arXiv:1403.3140v1 [hep-ex] 13 Mar 2014

Measurement of the neutrino-oxygen neutral-current interaction cross section
by observing nuclear de-excitation γ-rays
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 A. Gaudin,51 S. Giffin,39 C. Giganti,36 K. Gilje,32 D. Goeldi,2T. 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,11K. 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 C. Licciardi,39 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,7 M. Miura,46, ‡ L. Monfregola,16 S. Moriyama,46, ‡Th.A. Mueller,10 A. Murakami,25 M. Murdoch,27 S. Murphy,11 J. 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 V. Paolone,37 D. Payne,27
G.F. Pearce,44 O. Perevozchikov,28 J.D. Perkin,42 Y. Petrov,4 L. Pickard,42 E.S. Pinzon Guerra,58 C. Pistillo,2P. 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,11M. 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, ∗ I.J. Taylor,32 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.
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
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
We report the first measurement of the neutrino-oxygen neutral-current quasi-elastic (NCQE)
cross section. It is obtained by observing nuclear de-excitation γ-rays which follow neutrino-oxygen
interactions at the Super-Kamiokande water Cherenkov detector. We use T2K data corresponding to3.01 × 1020 protons on target. By selecting only events during the T2K beam window and with wellreconstructed vertices in the fiducial volume, the large background rate from natural radioactivity
is dramatically reduced. We observe 43 events in the 4 − 30 MeV reconstructed energy window,
compared with an expectation of 55.7, which includes an estimated 17.3 background events. The

3background is primarily non-quasielastic neutral-current interactions and has only 1.2 events fromnatural radioactivity. The flux-averaged NCQE cross section we measure is 1.35 × 10−38 cm2 with
a 68% confidence interval of (1.06, 1.94) × 10−38 cm2 at a median neutrino energy of 630 MeV,
compared with the theoretical prediction of 2.01 × 10−38 cm2 .
PACS numbers: 25.30.Pt, 29.40.Ka, 21.10.Pc, 23.20.Lv

I.

INTRODUCTION

Nuclear de-excitation γ-rays are a useful tool for detecting neutrino-nucleus neutral-current (NC) interactions where the final state neutrino and assosciated nucleon are not observed in a Cherenkov detector. They
have previously been observed in neutrino-carbon interactions [1, 2]. The most well known γ-ray production process on oxygen is coherent inelastic scattering,ν + 16 O → ν + 16 O∗ , where the residual oxygen nucleus
can de-excite by emitting a nucleon or γ-rays with energies between 1 − 10 MeV. This process can be used
to detect supernova neutrinos [3], which have an averageenergy of 20 − 30 MeV. Most theoretical work on γray production in NC interactions has been performed inthis low neutrino energy range with the assumption that
it is applicable up to neutrino energies of several hundred
MeV [4–6].
A recent calculation of γ-ray production in neutrino
NC interactions shows that quasi-elastic (QE) nucleon
knockout, ν + 16 O → ν + p + 15 N∗ (ν + n + 15 O∗ ) overwhelms the coherent process at Eν & 200 MeV [7]. The
NCQE cross section is more than an order of magnitudelarger than the NC coherent cross section from [5] at
Eν ≈ 500 MeV. The γ-rays produced when the residual
nucleus de-excites are labeled primary γ-rays. Secondary
γ-rays can also be produced when the knocked out nucleon goes on to interact with other nuclei in the water.
Both types of γ-rays, produced in interactions of atmospheric neutrinos, are a major background for the studyof astrophysical neutrinos in the 10 MeV range [8, 9] anda direct measurement of the rate of this process witha known neutrino source will be useful for ongoing andproposed projects [10–13].
This paper reports the first measurement of theneutrino-oxygen NCQE cross section via the detectionof de-excitation γ-rays. The neutrinos are produced using the narrow-band neutrino beam at J-PARC and measured with the Super-Kamiokande (SK) water Cherenkov
detector.

∗ 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.

II.

