arXiv:1403.1532v3 [hep-ex] 9 May 2014

Precise Measurement of the Neutrino Mixing Parameter θ23 from Muon Neutrino
Disappearance in an Off-Axis Beam
K. Abe,46 J. Adam,32 H. Aihara,45, 23 T. Akiri,9 C. Andreopoulos,44 S. Aoki,24 A. Ariga,2 T. Ariga,2 S. Assylbekov,8
D. Autiero,29 M. Barbi,39 G.J. Barker,54 G. Barr,35 M. Bass,8 M. Batkiewicz,13 F. Bay,11 S.W. Bentham,26
V. Berardi,18 B.E. Berger,8 S. Berkman,4 I. Bertram,26 S. Bhadra,58 F.d.M. Blaszczyk,28 A. Blondel,12 C. Bojechko,51
S. Bordoni,15 S.B. Boyd,54 D. Brailsford,17 A. Bravar,12 C. Bronner,25 N. Buchanan,8 R.G. Calland,27 J. Caravaca
Rodrı́guez,15 S.L. Cartwright,42 R. Castillo,15 M.G. Catanesi,18 A. Cervera,16 D. Cherdack,8 G. Christodoulou,27
A. Clifton,8 J. Coleman,27 S.J. Coleman,7 G. Collazuol,20 K. Connolly,55 L. Cremonesi,38 A. Dabrowska,13 I. Danko,37
R. Das,8 S. Davis,55 P. de Perio,49 G. De Rosa,19 T. Dealtry,44, 35 S.R. Dennis,54, 44 C. Densham,44 F. Di Lodovico,38
S. Di Luise,11 O. Drapier,10 T. Duboyski,38 K. Duffy,35 F. Dufour,12 J. Dumarchez,36 S. Dytman,37 M. Dziewiecki,53
S. Emery,6 A. Ereditato,2 L. Escudero,16 A.J. Finch,26 L. Floetotto,41 M. Friend,14, ∗ Y. Fujii,14, ∗ Y. Fukuda,30
A.P. Furmanski,54 V. Galymov,6 S. Giffin,39 C. Giganti,36 K. Gilje,32 D. Goeldi,2 T. Golan,57 M. Gonin,10 N. Grant,26
D. Gudin,22 D.R. Hadley,54 A. Haesler,12 M.D. Haigh,54 P. Hamilton,17 D. Hansen,37 T. Hara,24 M. Hartz,23, 50
T. Hasegawa,14, ∗ N.C. Hastings,39 Y. Hayato,46 C. Hearty,4, † R.L. Helmer,50 M. Hierholzer,2 J. Hignight,32
A. Hillairet,51 A. Himmel,9 T. Hiraki,25 S. Hirota,25 J. Holeczek,43 S. Horikawa,11 K. Huang,25 A.K. Ichikawa,25
K. Ieki,25 M. Ieva,15 M. Ikeda,46 J. Imber,32 J. Insler,28 T.J. Irvine,47 T. Ishida,14, ∗ T. Ishii,14, ∗ S.J. Ives,17 E. Iwai,14
K. Iyogi,46 A. Izmaylov,16, 22 A. Jacob,35 B. Jamieson,56 R.A. Johnson,7 J.H. Jo,32 P. Jonsson,17 C.K. Jung,32, ‡M. Kabirnezhad,31 A.C. Kaboth,17 T. Kajita,47, ‡ H. Kakuno,48 J. Kameda,46 Y. Kanazawa,45 D. Karlen,51, 50
I. Karpikov,22 E. Kearns,3, 23, ‡ M. Khabibullin,22 A. Khotjantsev,22 D. Kielczewska,52 T. Kikawa,25 A. Kilinski,31
J. Kim,4 J. Kisiel,43 P. Kitching,1 T. Kobayashi,14, ∗ L. Koch,41 A. Kolaceke,39 A. Konaka,50 L.L. Kormos,26
A. Korzenev,12 K. Koseki,14, ∗ Y. Koshio,33, ‡ I. Kreslo,2 W. Kropp,5 H. Kubo,25 Y. Kudenko,22, § S. Kumaratunga,50
R. Kurjata,53 T. Kutter,28 J. Lagoda,31 K. Laihem,41 I. Lamont,26 M. Laveder,20 M. Lawe,42 M. Lazos,27 K.P. Lee,47
T. Lindner,50 C. Lister,54 R.P. Litchfield,54 A. Longhin,20 L. Ludovici,21 M. Macaire,6 L. Magaletti,18 K. Mahn,50
