spectrum assuming three neutrino flavors, normal mass hierarchy andθ23 ≤ π/4 yields a best-fit mixing angle sin2 (2θ23 ) = 1.000 and mass splitting |∆m232 | = 2.44 × 10−3
eV2 /c4 . If θ23 ≥ π/4 is assumed, the best-fit mixing angle changes to sin2 (2θ23 ) = 0.999 and themass splitting remains unchanged.
PACS numbers: 14.60.Pq,14.60.Lm,12.27.-a,29.40.ka

Introduction.—Oscillations between different neutrino
flavor states are a physics process well described by
the 3 × 3 Pontecorvo-Maki-Nakagawa-Sakata mixing matrix [1], which is parametrized by three mixing angles
θ12 , θ23 , θ13 , and a CP violating phase δCP . In this mixing scheme, the angle θ23 and mass splitting ∆m232 are
the main parameters that govern atmospheric and longbaseline νµ disappearance oscillations. The oscillation
probability in natural units and in the limit |∆m232 | ≫|∆m221 | is
P (νµ → νµ ) ≃1 − [cos4 (θ13 ) sin2 (2θ23 ) + sin2 (θ23 )× sin2 (2θ13 )] sin2 (∆m232 L/4Eν ),(1)

where L is the neutrino propagation distance and Eν isthe neutrino energy. Recent measurements [2–5] are near
θ23 = π/4 where sin2 (2θ23 ) becomes maximal. In light ofrecent θ13 > 0 measurements [6], there is considerable interest to determine if θ23 is non-maximal. This can havean important impact on neutrino mass models and theinterpretation of νe appearance results. In this paper, we
report on new measurements on the value of sin2 (2θ23 ).
T2K Experiment.—The T2K experiment [7] uses a 30
GeV proton beam accelerated by the J-PARC accelerator
facility. This combines (1) a muon neutrino beam line,(2) the near detector complex, which is located 280 m
downstream of the neutrino production target, monitors
the beam, and constrains the neutrino flux parametrization and cross sections, and (3) the far detector, SuperKamiokande (SK), which detects neutrinos at a baseline
distance of L = 295 km from the target. The neutrino
beam is directed 2.5◦ away from SK producing a narrowband νµ beam [8] at the far detector. The off-axis angle
is chosen such that the energy peaks at Eν =∆m232 L/2π
≈ 0.6 GeV which corresponds to the first oscillation minimum of the νµ survival probability at SK. This enhances
the sensitivity to determine θ23 from the oscillation measurements and reduces backgrounds from higher-energy
neutrino interactions at SK.

∗ also at Kavli IPMU, U. of Tokyo, Kashiwa, Japan† also at J-PARC, Tokai, Japan‡ also at Institute of Particle Physics, Canada§ also at JINR, Dubna, Russia¶ deceased∗∗ also at BMCC/CUNY,

York, U.S.A..