THE T2K EXPERIMENTThe Tokai-to-Kamioka (T2K) experiment [14] is along-baseline neutrino oscillation experiment consistingof a neutrino beam, several near detectors, and using
Super Kamiokande as a far detector. It is designed tosearch for νµ → νe appearance, which is sensitive to theneutrino mixing angle θ13 , and to precisely measure themixing angle θ23 and the mass difference |∆m232 | by νµdisappearance.
The accelerator at the Japan Proton Accelerator Research Complex (J-PARC) provides a 30 GeV proton
beam which collides with a graphite target to produce
charged mesons. Positively-charged pions and kaons arecollected and focused by magnetic horns and ultimately
decay in flight to produce primarily muon neutrinos inside a 96 m long cavity filled with helium gas. The proton
beam is directed 2.5◦ away from SK. The off-axis neutrino
beam has a narrow peak with median energy 630 MeV
at SK because of the two-body decay kinematics of theπ + which dominate the focused beam. This peak energy
was chosen because it corresponds to the first maximum
in the neutrino oscillation probability at the location of
the far detector. The narrow energy peak also allows forthe measurement of the NC cross section at a particular energy. Typically, it is not possible to make energydependent measurements of this cross section because theinvisible outgoing neutrino makes accurate energy reconstruction impossible.
The T2K experiment has several near detectors located
280 m from the neutrino production target. The on-axis
near detector, INGRID, which consists of 16 modules
made up of alternating layers of iron and plastic scintillator arranged in a cross, monitors the neutrino beam
direction. The off-axis near detectors, ND280, measure
the neutrino beam spectrum and composition for the oscillation analyses. The neutrino measurements at the
INGRID and ND280 detectors are consistent with expectations [15], but this information is not used to constrainsystematic uncertainties in this analysis so that an absolute cross-section measurement can be made.
Super-Kamiokande [10] is a cylindrical water
Cherenkov detector consisting of 50 ktons of ultrapure water, located 295 km from the neutrino target at
J-PARC. It was built in the middle of Mt. Ikenoyama,
near the town of Kamioka, 1000 m below the peak.
The tank is optically separated into two regions whichshare the same water. The inner detector (ID) is acylinder containing the 22.5 kton fiducial volume and is
instrumented with 11,129 inward-facing photomultipliertubes (PMTs). The outer detector (OD) extends 2 m

4outward from all sides of the ID and is instrumented
with 1,885 outward-facing PMTs. It serves as a vetocounter against cosmic-ray muons as well as a shieldfor γ-rays and neutrons emitted from radioactive nuclei
in the surrounding rock and stainless steel support
structure.

III.

EVENT SIMULATION

T2K events at SK are simulated in three stages. First,
the neutrino beamline is simulated to predict the flux andenergy spectrum of neutrinos arriving at SK. Next, theinteractions of those neutrinos with the nuclei in the SK
detector are simulated, including final-state interactions
within the nucleus. Finally, the SK detector response to
all of the particles leaving the nucleus is simulated.
FLUKA [16] is used to simulate hadron productionin the target based on the measured proton beam profile. Hadron production data from NA61/SHINE at
CERN [17, 18] is used to tune the simulation and evaluate
the systematic error. Once particles leave the production target they are transported through the magnetic
horns, target hall, decay volume, and beam dump using a GEANT3 [19] simulation with GCALOR [20] forhadronic interactions. A more detailed description of theneutrino flux prediction and its uncertainty can be foundin Ref. [21].
Neutrino interactions based on the above flux are simulated using the NEUT event generator [22, 23]. The
NCQE cross section on oxygen is simulated using a spectral function model [24, 25] with the BBBA05 form factor parameterization [26], which is then reweighted asa function of neutrino energy to match the recent theoretical calculations from [7]. In order to simulate thede-excitation γ-ray emission, it is necessary to identify
which state the remaining nucleus is in after the neutrino
interaction. The spectroscopic factors for three possible
states, the ground state, 1p1/2 , and excited states, 1p3/2
and 1s1/2 are used for this determination. The excitedstates can release primary γ-rays at a variety of energies ranging from 3 to 15 MeV, though more than 80%
have an energy close to 6 MeV. The branching ratios for
γ-ray production from the 1p3/2 nucleon hole state aretaken from a theoretical estimate in Ref. [27], while thebranching ratios of the 1s1/2 proton hole state are estimated using the result of the 16 O(p, 2p)15 N experiment(RCNP-E148) [28]. We used the same branching ratiosfor γ-ray production from neutron hole states as fromproton hole states.
Non-QE NC interactions make up the largest neutrinoinduced background component and predominantly consist of NC single-pion production where the pion is absorbed during final state interactions in the nucleus. This
resonant production is simulated using the Rein-Sehgal
model [29], the position dependence within the nucleus
is calculated with the model from [30], and the scale ofthe microscopic pion interaction probabilities in the nu-