M. Malek,17 S. Manly,40 A.D. Marino,7 J. Marteau,29 J.F. Martin,49 T. Maruyama,14, ∗ J. Marzec,53 E.L. Mathie,39
V. Matveev,22 K. Mavrokoridis,27 E. Mazzucato,6 M. McCarthy,4 N. McCauley,27 K.S. McFarland,40 C. McGrew,32
C. Metelko,27 M. Mezzetto,20 P. Mijakowski,31 C.A. Miller,50 A. Minamino,25 O. Mineev,22 S. Mine,5 A. Missert,7M. Miura,46, ‡ L. Monfregola,16 S. Moriyama,46, ‡ Th.A. Mueller,10 A. Murakami,25 M. Murdoch,27 S. Murphy,11J. Myslik,51 T. Nagasaki,25 T. Nakadaira,14, ∗ M. Nakahata,46, 23 T. Nakai,34 K. Nakamura,23, 14, ∗ S. Nakayama,46, ‡T. Nakaya,25, 23 K. Nakayoshi,14, ∗ D. Naples,37 C. Nielsen,4 M. Nirkko,2 K. Nishikawa,14, ∗ Y. Nishimura,47
H.M. O’Keeffe,26 R. Ohta,14, ∗ K. Okumura,47, 23 T. Okusawa,34 W. Oryszczak,52 S.M. Oser,4 R.A. Owen,38
Y. Oyama,14, ∗ V. Palladino,19 J. Palomino,32 V. Paolone,37 D. Payne,27 O. Perevozchikov,28 J.D. Perkin,42 Y. Petrov,4
L. Pickard,42 E.S. Pinzon Guerra,58 C. Pistillo,2 P. Plonski,53 E. Poplawska,38 B. Popov,36, ¶ M. Posiadala,52
J.-M. Poutissou,50 R. Poutissou,50 P. Przewlocki,31 B. Quilain,10 E. Radicioni,18 P.N. Ratoff,26 M. Ravonel,12
M.A.M. Rayner,12 A. Redij,2 M. Reeves,26 E. Reinherz-Aronis,8 F. Retiere,50 A. Robert,36 P.A. Rodrigues,40
P. Rojas,8 E. Rondio,31 S. Roth,41 A. Rubbia,11 D. Ruterbories,8 R. Sacco,38 K. Sakashita,14, ∗ F. Sánchez,15 F. Sato,14
E. Scantamburlo,12 K. Scholberg,9, ‡ S. Schoppmann,41 J. Schwehr,8 M. Scott,50 Y. Seiya,34 T. Sekiguchi,14, ∗H. Sekiya,46, ‡ D. Sgalaberna,11 M. Shiozawa,46, 23 S. Short,17 Y. Shustrov,22 P. Sinclair,17 B. Smith,17 R.J. Smith,35
M. Smy,5 J.T. Sobczyk,57 H. Sobel,5, 23 M. Sorel,16 L. Southwell,26 P. Stamoulis,16 J. Steinmann,41 B. Still,38
Y. Suda,45 A. Suzuki,24 K. Suzuki,25 S.Y. Suzuki,14, ∗ Y. Suzuki,46, 23 T. Szeglowski,43 R. Tacik,39, 50 M. Tada,14, ∗S. Takahashi,25 A. Takeda,46 Y. Takeuchi,24, 23 H.K. Tanaka,46, ‡ H.A. Tanaka,4, † M.M. Tanaka,14, ∗ D. Terhorst,41
R. Terri,38 L.F. Thompson,42 A. Thorley,27 S. Tobayama,4 W. Toki,8 T. Tomura,46 Y. Totsuka,∗∗ C. Touramanis,27
T. Tsukamoto,14, ∗ M. Tzanov,28 Y. Uchida,17 K. Ueno,46 A. Vacheret,35 M. Vagins,23, 5 G. Vasseur,6 T. Wachala,13
A.V. Waldron,35 C.W. Walter,9, ‡ D. Wark,44, 17 M.O. Wascko,17 A. Weber,44, 35 R. Wendell,46, ‡ R.J. Wilkes,55
M.J. Wilking,50 C. Wilkinson,42 Z. Williamson,35 J.R. Wilson,38 R.J. Wilson,8 T. Wongjirad,9 Y. Yamada,14, ∗K. Yamamoto,34 C. Yanagisawa,32, †† S. Yen,50 N. Yershov,22 M. Yokoyama,45, ‡ T. Yuan,7 M. Yu,58 A. Zalewska,13J. Zalipska,31 L. Zambelli,36 K. Zaremba,53 M. Ziembicki,53 E.D. Zimmerman,7 M. Zito,6 and J. Żmuda57(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.