Science Department, New York, New

The J-PARC main ring accelerator provides a fastextracted high-intensity proton beam. The primarybeam line has 21 electrostatic beam position monitors,
19 secondary emission monitors, an optical transition radiation monitor, and five current transformers to measure
the proton current before a graphite target. Pions andkaons produced in the target decay in the helium-filled
secondary beam line, which contains three focusing horns
and a 96-m-long decay tunnel. This is followed by a beam
dump and a set of muon monitors.
The near detector complex contains an on-axis Interactive Neutrino Grid detector (INGRID) [9] and an off-axis
magnetic detector, ND280. The INGRID detector has
14 seven-ton iron-scintillator tracker modules arranged
in a 10-m horizontal by 10-m vertical crossed array. Thisdetector provides high-statistics monitoring of the beam
intensity, direction, profile, and stability. The off-axis detector is enclosed in a 0.2-T magnet that contains a subdetector optimized to measure π 0 s (PØD) [10], three time
projection chambers (TPC1,2,3) [11] alternating with
two one-ton fine grained detectors (FGD1,2) [12], and anelectromagnetic calorimeter (ECal) that surrounds the
TPC, FGD, and PØD detectors. A side muon range detector (SMRD) [13], built into slots in the magnet flux
return steel, detects muons that exit or stop in the magnet steel when the path length exceeds the energy loss
range. A schematic diagram of the detector layout has
been published elsewhere [7].
The SK water Cherenkov far detector [14] has a fiducial volume of 22.5 kt contained within a cylindrical innerdetector (ID) instrumented with 11129 inward facing 20inch phototubes. Surrounding the ID is a 2-meter wide
outer detector (OD) with 1885 outward-facing 8-inch
phototubes. A Global Positioning System with <150 ns
precision synchronizes the timing between reconstructed
SK events and the J-PARC beam spill.
These results are based on three running periods: Run
1 (January-June 2010), Run 2 (November 2010-March
2011), and Run 3 (January-June 2012). The proton beam
power on the target steadily increased from Run 1, reaching 200 kW with about 1014 protons per pulse on thetarget by the end of Run 3. The total neutrino beam
exposure on the SK detector corresponds to a total integrated 3.01 × 1020 protons on target (POT).
Analysis Strategy.—The analysis method estimates oscillation parameters by comparing the observed and predicted νµ interaction rate and energy spectrum at thefar detector. The rate and spectrum depend on the os-4cillation parameters, the incident neutrino flux, neutrino
interaction cross sections, and the detector response. The
initial estimate of the neutrino flux is determined by detailed simulations incorporating proton beam measurements, INGRID measurements, and the pion and kaon
production measured by the NA61/SHINE [15] experiment. The ND280 detector measurement of νµ charged
current (CC) events is used to constrain the initial flux estimates and parameters of the neutrino interaction models that affect the predicted rate and spectrum of neutrino interactions at both ND280 and SK. At SK, νµcharged current quasi-elastic (CCQE) events are selected
and efficiencies are determined, along with their dependence on final state interactions (FSI) inside the nucleus
and secondary pion interactions (SI) in the detector material. These combined results are used in a binned likelihood ratio fit to determine the oscillation parameters.
Initial Neutrino Flux Model.—To predict the neutrino flux at the near and far detectors, the interactions of the primary beam protons and subsequent secondary particles in a graphite target are modeled with a
FLUKA2008 [16] simulation. GEANT3 [17] simulations
model the secondary particles in the magnetic horns andthe decay region, and their decays into neutrinos. The
hadron interactions are modeled with GCALOR [18].
The simulation is tuned using measurements of the
primary proton beam profile and the T2K horn magnetic fields and the NA61/SHINE hadron production results [15]. In addition, the contribution to the flux uncertainty from the secondary beam line component alignment and the neutrino beam direction are evaluated. The
stability of the beam direction and neutrino rate per proton on target are monitored continuously with INGRID,
and the variations are measured to be less than the assigned systematic uncertainties [19]. The total uncertainties in the flux are 10-20% in the relevant energy range,
dominated by the hadron production uncertainties. Moredetails of the flux calculation are described elsewhere [8].
Neutrino Interaction Simulations and Cross Section
Parameters—Neutrino interactions in the ND280 and SK
detectors are simulated with the NEUT Monte Carlogenerator [20]. External data, primarily from the MiniBooNE experiment [21], are used to tune some NEUT
neutrino interaction parameters. These determine the input parameter uncertainties used in the fit to the ND280
data [19]. Neutrino interaction parameters fall into two
categories: parameters that are common between ND280
and SK, and independent parameters affecting interactions at only one of the detectors. The common parameters include the axial masses for CCQE and resonant
pion production, as well as 5 energy dependent normalizations; these are included in the fit to the ND280 data,
which is discussed in the next section. Since the ND280
target is mainly carbon and differs from the SK target
which is mainly oxygen, additional independent parameters are required. These affect the nuclear model for
CCQE (Fermi momentum, binding energy and spectral
function modeling) and include five cross section parame-ters related to pion production, the neutral current (NC)cross section, the νe /νµ CC cross section ratio, and theν/ν̄ CC cross section ratio. These independent cross section uncertainties (11 parameters) produce a 6.3% fractional error in the expected number of SK events as listed
in Table I. Not simulated by NEUT are multi-nucleon
knock-out processes [22] that may affect strongly [23] thedetermination of the oscillation parameters by causing an
additional bias between reconstructed and true neutrinoenergy. An estimation of the bias on the oscillation parameters from these processes [22] appears to be smaller
than the current statistical precision when the overall
rate of CC interactions with ND280 data is constrained
and the uncertainties in pion-less ∆ particle decay areincluded.
ND280 Measurements, Flux and Common Cross Section fits.—The ND280 detector measures a sample of inclusive CC events with a vertex in FGD1 located upstream of FGD2 and with the muon passing throughTPC2. The event selection uses the highest-momentum
negatively charged track entering TPC2 that matches avertex inside the upstream FGD1 fiducial volume. In
addition, the measured track energy loss in TPC2 must
be compatible with a muon. Events originating from interactions in upstream detectors are vetoed by excluding
events with a track in the TPC1 upstream of FGD1. This
suppresses events with interactions occuring upstream of
FGD1 or with a charged particle going backwards from
FGD1 into TPC1. Using an inclusive CC selection, theefficiency is 47.6% with a purity of 88.1%. The main
backgrounds are events where the neutrino interactions
occur outside FGD1 and migrate into the fiducial volume due to mis-reconstruction, or from neutral particles
interacting within the FGD1.
This CC inclusive sample is further subdivided into two
mutually exclusive samples: a CCQE-enhanced sample
and the remaining events which are called the CC-nonQE-enhanced sample (CCnQE). This separation is madeto improve constraints on the neutrino flux and cross section parameters. The CCQE selection vetoes events withadditional tracks that cross FGD1 and TPC2 or haveelectrons from muon decay found inside FGD1. Afterbeam and data quality cuts, there are 5841 CCQE and5214 CCnQE events that correspond to an integrated
dataset of 2.66 × 1020 POT. These two data selections
are each subdivided into 5(momentum) × 4(angular) bins
which produces a 40-bin histogram used in a fit to the
ND280 data.
The 40-bin histogram and cosmic ray control samples
are fit to estimate the neutrino flux crossing ND280 in
11 bins of Eνµ , 7 common and 4 ND280 neutrino interaction parameters, detector response parameters, and theircovariance. This ND280 fit also estimates the SK flux
parameters, which are constrained through their priorcovariance with the ND280 flux parameters as calculatedby the beam simulation described earlier. The largest
detector systematics are from the absolute track momentum scale, pion secondary interactions, and background