clear medium is determined from fits to pion scattering
data [31–33]. The simulation of primary de-excitation γrays from this process is based on measurements of π −absorption-at-rest on H2 O at CERN [34]. These pionabsorption interactions can also release nucleons which
go on to produce secondary γ-rays as described below.
More details about NEUT, including the models used tosimulate the smaller charged current backgrounds can befound in [14, 23].
SK’s GEANT3-based simulation [19] is used to transport all the particles leaving the nucleus through the detector, produce and transport the Cherenkov light, andto simulate the response of the photodetectors and electronics. Charged pions with momenta above 500 MeV/c
are simulated with GCALOR [20] while lower momentum
pions are simulated with a custom routine based on the
NEUT cascade model for final state hadrons. GCALOR
also simulates the interactions of nucleons with nuclei inthe water, including the production of secondary γ-rays.
In this simulation, secondary γ-rays are typically produced in multiples: 95% of events with secondary γ-rays
have at least two. The total secondary γ-ray energy per
event is distributed widely with a peak around 7 MeV
and a long tail towards higher energies.
There is an additional signal-like contribution from thecoherent inelastic process, ν + 16 O → ν + 16 O∗ . However,since there is no accurate estimation of γ-ray production
induced by the NC coherent process in the T2K energy
range, we do not subtract its contribution in the final
result. If we assume that the rate of γ-ray production after a coherent interaction is similar to that of a nucleon
knockout reaction, and extrapolate the NC coherent crosssection predicted in [5] to the energy region of this analysis, we expect its contribution to be no larger than a few
percent of our final sample.

IV.

ANALYSIS

The results presented in this paper are based on
T2K RUN1-3 data from 3.01 × 1020 protons on target (POT) [35]. The expected number of beam-related
events after the selections described in the next section
are summarized in Tab. I, which categorizes them by neutrino flavor and interaction mode. For the computationof the CC components, we assume three-flavor oscillations with |∆m232 | = 2.44 × 10−3 eV2 , sin2 θ23 = 0.50,
sin2 2θ13 = 0.097. The majority of the beam-related
background comes from non-quasi-elastic NC events, inparticular single-pion production followed by pion absorption within the nucleus. The CC background comesfrom interactions where the outgoing charged lepton
has low momentum and is misidentified as an electron
or where the charged lepton itself is below Cherenkov
threshold but de-excitation γ-rays are emitted.
The expected number of beam-unrelated events after
all selections are applied is estimated to be 1.2 by sampling events at least 5 µs before the T2K beam trigger soA.