2
4

University of British Columbia, Department of Physics and Astronomy, Vancouver, British Columbia, Canada
5
University of California, Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.
6
IRFU, CEA Saclay, Gif-sur-Yvette, France
7
University of Colorado at Boulder, Department of Physics, Boulder, Colorado, U.S.A.
8
Colorado State University, Department of Physics, Fort Collins, Colorado, U.S.A.
9
Duke University, Department of Physics, Durham, North Carolina, U.S.A.
10
Ecole Polytechnique, IN2P3-CNRS, Laboratoire Leprince-Ringuet, Palaiseau, France
11
ETH Zurich, Institute for Particle Physics, Zurich, Switzerland
12
University of Geneva, Section de Physique, DPNC, Geneva, Switzerland
13
H. Niewodniczanski Institute of Nuclear Physics PAN, Cracow, Poland
14
High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan
15
Institut de Fisica d’Altes Energies (IFAE), Bellaterra (Barcelona), Spain
16
IFIC (CSIC & University of Valencia), Valencia, Spain
17
Imperial College London, Department of Physics, London, United Kingdom
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 and Università di Roma “La Sapienza”, Roma, Italy
22
Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
23
Kavli Institute for the Physics and Mathematics of the Universe (WPI),
Todai Institutes for Advanced Study, University of Tokyo, Kashiwa, Chiba, Japan
24
Kobe University, Kobe, Japan
25
Kyoto University, Department of Physics, Kyoto, Japan
26
Lancaster University, Physics Department, Lancaster, United Kingdom
27
University of Liverpool, Department of Physics, Liverpool, United Kingdom
28
Louisiana State University, Department of Physics and Astronomy, Baton Rouge, Louisiana, U.S.A.
29
Université de Lyon, Université Claude Bernard Lyon 1, IPN Lyon (IN2P3), Villeurbanne, France
30
Miyagi University of Education, Department of Physics, Sendai, Japan
31
National Centre for Nuclear Research, Warsaw, Poland
32
State University of New York at Stony Brook, Department of Physics and Astronomy, Stony Brook, New York, U.S.A.
33
Okayama University, Department of Physics, Okayama, Japan
34
Osaka City University, Department of Physics, Osaka, Japan
35
Oxford University, Department of Physics, Oxford, United Kingdom
36
UPMC, Université Paris Diderot, CNRS/IN2P3, Laboratoire dePhysique Nucléaire et de Hautes Energies (LPNHE), Paris, France
37
University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, Pennsylvania, U.S.A.
38
Queen Mary University of London, School of Physics and Astronomy, London, United Kingdom
39
University of Regina, Department of Physics, Regina, Saskatchewan, Canada
40
University of Rochester, Department of Physics and Astronomy, Rochester, New York, U.S.A.
41
RWTH Aachen University, III. Physikalisches Institut, Aachen, Germany
42
University of Sheffield, Department of Physics and Astronomy, Sheffield, United Kingdom
43
University of Silesia, Institute of Physics, Katowice, Poland
44
STFC, Rutherford Appleton Laboratory, Harwell Oxford, and Daresbury Laboratory, Warrington, United Kingdom
45
University of Tokyo, Department of Physics, Tokyo, Japan
46
University of Tokyo, Institute for Cosmic Ray Research, Kamioka Observatory, Kamioka, Japan
47
University of Tokyo, Institute for Cosmic Ray Research, Research Center for Cosmic Neutrinos, Kashiwa, Japan
48
Tokyo Metropolitan University, Department of Physics, Tokyo, Japan
49
University of Toronto, Department of Physics, Toronto, Ontario, Canada
50
TRIUMF, Vancouver, British Columbia, Canada
51
University of Victoria, Department of Physics and Astronomy, Victoria, British Columbia, Canada
52
University of Warsaw, Faculty of Physics, Warsaw, Poland
53
Warsaw University of Technology, Institute of Radioelectronics, Warsaw, Poland
54
University of Warwick, Department of Physics, Coventry, United Kingdom
55
University of Washington, Department of Physics, Seattle, Washington, U.S.A.
56
University of Winnipeg, Department of Physics, Winnipeg, Manitoba, Canada
57
Wroclaw University, Faculty of Physics and Astronomy, Wroclaw, Poland
58
York University, Department of Physics and Astronomy, Toronto, Ontario, Canada(Dated: May 12, 2014)
New data from the T2K neutrino oscillation experiment produce the most precise measurementof the neutrino mixing parameter θ23 . Using an off-axis neutrino beam with a peak energy of
0.6 GeV and a data set corresponding to 6.57 × 1020 protons on target, T2K has fit the energydependent νµ oscillation probability to determine oscillation parameters. The 68% confidence limit

