arXiv:1407.7389v2 [hep-ex] 31 Jul 2014

Measurement of the Inclusive Electron Neutrino Charged Current Cross Section on
Carbon with the T2K Near Detector
K. Abe,46 J. Adam,32 H. Aihara,45, 23 T. Akiri,9 C. Andreopoulos,44 S. Aoki,24 A. 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 V. Berardi,18
B.E. Berger,8, 23 S. Berkman,4 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,23 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 D. Dewhurst,35 F. Di
Lodovico,38 S. Di Luise,11 O. Drapier,10 T. Duboyski,38 K. Duffy,35 J. Dumarchez,36 S. Dytman,37 M. Dziewiecki,53
S. Emery-Schrenk,6 A. Ereditato,2 L. Escudero,16 A.J. Finch,26 M. Friend,14, ∗ Y. Fujii,14, ∗ Y. Fukuda,30
A.P. Furmanski,54 V. Galymov,29 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, 23 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, ∗E. Iwai,14 K. Iwamoto,40 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 T. Katori,38 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 Y. Koshio,33, ‡ W. Kropp,5 H. Kubo,25 Y. Kudenko,22, §R. Kurjata,53 T. Kutter,28 J. Lagoda,31 I. Lamont,26 E. Larkin,54 M. Laveder,20 M. Lawe,42 M. Lazos,27 T. Lindner,50
C. Lister,54 R.P. Litchfield,54 A. Longhin,20 L. Ludovici,21 L. Magaletti,18 K. Mahn,50 M. Malek,17 S. Manly,40
A.D. Marino,7 J. Marteau,29 J.F. Martin,49 S. Martynenko,22 T. Maruyama,14, ∗ 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 P. Mijakowski,31
C.A. Miller,50 A. Minamino,25 O. Mineev,22 A. Missert,7 M. Miura,46, ‡ S. Moriyama,46, ‡ Th.A. Mueller,10
A. Murakami,25 M. Murdoch,27 S. Murphy,11 J. Myslik,51 T. Nakadaira,14, ∗ M. Nakahata,46, 23 K. Nakamura,23, 14, ∗S. Nakayama,46, ‡ T. Nakaya,25, 23 K. Nakayoshi,14, ∗ 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.L. 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 P.A. Rodrigues,40 P. Rojas,8
E. Rondio,31 S. Roth,41 A. Rubbia,11 D. Ruterbories,40 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,38 Y. Shustrov,22 P. Sinclair,17 B. Smith,17 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,23, 23 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 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, †† T. Yano,24 S. Yen,50 N. Yershov,22 M. Yokoyama,45, ‡ T. Yuan,7 M. Yu,58 A. Zalewska,13J. Zalipska,31 L. Zambelli,14, ∗ 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(Dated: August 1, 2014)
The T2K off-axis near detector, ND280, is used to make the first differential cross-section
measurements of electron neutrino charged current interactions at energies ∼1 GeV as a function of electron momentum, electron scattering angle and four-momentum transfer of the interaction. The total flux-averaged νe charged current cross-section on carbon is measured to be
hσiφ = 1.11 ± 0.09 (stat) ± 0.18 (syst) × 10−38 cm2 /nucleon. The differential and total crosssection measurements agree with the predictions of two leading neutrino interaction generators,

3
NEUT and GENIE. The NEUT prediction is 1.23 × 10−38 cm2 /nucleon and the GENIE predictionis 1.08 × 10−38 cm2 /nucleon. The total νe charged current cross-section result is also in agreementwith data from the Gargamelle experiment.
PACS numbers: 14.60.Pq, 14.60.Lm, 25.30.Pt, 29.40.Ka