Event selection

The reconstruction of the event vertex, direction, andenergy is the same as that used in the SK solar neutrino
analysis [36]. The reconstructed energy is defined as thetotal energy of a single electron that would have produced
all Cherenkov photons in the event. We use this definition because it is used by the SK low-energy reconstruction tools, though we know many events have multiple
particles and a variety of particle species. The first selections applied are a cut on the reconstructed energy, only
allowing events between 4 MeV and 30 MeV, a standard
fiducial volume cut of 2 m from the detector wall, and an
event timing cut. An energy threshold of 4 MeV, lower
than previous SK analyses, is possible in this analysis
thanks to the sharp reduction in accidental backgrounds
due to the beam timing cut. This low threshold significantly increases the detection efficiency for these lowenergy events, which is predicted by the Monte Carlo to
be greater than 99% for 6 MeV de-excitation γ-rays from
1p3/2 proton and neutron hole states.
The neutrino beam spill has a bunch structure, reflecting the underlying proton bunch structure, with 6 or 8
bunches separated by 581 ns gaps, delivered every 3 s.
A timing cut of ±100 ns, much longer than the lifetimesof the de-excitation modes relevant to this analysis [37],is applied between the event time and the closest neutrino beam bunch time, which is synchronized between
the near and far sites using a common-view GPS system.
The bunch timing is calibrated using the higher energy
T2K neutrino events at SK, and the RMS of the observed
timing distribution is about 24 ns.

TABLE I. Observed and expected numbers of events in T2K
Runs 1-3. The CC samples are based on the flux at SK including three-flavor oscillations (parameters described in thetext). The NC samples are based on the unoscillated flux.
The νe NCQE events are treated as signal, but the ν̄µ NCQE
are considered background since there is a different predictedcross-section for antineutrinos.
Beam-related expectation νµ
νe
ν̄µ
NCQE
37.88 0.51 0.78
NC non-QE
12.42 0.27 0.47
CC
2.15 0.001 0.025
Signal38.38
Background (beam)
16.11
Beam-unrelated
1.20
Observed events
43

15
Beforeselection

10

-0.4

-0.2

0

0.2

0.4

0.6

RUN1-3 data
NCQE
NC non-QE

5CC
Beam-unrelated

0
-0.4

-0.2

0

0.2

0.4

0.6

Qrec

FIG. 1. (color online) Distribution of the reconstruction quality parameter, Qrec , after the beam-unrelated selection cuts(timing, fiducial volume, Qrec ) have been applied. The inset
shows the distribution before the energy-dependent cut on
Qrec , but including the timing and fiducial volume cuts. The
T2K RUN1-3 data are represented by points with statisticalerror bars and the expectation is represented by stacked histograms showing the NCQE signal and the NC non-QE, CC,and beam-unrelated background components.

Number of events

that no beam-related activity is included. The measured
event rate is normalized to the total livetime of the analyzed beam spills. Since the beam-unrelated backgroundis directly measured with data outside the beam window,
the systematic uncertainty associated with it is small.

Number of events

5

RUN1-3 data
NCQE
NC non-QE

8CC
Beam-unrelated

6

4

2

0

20

40

60

80

Cherenkov angle (°)

FIG. 2. (color online) The Cherenkov angle distribution
in data and MC expectation after the beam-unrelated selections and the pre-activity cut. The expectation has athree-peak structure corresponding to low-momentum muons
around 28◦ , single γ-rays around 42◦ , and multiple γ-raysaround 90◦ . A selection cut is applied at 34◦ to remove themuon events, but no attempt is made to separate single- andmultiple-γ events.