3
on sin2 (θ23 ) is 0.514+0.055−0.056 (0.511 ± 0.055), assuming normal (inverted) mass hierarchy. The bestfit mass-squared splitting for normal hierarchy is ∆m232 = (2.51 ± 0.10) ×10−3 eV2 /c4 (inverted
hierarchy: ∆m213 = (2.48 ± 0.10) ×10−3 eV2 /c4 ). Adding a model of multinucleon interactions that
affect neutrino energy reconstruction is found to produce only small biases in neutrino oscillation
parameter extraction at current levels of statistical uncertainty.
PACS numbers: 14.60.Pq,14.60.Lm,13.15+g,29.40.ka

Introduction.—Muon neutrinos oscillate to other flavors with a survival probability approximated by
P (νµ → νµ ) '1 − 4 cos2 (θ13 ) sin2 (θ23 )[1 − cos2 (θ13 )× sin2 (θ23 )] sin2 (1.267∆m2 L/Eν ),(1)

where L(km) is the neutrino propagation distance,Eν (GeV) is the neutrino energy and ∆m2 (eV2 /c4 ) is therelevant neutrino mass-squared splitting: ∆m232 = m23 −m22 for normal hierarchy (NH), or ∆m213 = m21 − m23 forinverted hierarchy (IH). Oscillation occurs because neutrino flavor eigenstates are linear superpositions of mass
eigenstates, related by a mixing matrix parametrized bythree mixing angles θ12 , θ23 , θ13 , and a CP violatingphase δCP [1]. Previous measurements [2–7] have foundθ23 ≈ π/4. There is considerable interest in precise
measurements of θ23 that can constrain models of neutrino mass generation (see reviews in [8–13]), determine
if sin2 (2θ23 ) is nonmaximal, and, if so whether θ23 is lessor greater than π/4.
In this Letter, we report the world’s most precise measurement of sin2 (θ23 ), using more than twice as muchdata as our previous result [2], as well as new data selections in T2K’s near detector that measure single pion
production processes that can mimic the oscillation signal in T2K’s far detector, Super-Kamiokande (SK). We
also consider the effects of multiple nucleons ejected inneutrino-nucleus interactions that can cause incorrect
neutrino energy estimates and so affect the oscillation
probability measurement.
T2K experiment.—The T2K experiment [14] combines(1) a muon neutrino beam line, (2) near detectors, located 280 m downstream of the neutrino production
target, that characterize the neutrino beam and constrain the neutrino flux parametrization and cross sections, and (3) the far detector, SK, located at a distance of L = 295 km from the target. The neutrino
beam axis is 2.5◦ away from SK, producing a narrowband beam [15] at the far detector, which reduces back-∗ also at J-PARC, Tokai, Japan† also at Institute of Particle Physics, Canada‡ affiliatedmember at Kavli IPMU (WPI), the University ofTokyo, Japan§ also at Moscow Institute of Physics and Technology and National
Research Nuclear University ”MEPhI”, Moscow, Russia¶ also at JINR, Dubna, Russia∗∗ deceased†† also at BMCC/CUNY, Science Department, New York, New
York, U.S.A.