64+4
78+49
::;'
::*;'
<42=>?8@*A

&!!
!
%!!
$!!
#!!
"!!
!
!

!43

.53

"

#

$

%
&
.0)1-23

FIG. 1. The ND280 momentum data distributions of (a) the
CCQE and (b) CCnQE-enhanced selections. The predicted
total, CCQE, CCnQE and background event distributions
from the ND280 fit are overlaid on both figures.

uncertainties. The reconstructed ND280 µ− momentum
distribution for CCQE and CCnQE selections and predicted event distributions from the ND280 fit to data isshown in Fig. 1. For the oscillation fits, the ND280 fit
provides a systematic parameter error matrix which consists of 11 Eνµ SK flux normalizations, 5 Eν̄µ SK flux
normalizations and the 7 common neutrino interaction
parameters. The fractional error on the predicted number of SK candidate events from the uncertainties in these23 parameters, as shown in Table I, is 4.2%. Without theconstraint from the ND280 measurements this fractional
error would be 21.8%.
SK Measurements.—The SK far detector νµ candidate
events are selected from fully-contained beam events.
The SK phototube hits must be within ±500 µs of the
expected neutrino arrival time, and there must be lowouter detector activity to reject entering background.
The events must also satisfy: visible energy > 30 MeV,
exactly one reconstructed Cherenkov ring, µ-like particle
ID, reconstructed muon momentum > 200 MeV, and ≤ 1reconstructed decay electron. The reconstructed vertex
must also be in the fiducial volume (at least 2 m awayfrom the ID walls). Criteria to remove “flasher” (intermittent light-emitting phototube) backgrounds are also
applied. More details about the event selection and reconstruction in SK are found elsewhere [14].
Assuming a quasi-elastic interaction with a bound neutron and neglecting the Fermi motion, the neutrino energy is deduced from the detected muon and given by
Ereco =