6
Further selection cuts are applied based on the event
vertex and reconstruction quality to remove beamunrelated background, similar to those used in SK solar [36] and supernova relic neutrino analyses [8]. These
cut criteria are simultaneously optimized in an energydependent√way to maximize the figure-of-merit definedas Nbeam/ Nbeam + Nunrel, where Nbeam and Nunrel denote the number of expected beam-related and beamunrelated events, respectively. The cut optimization isdone separately for each of the three T2K run periods
since the beam intensities and beam bunch structuresdiffer.
Most of the beam-unrelated background comes fromradioactive impurities in the PMT glass, cases, and support structure and so is concentrated near the ID wall.
Cuts on the distance from the nearest wall, D1 , and the
distance from the wall along the backward direction of
the reconstructed track, D2 , together effectively eliminate background events produced at or near the ID wall.
A minimum cut of 2 m is applied for both, with the cut
on D1 increasing linearly below 4.75 MeV to about 3.2 m
and the cut on D2 increasing linearly below 5.75 MeV toabout 10 m.
Beam-unrelated background events that pass the fiducial cuts typically have reconstruction errors which movethe vertex to the center of the tank. These errors canbe identified based on the distribution of hits in timeand space. The hit time distribution should be a sharp
peak after time-of-flight correction from the correct vertex, which we quantify as the timing goodness, gt . The
hit pattern should also be azimuthally symmetric aroundthe reconstructed particle direction, which we test using
gp , the Kolmogorov-Smirnov distance between the observed hit distribution and a perfectly symmetric one.
The reconstruction quality cut criterium, Qrec , is definedas the hyperbolic combination of these two parameters:
Qrec ≡ gt2 − gp2 and is shown in Fig. 1. The cut on Qrec isalso energy-dependent and varies from about 0.25 at its
tightest at the low end of the energy spectrum to effectively no cut above 11 MeV. More detailed descriptionsof gt and gp are found in Ref. [38].
Before selection, the beam-unrelated background ratefrom natural radioactivity is 284 counts per second, or
1.2 million events expected during the 1 ms beam windows used for other T2K analyses [39]. Applying thetight timing cut reduces this background to 1,816 events.
The fiducial and reconstruction quality cuts further reduce the beam-unrelated background to 1.77 events, or
2.2% contamination. These beam-unrelated selection
cuts reduce the estimated NCQE signal efficiency to 74%.
Among the selected signal events, we estimate 97% havetrue vertices within the fiducial volume.
Finally, to suppress the beam-related charged-current(CC) interaction events, two additional cuts are applied: a pre-activity cut and a Cherenkov opening angle
cut. The pre-activity cut rejects electrons produced inmuon decays with more than 99.9% efficiency by rejecting events which occur less than 20 µs after a high-energy

event, defined as a group of 22 or more hits in a 30 ns
window. The likelihood of this selection rejecting a signal event because of accidental dark noise hits is less than
0.1%.
For this low-energy sample, the Cherenkov angle ofan event is defined as the peak of the distribution of
Cherenkov angles calculated for every combination of
three PMTs with hits following the technique from [8].
For single particles this peak will be close to the opening
angle of the particle while the more isotropic light distributions from multiple particles will have peaks close
to 90◦ . The Cherenkov angle depends on the velocity ofthe particle, approaching 42◦ as the velocity approachesc. The electrons produced by the de-excitation γ-rays
selected in this analysis are highly relativistic and sopeak at 42◦ . The heavier muons from CCνµ events havesmaller opening angles, peaking around 28◦ ; the higher
momentum muons with larger opening angles having already been removed by the energy cut at 30 MeV. Thesemuons are removed by a cut at 34◦ . The Cherenkov angle
distribution for events passing all other selection criteria
can be seen in Fig. 2. The data-expectation disagreement in the multi-γ peak is likely due to the approximations made in the model of γ-ray emission induced bysecondary neutron interactions used by GEANT3 andGCALOR.
After all selections, 55.7 events are expected, of which
38.4 are expected to be NCQE signal for a purity of
69%. The overall selection efficiency is estimated to be
70% relative to the number of true NCQE events in thetrue fiducial volume which produce either primary or
secondary γ-rays (approximately 25% of NCQE events
produce no photons and are consequently unobservable).
The beam-unrelated contamination remains 2.2% after
the final beam-related selections, giving 1.2 background
events in the final sample.

B.