grounds from higher-energy neutrino interactions and enhances the sensitivity to θ23 . The beam’s peak energy ofEν =2(1.267∆m2 L/π) ≈ 0.6 GeV corresponds to the firstminimum of the νµ survival probability at this distance.
A 30 GeV proton beam is extracted in 5 µs spills fromthe J-PARC main ring, directed toward Kamioka in the
primary beam line, and hits a graphite target. Beammonitors measure the beam’s intensity, trajectory, profile, and beam losses. Pions and kaons produced in thetarget decay into neutrinos in the secondary beam line,
which contains three focusing horns and a 96-m-long decay tunnel. This is followed by a beam dump and a setof muon monitors.
The near detector complex [14] contains an on-axis
Interactive Neutrino Grid detector (INGRID) [16] andan off-axis magnetized detector, ND280. INGRID provides high-statistics monitoring of the beam intensity,
direction, profile, and stability. ND280 is enclosed ina 0.2 T magnet containing a subdetector optimized tomeasure π 0 s (PØD) [17], three time projection chambers (TPC1,2,3) [18] alternating with two one-tonne finegrained detectors (FGD1,2) [19], and an electromagnetic
calorimeter [20] that surrounds the central detectors. A
side muon range detector [21] identifies muons that exit
or stop in the magnet steel.
The SK water-Cherenkov far detector [22] has a 22.5 kt
fiducial volume within a cylindrical inner detector (ID)with 11 129 inward-facing 20 00 phototubes. Surrounding the ID is a 2 meter wide outer detector with 1885
outward-facing 8 00 phototubes. A global positioning system with <150 ns precision synchronizes the timing between SK events and the J-PARC beam spill.
Data were collected during four periods: January-June
2010, November 2010-March 2011, January-June 2012,
and October 2012-May 2013. The proton beam poweron the target steadily increased, reaching 220 kW witha world record of 1.2 × 1014 protons on target (POT)
per spill. The total neutrino beam exposure on the SK
detector was 6.57 × 1020 POT.
Analysis strategy.—The analysis determines oscillation
parameters by comparing the observed and predicted νµinteraction rates and energy spectra at the far detector.
These predictions depend on the oscillation parameters,
the incident neutrino flux, neutrino interaction cross sections, and the detector response.
A measurement of νµ charged current (CC) events in
ND280 is used to tune both the initial flux estimatesand parameters of the neutrino interaction models. The
measurement also estimates the uncertainties in the predicted neutrino spectrum at the far detector. In this4
new analysis, the ND280 measurement provides better
constraints on the flux and interaction model parameters
by using improved event selections, reconstruction, andhigher ND280 statistics. This improvement was achievedby dividing CC events into three categories based on thenumber of pions in the final state.
At SK, the rate and energy spectrum of νµ charged
current quasielastic (CCQE) events are used to determine
the oscillation parameters through a maximum likelihood
fit. The fit accounts for uncertainties in the predicted
spectrum not only from the ND280-constrained flux andinteraction models but also SK detector selection efficiencies, final state interactions (FSI) inside the nucleus, andsecondary pion interactions (SI) in the detector material.
Initial neutrino flux model.—Detailed simulations ofhadron production and secondary interactions for primary beam protons striking T2K’s graphite target predict the neutrino fluxes at ND280 and SK [15]. The
simulation is tuned to hadron production data suchas those from NA61/SHINE for 30 GeV protons ongraphite [23]. Pions and kaons produced outside theexperimentally measured phase space are modeled using FLUKA2008 [24]. The GEANT3-based simulations
model the horns’ magnetic field, particle interactions in
the horns and decay region, and neutrino production
from hadron decays. Flux uncertainties are 10%-20%,
varying with energy, and are dominated by hadron production uncertainties. Full covariances between all SK
and ND280 energy bins and ν flavors are calculated [25].
Neutrino interaction simulations and cross section Parameters.—The NEUT Monte Carlo (MC) generator [26]is used to simulate neutrino interactions in T2K’s detectors. External data, especially from the MiniBooNE experiment [27], set the initial parameters and their uncertainties subsequently used in the fit to the ND280
data [25]. Neutrino interaction parameters fall into two
categories: parameters common between ND280 andSK, and independent parameters affecting interactions
at only one detector. 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, as discussed
in the next section. Since the ND280 target is mainly
carbon while SK’s target is mainly oxygen, additional
independent parameters are required which describe thenuclear model used for CCQE simulation (Fermi momentum, binding energy and spectral function modeling).
Five additional cross section parameters relate to pion
production, the neutral current (NC) cross section, theνe /νµ CC cross section ratio, and the ν/ν̄ CC cross section ratio. These independent cross section uncertainties(11 parameters) produce a 4.9% fractional error in the expected number of SK events (see Table I). Multinucleon
interactions are thought to lead to an enhancement of
the low-energy cross section [28–32] and have been modeled with a variety of approaches [33–37]. These effects,
not currently included in NEUT, may affect the oscillation parameter determination [38–43]. The penultimate