m2p − (mn − Eb )2 − m2µ + 2(mn − Eb )Eµ, (2)2(mn − Eb − Eµ + pµ cos θµ )where pµ , Eµ , and θµ are the reconstructed muon momentum, energy, and the angle with respect to the beam
direction, respectively; mp , mn , and mµ are masses ofthe proton, neutron, and muon, respectively, and Eb =27 MeV is the average binding energy of a nucleon in

35
30

T2K data
No oscillation hypothesis
T2K best fit

25
20
15
10
5

Ratio to no
oscillations'()*+, - .!/" 0)1-23"!!!

Events / (0.1 GeV)

5

0
1.5
1
0.5
0
0

1

2

3

4

5

6

Reconstructed ν energy (GeV)

FIG. 2. The 58 event 1-ring µ-like SK reconstructed energy
spectrum. Top: The expected spectrum assuming no oscillations, and the best fit from the primary analysis for octant
1. The octant 2 best-fit spectrum is almost identical. Bottom: The ratio of the observed spectrum and best fit to no
oscillations. The fit uses finer binning than is shown here.

16

O. The Ereco distribution of the 58 events satisfying theselection criteria is shown in Fig. 2. The no-oscillation
hypothesis prediction is the solid line in Fig. 2 and the
MC expectation is 205±17 (syst.) events, of which 77.7%
are νµ +ν̄µ CCQE, 20.7% are νµ +ν̄µ CCnQE, 1.6% are
NC and 0.02% are νe +ν̄e CC. The expected resolution
on reconstructed energy for νµ +ν̄µ CCQE events aroundthe oscillation maximum is ∼0.1 GeV.
Eight SK detector systematic uncertainties are associated with event selection and reconstruction. The SKenergy scale uncertainty is evaluated by comparing energy loss in data and MC for samples of cosmic-ray stopping muons and associated decay-electrons, as well as
by comparing reconstructed invariant mass for data andMC for π 0 s produced by atmospheric neutrinos. The
other seven SK event-selection-related uncertainties arealso evaluated by comparing MC and data results foratmospheric neutrino samples. The νµ +ν̄µ CCQE ringcounting-based selection uncertainty is evaluated in threeenergy bins, including correlations between energy bins.
Other uncertainties result from additional νµ +ν̄µ CCQE
selection criteria, as well as selection criteria (including
ring-counting) for νµ +ν̄µ CCnQE, νe +ν̄e CC, and NC
events. These uncertainties (8 parameters) produce a
10.1% fractional error on the expected number of SK
events, as listed in Table I.
Systematic uncertainties on pion interactions in thetarget nucleus (FSI) and SK detector (SI) are evaluatedby varying underlying pion scattering cross sections in
the NEUT and SK detector simulations. These uncertainties are evaluated separately for νµ +ν̄µ CCQE inthree energy bins, νµ +ν̄µ CCnQE, νe +ν̄e CC, and NC
events. The total FSI+SI uncertainty (6 parameters) on
the predicted SK event rate is 3.5% as listed in Table I.
Oscillation Fits.—The oscillation parameters are esti-

TABLE I. Effect of 1σ systematic parameter variation on thenumber of 1-ring µ-like events, computed for oscillations withsin2 (2θ23 ) = 1.0 and |∆m232 | = 2.4 × 10−3 eV2 /c4 .