Observed Events

Figure 3 shows the observed event timing distribution
in a region from −1 µs to 5 µs with respect to the beam
trigger time, before the tight ±100 ns timing cut on eachbunch has been applied. Six events are found outside
the tight bunch time windows, which is consistent withthe 3.6 beam-unrelated events expected for this amountof integrated livetime. These events are separate fromthe 1.2 beam-unrelated events expected to fall within the
200 ns bunch windows.
After all cuts, 43 events remain in the 4 − 30 MeV reconstructed energy range, compared with 55.7 expected.
The vertex distribution of the sample is shown in Fig. 4,
in which no non-uniformity or biases with respect to theneutrino beam direction are found. The energy distribution of the data after all the selection cuts is shownin Fig. 5. A peak due to 6 MeV prompt de-excitation γrays is clearly seen in data, and the observed distribution
matches well with the expectation. The high energy tail

Number of events

Number of events

7

6

4

2

12
10

RUN1-3 data
NCQE
NC non-QE

8CC
Beam-unrelated

6
4
2

0
-1

0

1

2

3

0

4

∆T0 (µs)

Vertex Y (m)FIG. 3. (color online) ∆T0 distribution of the data sample
after all selection cuts except for beam timing, compared tothe bunch center positions determined from high energy T2K
neutrino events, indicated by eight dashed vertical lines. The
on-timing and off-timing events are shown in solid and hashed,respectively.

5

10

15

20

25

30

Reconstructed energy (MeV)

FIG. 5. (color online) Comparison of the reconstructed energy
spectrum between the selected data sample and the expectation after all selection cuts have been applied. The CC component is actually about twice as large as the beam-unrelated
background, but it is less apparent since it is spread acrossall energies.

20
15
10
5
0
-5
-10
-15
-20

-20 -15 -10 -5

0

5 10

15

20

Vertex X (m)FIG. 4. (color online) Vertex distribution of the final data
sample in Y vs X after all selections have been applied. The
solid and dotted lines indicate the boundaries of the innerdetector and fiducial volume, respectively. The neutrino beam
direction is indicated by the arrow.

originates primarily from the contribution of additional
secondary γ-rays overlapping the primary γ-rays.
C.

Systematic uncertainties

The sources of systematic uncertainty on the expected
number of signal and background events and their size

are summarized in Tab. II. The methods for calculatingthese uncertainties are described below.
The flux errors, calculated in correlated energybins, are determined based on beam monitoring,
constraints from external measurements (particularly
NA61/SHINE [17, 18]), and Monte Carlo studies of focusing parameters (e.g. horn current, beam alignment,etc.) [21]. The neutrino interaction uncertainties which
affect the normalization of the background are evaluatedby comparing NEUT predictions to external neutrinonucleus data sets in an energy region similar to T2K [15].
The systematic uncertainty on primary γ-ray production in signal (and the QE component of the CC background) comes from several sources. The largest contribution is from final-state nuclear interactions: NEUT
assumes that the de-excitation γ-ray production is thesame whether the final state contains a single nucleon
or multiple nucleons. We estimate the systematic uncertainty introduced by this assumption by observing thechange in the number of signal events with the extreme
alternate assumption that no de-excitation γ-rays are released from events with multi-nucleon final states. Additional uncertainty comes from the spectroscopic factors,
the errors on which are estimated as the difference between models from Benhar [24] and Ejiri [27], and therelative branching ratios for the 1s1/2 state, estimatedfrom Kobayashi et al. [28]. For the non-QE NC background events, a conservative uncertainty was calculated
by removing all primary γ-rays from the events and evaluating the difference in total selected events. The effectis relatively small since the pion-absorption events whichmake up the bulk of the NC non-QE background produce

TABLE II. Summary of systematic uncertainties on the expected number of signal and background events. While the
CC component has the largest uncertainty, it has a relatively
small effect on the final result since there are relatively few
CC events in the final sample.
SignalBackground
NCQE NC non-QE CC Unrel.
Fraction of Sample
69%
25%
4%
2%
Flux
11%
10%
12%
Cross sections
18%
24%
Primary γ production
10%
3%
6%
Secondary γ production 13%13%
7.6%
Detector response
2.2%
2.2%
2.2%
Oscillation Parameters
10%
Total Systematic Error 20%
25%
30% 0.8%