section presents a study of this potential bias.
ND280 measurements and fits.—The neutrino flux,
spectrum, and cross section parameters are constrainedusing νµ CC interactions in ND280. We select thehighest-momentum negatively charged track entering
TPC2 with a vertex inside FGD1’s fiducial volume andan energy loss in TPC2 consistent with a muon. Events
originating from interactions in upstream detectors are
vetoed by excluding events with a track in TPC1, which
is upstream of FGD1.
The ND280 analysis includes many improvements [44]over T2K’s previous νµ disappearance measurement [2],and used a data set with 5.90 × 1020 POT. The selected
CC candidate events are now divided into three samples:
CC-0π, with no identified pions; CC-1π + , with exactly
one π + and no π − or π 0 ; and CC-other, with all theother CC events. The CC-0π are dominated by CCQE
interactions; CC-1π + are dominated by CC resonant pion
production; and CC-other, a mixture of resonant production and deep inelastic scattering having final states with
π 0 ’s, π − ’s, or multiple pions.
A π + is identified in one of three ways: an FGD+TPC
track with positive curvature and a TPC charge deposition consistent with a pion, an FGD-contained trackwith a charge deposition consistent with a pion, or a delayed energy deposit due to a decay electron from stopped
π + → µ+ in the FGD. A π − is tagged only by a negatively curved FGD+TPC track. A π 0 is identified froma track in the TPC with a charge deposition consistent
with an electron from a γ conversion.
The dominant sources of uncertainty are events occurring outside the FGD fiducial volume and pion reinteractions in the detector.
We fit these three samples for 25 parameters describing the beam flux in bins of energy and neutrino type at
ND280. These parameters strongly correlate with flux
parameters at SK. We also fit for 19 cross section parameters and for nuisance parameters describing correlated
detector uncertainties of the data bins (10 momentum ×
7 angle bins for each sample).
We observe 17 369, 4047, and 4173 data events in theCC-0π, CC-1π + , and CC-other samples, respectively.
Using the best-fit parameters, the simulated numbers ofevents are 17 352, 4110, and 4119 for the CC-0π, CC1π + , and CC-other samples. Figure 1 shows distributions of the muon momentum and angle relative to thebeam direction for the CC-0π sample and the improvement in data and MC agreement when using the best-fit
parameters. The fit uses the neutrino interaction model
to extrapolate ND280 measurements, primarily coveringcos(θµ ) > 0.5, over SK’s 4π angular acceptance.
The fit gives estimates for 16 beam flux parametersat SK, the seven common cross section parameters, andtheir covariance. Using the ND280 data reduces the uncertainty on the expected number of events at SK due tothese parameters from 21.6% to 2.7%.
SK measurements.—An enriched sample of νµ CCQE
events, occurring within -2 µs to +10 µs of the ex-2500

Prediction before ND ν µ constraint

2000

Prediction after ND ν µ constraint

Events/0.10 GeV

Events

5

Data

1500
1000
500
0
0

0.5

1

1.5

2

2.5

>3

2000
1500
1000
500
0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Muon cos(θ)

FIG. 1. The momentum and angular distributions for muonsin ND280’s CC-0π selection. The predicted distributions before and after the ND280 fit are overlaid on both figures.

pected neutrino arrival time, is selected in SK. We require low activity in the outer detector to reduce entering backgrounds. We also require: visible energy> 30 MeV, exactly one reconstructed Cherenkov ring, µlike particle identification, reconstructed muon momentum > 200 MeV, and ≤ 1 reconstructed decay electron.
The reconstructed vertex must be in the fiducial volume(at least 2 m away from the ID walls) and we reject“flasher” events (produced by intermittent light emission
inside phototubes). More details about the SK event selection and reconstruction are found in [22].
The neutrino energy for each event is calculated under the quasielastic assumption as in [2] using an average binding energy of 27 MeV for nucleons in 16 O. The
Ereco distribution of the 120 selected events is shownin Fig. 2. The MC expectation without oscillations is446.0 ± 22.5 (syst.) events, of which 81.0% are νµ +ν̄µ
CCQE, 17.5% are νµ +ν̄µ CC non-QE, 1.5% are NC and
0.02% are νe +ν̄e CC. The expected resolution in reconstructed energy for νµ +ν̄µ CCQE events near the oscillation maximum is ∼0.1 GeV.
Systematic uncertainties in the analysis are evaluatedwith atmospheric neutrinos, cosmic-ray muons, and theirdecay electrons. Correlated selection efficiency parameters are assigned for six event categories: νµ +ν̄µ CCQE
in three energy bins, νµ +ν̄µ CC non-QE, νe +ν̄e CC, andNC events. An energy scale uncertainty of 2.4% comesfrom comparing reconstructed momenta in data and MC
for cosmic-ray stopping muons and associated decay electrons, and from comparing reconstructed invariant massin data and MC simulations for π 0 ’s produced by atmospheric neutrinos. Systematic uncertainties in pion
interactions in the target nucleus (FSI) and SK detector(SI) are evaluated by varying pion interaction probabilities in the NEUT cascade model. These SK detector and
FSI+SI uncertainties produce a 5.6% fractional error in
the expected number of SK events (see Table I).