6
4
2
0
0.003

|∆m232| (eV2/c4)

exp
Source of uncertainty (no. of parameters) δnexp
SK / nSK
ND280-independent cross section (11)6.3%
Flux & ND280-common cross section (23)
4.2%
10.1%
Super-Kamiokande detector systematics (8)Final-state and secondary interactions (6)3.5%
Total (48)
13.1%

∆χ2

6

0.00280.00260.00240.0022

+2

73
X

exp
exp
obs
− nobsnobs
i ).
i ln(ni /ni ) + (ni(3)

T2K best fit (θ23 ≤ π/4)
T2K best fit (θ23 ≥ π/4)

0.002
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 10mated using a binned likelihood ratio to fit the SK spectrum in the parameter space of sin2 (2θ23 ), |∆m232 |, andall 48 systematic parameters, f , by minimizingχ2 (sin2 (2θ23 ), |∆m232 |; f ) = (f − f0 )T · C−1 · (f − f0 )T2K (θ23 ≤ π/4) 68% C.L.
T2K (θ23 ≤ π/4) 90% C.L.
T2K (θ23 ≥ π/4) 68% C.L.
T2K (θ23 ≥ π/4) 90% C.L.

sin2(2θ23)

2

4

∆χ2

6

FIG. 3. The 68% and 90% C.L. contour regions for sin2 (2θ23 )and |∆m232 | are shown for the primary analysis for octant 1(black) and octant 2 (red). The 1D profile likelihoods for each
oscillation parameter separately are also shown. The |∆m232 |1D profiles for both octants are identical.

i=1

f0 is a 48-dimensional vector with the prior valuesof the systematics parameters, C is the 48 × 48 systematic parameter covariance matrix, nobs
is the obi
served number of events in the ith bin and nexp
=
i
2
2
nexp
(sin
(2θ
),
|∆m
|;
f
)
is
the
corresponding
expected
23
32
i
number of events. The sum is over 73 variable-widthenergy bins, with finer binning in the oscillation peakregion. Oscillation probabilities are calculated using
the full three neutrino oscillation framework. Normal
mass hierarchy is assumed, octants 1 (θ23 ≤ π/4) and2 (θ23 ≥ π/4) are separately fit, matter effects are included with an Earth density of ρ = 2.6 g/ cm3 [24], andother oscillation parameters are fixed at the 2012 PDG
recommended values [25] (sin2 (2θ13 ) = 0.098, ∆m221 =7.5×10−5 eV2 /c4 , sin2 (2θ12 ) = 0.857), and with δCP = 0.
The fit to the 58 events using Eq. 3 yields the bestfit point for octant 1(2) at sin2 (2θ23 ) = 1.000(0.999)
and |∆m232 | = 2.44(2.44) × 10−3 eV2 /c4 , with χ2 /ndf =56.04(56.03)/71. The best-fit neutrino energy spectrum
is shown in Fig. 2. for octant 1; the best-fit spectrum foroctant 2 is essentially identical. The point estimates of
the 48 nuisance parameters are all within 0.35 standard
deviations of their prior values.
The 2D confidence regions for the oscillation parameters sin2 (2θ23 ) and |∆m232 | are constructed using theconstant ∆χ2 method [25] The 68% and 90% contour
regions are shown in Fig. 3 for both octant 1 and 2 separately. Since θ13 is non-zero, the oscillation probability(Eq. 1) as a function of sin2 (2θ23 ) is different for octant
1 and 2 and this results in a contour that is wider inthe sin2 (2θ23 ) direction for octant 2 than octant 1. Also
shown in this figure are the 1D profile likelihoods for each
oscillation parameter separately.
An alternative analysis employing a maximum likelihood fit was performed with the following likelihood func-tion:
L =Lnorm (sin2 (2θ23 ), |∆m232 |, f )× Lshape (sin2 (2θ23 ), |∆m232 |, f )Lsyst (f ),(4)where Lnorm is the Poisson probability for the observed
number of events, Lshape is the likelihood for the reconstructed energy spectrum, and Lsyst is analogous to
the first term in Eq. 3. The best-fit point for octant 1(2) is at sin2 (2θ23 ) = 1.000(0.999) and |∆m232 | =2.44(2.44) × 10−3 eV2 /c4 .
The primary and alternative analyses are consistent;
the binned maximum fractional difference between bestfit spectra is 1.7%, and the confidence regions are almost
identical.
A complementary analysis was performed, using
Markov Chain Monte Carlo [25] methods to produce asample of points in the full parameter space distributed
according to the posterior probability density. This
analysis uses both ND280 and SK data simultaneously,
rather than separately fitting the ND280 and SK measurements; the likelihood is the product of the ND280
and SK likelihoods, with the shared systematics treatedjointly. The maximum probability density is found to besin2 (2θ23 ) = 0.999 and |∆m232 | = 2.45 × 10−3 eV2 /c4 forboth octants, using a uniform prior probability distribution for the oscillation parameters. The contours fromthis analysis, evaluated separately for the two octants,
are similar in shape and size to the two previously described analyses, but are not expected to be identical dueto the difference between Bayesian and classical intervals.
This analysis also has similar results to the ND280 data
fit described previously and provides a cross check.
Conclusions.—Other recent experimental results arecompared in Figure 4 to the T2K primary result(90% C.L. region) which is consistent with maximal mixing. In this paper the νµ disappearance analysis, based|∆m232| (eV2/c4)