many secondary γ-rays and so are still detected thanks
to the low threshold of the analysis.
The uncertainty on secondary γ-ray production is dominated by uncertainties on the production of neutrons. It
was evaluated by comparing alternate models of neutron
production and how they altered the observed Cherenkov
light level for our simulated events, for both signal eventsand the pion-absorption background. The detector uncertainty includes contributions from uncertainties in the
SK energy scale, vertex resolution, and selection efficiency. It is estimated by comparing simulation and datafrom the linear electron accelerator (LINAC) installed
above SK [40]. The systematic uncertainty due to the atmospheric oscillation parameters, θ23 and |∆m232 |, is estimated by varying the parameters within the uncertainties
from the T2K measurement of these parameters [35].
There are two final systematic uncertainties that were
evaluated but have a negligible impact on the result. We
evaluated the potential non-uniformity of the selection
efficiency with respect to Q2 by changing the value ofthe MC axial mass to distort the differential cross section.
This variation changes the final calculated cross section
by less than a percent. The beam-unrelated backgroundis estimated from the out-of-time events which have astatistical error of 0.8%.

V.

MEASURED CROSS SECTION

The NCQE cross section is measured by comparing the
NCQE cross section as calculated in recent theoreticalwork [7] averaged over the unoscillated T2K flux with theobserved number of events after background subtraction:
obs
hσν,NCQEi=exp
N obs − Nbkg

exp
N exp − Nbkg

theoryhσν,NCQEi,(1)

σ (10-38 cm2)

8
4
Ankowski NCQE cross section
Flux-averaged Ankowski NCQE cross section

3

T2K data
T2K ν flux

2

1

0
0

0.5

1

1.5

2

Neutrino Energy (GeV)
FIG. 6. (color online) The T2K measurement of the fluxaveraged NCQE cross section, represented by a black point,
compared with the calculated cross section from [7]. The
dashed line shows the cross section versus neutrino energy,
the solid horizontal line shows the flux-averaged cross section. The vertical error bar on the data represents the 68%
confidence interval on the measured cross section while thehorizontal error bar is placed at the central value from ourdata and represents 68% of the flux at each side of the median energy. The solid gray histogram shows the unoscillated
T2K neutrino flux.

obs
where hσν,NCQE
i is the observed flux-averaged NCQE
theorycross section and hσν,NCQE
i = 2.01 × 10−38 cm2 is theflux-averaged cross section from [7]. The total numberof observed events is N obs (43), the total number of exexp
pected events is N exp (55.7), and Nbkg
(17.3) denotes
the expected number of background events.
The obtained flux-averaged neutrino-oxygen NCQE
cross section is 1.35 × 10−38 cm2 at a median neutrino
flux energy of 630 MeV. The 68% confidence interval on
the cross section is (1.06, 1.94) × 10−38 cm2 and the 90%
confidence interval is (0.84, 2.34) × 10−38 cm2 . They include both statistical and systematic errors and were calculated using a Monte Carlo method to account for thesystematic errors that are correlated between different
samples. While the underlying systematic uncertainties
are symmetric and gaussian, the confidence interval isasymmetric around the central value because some of
the uncertainties, primarily the production of secondary
γ-rays and to a lesser extent the neutrino flux, are correlated between the background expectation and the signal
expectation which are found in the numerator and denominator, respectively, of Eq. 1. Figure 6 shows our result compared with a theoretical calculation of the NCQE
cross section [7]. The vertical error bar for data shows
the 68% confidence interval on the data, and the horizontal error bar represents 68% of the flux at each side of
the median energy. The measurement is lower than the9recent theoretical calculation and outside the 68% confidence level, but consistent at the 90% confidence level.

VI.

SUMMARY

We have reported the first measurement of the crosssection of neutrino-oxygen NCQE interactions via thedetection of nuclear de-excitation γ-rays in the SuperKamiokande detector using the T2K narrow-band neutrino beam, below but consistent with the theoretical expectation at the 90% confidence level. Due to the similar
peak energies for T2K neutrinos and atmospheric neutrinos, the present work will shed light on the study of
the atmospheric background events for low energy astrophysical phenomena in neutrino experiments.

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