Introduction—T2K is a long baseline neutrino oscillation experiment measuring νe appearance and νµ disappearance from a νµ beam. Neutrino oscillations are described by a mixing matrix parametrized by three mixing
angles and a CP violating phase, δCP [1, 2]. The three
mixing angles have been measured to better than 10%
precision [3], and measuring δCP is currently a major goalin neutrino physics [4].
Future νe appearance measurements can be used tosearch for CP violation in neutrino interactions, andthese rely on precise understanding of both νµ and νecharged-current (CC) interaction cross-sections at energies ∼1 GeV. Many νµ cross-section measurements havebeen made at the GeV scale, both of the total CC inclusive cross-section and of individual interaction modes (seeRef. [5] for a review of cross-section data, and Refs. [6–8]
for recent results). Only the Gargamelle experiment has
measured the νe CC inclusive cross-section at the GeV
scale [9], and there are currently no νe differential crosssection results as a function of the electron kinematics.
Theoretical differences are expected between νe and νµcross-sections [10], and measuring these with data is critical to understand the systematic uncertainties related tothe search for CP violation in the lepton sector. The
uncertainty in νe cross-sections will become increasingly
important in future oscillation experiments as statisticaland other systematic uncertainties are reduced.
In this Letter we present the first νe CC inclusive differential cross-section measurements for neutrinos withenergy ∼1 GeV as a function of the electron momentum(pe ), electron scattering angle (cos(θe )) and the fourmomentum transfer of the interaction (Q2 ). The total flux-averaged CC inclusive cross-section is also presented.
T2K Experiment—T2K [11] operates from the J-PARC
facility in Tokai, Japan. A muon neutrino beam is produced from the decay of charged pions and kaons generated by 30 GeV proton collisions on a graphite target
and focused by three magnetic horns. Downstream of thehorns is the decay volume, 96 meters in length, followedby the beam dump and muon monitors (MUMON [12]).
The neutrino beam illuminates an on-axis near detector(INGRID [13]), an off-axis near detector (ND280) and an
off-axis far detector (Super-Kamiokande [14]). The offaxis detectors are positioned at an angle of 2.5◦ relative tothe beam axis direction. The near detectors are located
280 meters from the target and are used to determine theneutrino beam direction, spectrum, and composition before oscillations, and to measure neutrino cross-sections.
Super-Kamiokande, a 50 kt water Cherenkov detector sit-uated 295 km away, is used to detect the neutrinos after
oscillation.
ND280 is a magnetized multi-purpose detector designed to measure interactions of both νµ and νe fromthe T2K beam before oscillations. It is composed of anumber of subdetectors installed inside the refurbishedUA1/NOMAD magnet, which provides a magnetic fieldof 0.2 T. The central subdetectors form a tracking detector, composed of two fine-grained scintillator detectors (FGDs [15]) and three time projection chambers(TPCs [16]). The FGDs are used as the target for
the neutrino interactions, and while the upstream FGD(FGD1) is composed solely of scintillator bars, the downstream FGD (FGD2) also contains water layers. Upstream of the tracker is a π 0 detector (P0D [17]), explicitly built to measure neutrino interactions with a π 0
in the final state. The tracker and P0D are surrounded
by a set of electromagnetic calorimeters (ECals [18]), andthe magnet yokes are instrumented with side muon range
detectors (SMRDs [19]) to track high angle muons.
The results presented here are based on data takenfrom January 2010 to May 2013. During this period theproton beam power has steadily increased and reached
220 kW continuous operation with a world record of 1.2×
1014 protons per pulse. The physics-quality data for thisanalysis corresponds to a total of 5.90 × 1020 protons on
target (p.o.t.).
Neutrino Beam Flux—The neutrino beam flux [20] is
predicted by modeling interactions of the primary beam
protons with a graphite target using the FLUKA2008
package [21] and external hadron production datafrom the CERN NA61/SHINE experiment [22, 23].
GEANT3 [24] with GCALOR [25] is used to simulate thepropagation of secondary and tertiary pions and kaons,and their decays into neutrinos. Decays of kaons andmuons, in the decay volume, create the approximately
1% νe component of the beam. Muon decays are thedominant source of νe with energies below 1 GeV, withhigher energy neutrinos produced by kaon decays.
The neutrino flux uncertainties are dominated byhadron production uncertainties, with contributions fromthe neutrino beam direction and the proton beam uncertainties. The neutrino beam direction—monitored indirectly by MUMON on a spill-by-spill basis, and directly by INGRID [26]—has been well within the required±1 mrad during the full run period. The neutrino interaction rate per p.o.t. has also been measured by INGRID, and is stable within 0.7%. The total systematic
uncertainty on the νe flux is 13% at the mean νe energy(1.3 GeV).