DATA
νµ+νµ CCQE
νµ+νµ CC non-QE
νe+νe CC
NC

12
10
8
6
2
00

2500

Ratio to no
oscillations

Events14

4

Muon Momentum (GeV/c)

< 0.6

16

0

1.5
1
0.5
0

0

1
MC Best-fit

1

2

3

4

5

2

3

4

>5

Reconstructed ν Energy (GeV)

FIG. 2.
Reconstructed energy spectrum for single-ringµ-like SK events. Top: The observed spectrum and expected
spectrum with interaction modes for the T2K best fit. Bottom: The ratio of the observed spectrum (points) to the nooscillation hypothesis, and the best oscillation fit (solid).
exp
Source of uncertainty (number of parameters) δnexp
SK / nSK
ND280-independent cross section (11)4.9%
Flux and ND280-common cross section (23)
2.7%
SK detector and FSI+SI systematics (7)5.6%
sin2 (θ13 ), sin2 (θ12 ), ∆m221 , δCP (4)0.2%
Total (45)8.1%

TABLE I. Effect of 1σ systematic parameter variation on thenumber of 1-ring µ-like events, computed for oscillations withsin2 (θ23 ) = 0.500 and |∆m232 | = 2.40 × 10−3 eV2 /c4 .

Oscillation fits.—We estimate oscillation parameters
using an unbinned maximum likelihood fit to the SK
spectrum for the parameters sin2 (θ23 ) and either ∆m232
or ∆m213 for the normal and inverted mass hierarchies
respectively, and all 45 systematic parameters. The fit
uses 73 unequal-width energy bins, and interpolates the
spectrum between bins. Oscillation probabilities are calculated using the full three-flavor oscillation framework.
Matter effects are included with an Earth density of ρ =2.6 g/ cm3 [45], δCP is unconstrained in the range [−π, π],and other oscillation parameters are fit with constraints
sin2 (θ13 ) = 0.0251 ± 0.0035, sin2 (θ12 ) = 0.312 ± 0.016,
and ∆m221 = (7.50 ± 0.20) × 10−5 eV2 /c4 [46]. Figure 2
shows the best-fit neutrino energy spectrum. The point
estimates of the 45 nuisance parameters are all within
0.25 standard deviations of their prior values.
Two-dimensional confidence regions in the oscillation
parameters are constructed using the Feldman-Cousins
method [47], with systematics incorporated using the
Cousins-Highland method [48]. Figure 3 shows 68%
and 90% confidence regions for the oscillation parameters for both normal and inverted hierarchies. The 68%
and 90% expected sensitivity curves are each 0.04 wider
in sin2 (θ23 ) than these contours. An alternative analy-

43
2

90% CL-2∆lnLcrit.
68% CL1∆m232 [NH]/∆m213 [IH] (10-3 eV2/c4)

Arbitrary Units-2∆lnL

6

×10
00
4.2
4

68% (dashed) and 90% (solid) CL Contours

3.8
3.6

T2K [NH]

T2K [IH]

SK I-IV [NH]MINOS 3-flavor+atm [NH]CCQE
Nieves multinucleon (×5)
pionless ∆-decay (×5)

3.4
3.2
3

-1

2.8

-0.5

0

0.5
QE

Ereco - Etrue (GeV)

2.6
2.4
2.2
2

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

00

sin2(θ23)

1

2

3

4

-2∆lnL

FIG. 3.
The 68% and 90% C.L. confidence regions forsin2 (θ23 ) and ∆m232 (NH) or ∆m213 (IH). The SK [49] and MINOS [7] 90% C.L. regions for NH are shown for comparison.
T2K’s 1D profile likelihoods for each oscillation parameter
separately are also shown at the top and right overlaid withlight blue lines and points representing the 1D −2∆ ln Lcriticalvalues for NH at 68% and 90% C.L.