7

0.004

0.00350.003

other accelerator and reactor measurements will lead toimportant constraints and more precise determinationsof the fundamental neutrino mixing parameters.

T2K 3ν (θ ≤ π/4) 90% CL
23
T2K 3ν (θ ≥ π/4) 90% CL
23
T2K 2011 2ν 90% CL
MINOS 2013 2ν 90% CL
SK zenith 2012 3ν 90% CL
SK L/E 2012 2ν 90% CL

0.0025

0.002
0.82

T2K 3ν (θ23 ≤ π/4) best fit
T2K 3ν (θ23 ≥ π/4) best fit
0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

sin2(2θ23)
FIG. 4. The 90% C.L. contour regions for sin2 (2θ23 ) and|∆m232 | for the primary T2K analysis, are shown for octant 1(solid) and octant 2 (dashed). The T2K 2011[2], SK[26], andMINOS[5] 90% C.L. contours with different flavor assumptions are shown for comparison.

on the 3.01 × 1020 POT off-axis beam exposure, has determined, assuming octant 1(2), a best-fit mass splittingof |∆m232 | = 2.44(2.44) × 10−3 eV2 /c4 and mixing angle,
sin2 (2θ23 ) = 1.000(0.999). The results from either octant
assumption favor maximal mixing. We anticipate future
T2K data will improve our neutrino disappearance measurements, and our own measurements combined withWe thank the J-PARC accelerator team for the superb accelerator performance and CERN NA61 colleagues for providing particle production data and fortheir collaboration. We acknowledge the support of
MEXT, Japan; NSERC, NRC and CFI, Canada; CEA
and CNRS/IN2P3, France; DFG, Germany; INFN, Italy;
Ministry of Science and Higher Education, Poland; RAS,RFBR and the Ministry of Education and Science of theRussian Federation; MICINN and CPAN, Spain; SNSF
and SER, Switzerland; STFC, U.K.; DOE, U.S.A. We
also thank CERN for donation of the UA1/NOMAD
magnet and DESY for the HERA-B magnet mover system. In addition, participation of individual researchers
and institutions in T2K has been further supported byfunds from: ERC (FP7), EU; JSPS, Japan; Royal Society, UK; DOE Early Career program, and the A. P.
Sloan Foundation, U.S.A. SINET4 network support by
the National Institute of Informatics is also acknowledged. Computations were performed on the LHC computing grid (LCG), supported in the UK by GridPP,
and the supercomputers at the SciNet HPC Consortium.
SciNet is funded by: the Canada Foundation for Innovation (Compute Canada); the Government of Ontario;
Ontario Research Fund (Research Excellence); and the
University of Toronto.

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