sis employing a binned likelihood ratio gave consistent
results. Also shown are 90% confidence regions fromother recent experimental results. Statistical uncertainties dominate T2K’s error budget.
We calculate one-dimensional (1D) limits using a new
method inspired by Feldman-Cousins [47] and CousinsHighland [48] that marginalizes over the second oscillation parameter. Toy experiments are used to calculate−2∆ ln Lcritical values, above which a parameter value is
excluded, for each value of sin2 (θ23 ). These toy experiments draw values for ∆m232 or ∆m213 in proportion to
the likelihood for fixed sin2 (θ23 ), marginalized over systematic parameters. The toy experiments draw valuesof the 45 systematic parameters from either Gaussian or
uniform distributions. We generate ∆m232 or ∆m213 limits with the same procedure. Figure 3 shows the 1D
profile likelihoods for both mass hierarchies, with the−2∆ ln Lcritical MC estimates for NH.
The 1D 68% confidence intervals are sin2 (θ23 ) =20.514+0.055−0.056 (0.511 ± 0.055) and ∆m32 = 2.51 ± 0.10
2−3
2 4(∆m13 = 2.48 ± 0.10) ×10 eV /c for the NH (IH).
The best fit corresponds to the maximal possible disappearance probability for the three-flavor formula.
Effects of multinucleon interactions.—Inspired bymore precise measurements of neutrino-nucleus scattering [50–53], recent theoretical work suggests that neutrino interactions involving multinucleon mechanisms
may be a significant part of the cross section in T2K’senergy range and might introduce a bias on the oscillation parameters as large as a few percent [28–43]. We
are the first oscillation experiment to consider the potential bias introduced by multinucleon interactions including potential cancellation from measurements at the near

FIG. 4.
The difference between the reconstructed energy
assuming QE kinematics and the true neutrino energy. True
QE events with energies below 1.5 GeV show little bias while
multinucleon events based on [43] and NEUT pionless ∆ decay(shown scaled up by a factor of 5) are biased towards lower
energies.

detector. At T2K beam energies most interactions produce final-state nucleons below SK’s Cherenkov threshold, making multinucleon interactions indistinguishable
from quasielastic (QE) interactions. Even if the additional nucleon does not leave the nucleus, the multinucleon mechanism alters the kinematics of the outgoing lepton, distorting the reconstructed neutrino energy which assumes QE kinematics (see Fig. 4) in addition to increasing the overall QE-like event rate.
The T2K neutrino interaction generator, NEUT, includes an effective model (pionless ∆ decay) that models
some but not all of the expected multinucleon cross section. In order to evaluate the possible effect on the oscillation analysis, we perform a Monte Carlo study where
the existing effective model is replaced with a multinucleon prediction based on the work of Nieves [43] goingup to 1.5 GeV in energy. We used this modified simulation to make ND280 and SK fake data sets with randomly chosen systematic uncertainties but without statistical fluctuations, and performed oscillation analyses
as described above on each of them, allowing ND280 fakedata to renormalize the SK prediction. The mean biases
in the determined oscillation parameters are < 1% for
the ensemble, though the sin2 (θ23 ) biases showed a 3.5%
rms spread.
Conclusions.—The measurement of sin2 (θ23 ) =0.514+0.055−0.056 (0.511 ± 0.055) for NH (IH) is consistent
with maximal mixing and is more precise than previous measurements. The best-fit mass-squared splitting is ∆m232 = 2.51 ± 0.10 (IH: ∆m213 = 2.48 ±0.10) ×10−3 eV2 /c4 . Possible multinucleon knockout inneutrino-nucleus interactions produces a small bias in thefitted oscillation parameters and is not a significant uncertainty source at present precision.
We thank the J-PARC staff for superb accelerator performance and the CERN NA61 collaboration for providing valuable particle production data. We acknowledge the support of MEXT, Japan; NSERC, NRC, and7
CFI, Canada; CEA and CNRS/IN2P3, France; DFG,
Germany; INFN, Italy; National Science Centre (NCN),
Poland; RAS, RFBR, and MES, Russia; MICINN and
CPAN, Spain; SNSF and SER, Switzerland; STFC,
UK; and DOE, USA. We also thank CERN for the
UA1/NOMAD magnet, DESY for the HERA-B magnet mover system, NII for SINET4, the WestGrid and

SciNet consortia in Compute Canada, GridPP, UK, andthe University of Oxford Advanced Research Computing(ARC) facility. In addition participation of individual
researchers and institutions has been further supported
by funds from: ERC (FP7), EU; JSPS, Japan; Royal
Society, UK; DOE Early Career program, USA.

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