P (tk |rj ) =P (rj |tk )P (tk ),ntPP (rj |tα )P (tα )

(1)

α=1

where P (rj |tk ) is the smearing matrix and P (tk ) is theMonte Carlo (MC) prior probability of finding a signal, the estievent in true bin tk . Given a dataset Nrmeasjmated number of events in each true bin is given by
n

Ntk =

r
1 X
− Brj ),
P (tk |rj )(Nrmeasjǫtk j=1(2)

where Brj is the number of background events that wereselected and ǫtk is the efficiency of detecting a signal eventin bin tk . The unfolding is performed separately for each

100

Data
νe CC interactions

80

γ background60µ background40

Other background

20
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Entries

Reconstructed pe (GeV/c)
200
150

Data
νe CC interactions

100µ backgroundγ background
Other background

50
0
-1

Entries/(0.04 GeV2/c2)

Selection of Electron Neutrino Interactions in
ND280—Full details of the event selections can be foundin Ref. [27], where the only difference is that in thisanalysis only interactions in FGD1 are selected, rather
than FGD1 and FGD2. This is so that interactions onwater in FGD2 are not included.
Electron neutrino interactions are selected using thehighest momentum negative track starting inside thefiducial volume of FGD1. To reduce the large backgroundfrom νµ charged current interactions, electron particle
identification criteria are applied using TPC dE/dx andECal shape and energy measurements. These remove
99.9% of µ− tracks, and although a clean sample of e−is selected, 62.4% of events are from photons which produce e+ e− pairs in FGD1. This γ background is reduced
by searching for a positron and applying an invariant
mass cut, and vetoing on activity in TPC1, the P0D, andECals upstream of FGD1. After this procedure, 315 νe
CC interaction candidates are selected, with an expected
purity of 65%. The reconstructed momentum, scattering
angle, and Q2 distributions are shown in Fig. 1, and compared to the prediction from the NEUT neutrino interaction generator [28]. Q2 is reconstructed assuming CC
quasi-elastic (CCQE) kinematics [29], with a stationary
target nucleon and 25 MeV binding energy.
The background from γ → e+ e− conversions in theνe sample is 23%, 70% of which are from neutrinos interactions outside the FGD1 fiducial volume. A control
sample, referred to as the γ sample, is used to constrain
this, and is selected by finding electron-positron pairsthat enter the TPC and that have a low invariant mass.
The data shows a deficit at low momentum in both theνe and γ samples. This deficit is also visible in Ref. [27],which selects events in FGD2 as well as FGD1.
Unfolding method—The Bayesian technique byd’Agostini [30] is used to unfold from the measured
reconstructed distributions to the underlying true distributions. For each observable, the true (reconstructed)
bins are denoted by tk (rj ). There are nt (nr ) true(reconstructed) bins in total. Bayes’ theorem is used togenerate the unsmearing matrix

Entries/(0.2 GeV/c)4-0.8 -0.6 -0.4 -0.2

0

0.2

0.4

0.6

0.8

1

Reconstructed cos(θ e)Data
νe CC interactions

100
80

γ background60µ background40

Other background

20
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Reconstructed Q2 (GeV2/c2)
FIG. 1. Reconstructed pe (top), cos(θe ) (middle) and Q2(bottom) distributions of νe event candidates. The NEUT
Monte Carlo prediction is separated into the νe CC interaction
signal, background from γ → e+ e− conversions, backgroundfrom µ− tracks and all other backgrounds. The last bins in the
top and bottom plots do not include the overflow of events.

variable. For defining the true bin of each interaction,
the true momentum of the electron, true angle of theelectron, and true Q2 of the interaction from the generator are used for pe , cos(θe ) and Q2 , respectively. The
NEUT neutrino generator is used for the unfolding results presented in this Letter.
The Bayesian unfolding technique was also used inRef. [6] for measuring the νµ CC inclusive cross-section
with ND280. The main difference in the unfolding
method for this analysis is that the MC background prediction, Brj , is estimated using the γ sample. Specifically, the background from neutrino interactions occurring outside of the fiducial volume (out-of-fiducial events)
is re-weighted based on the γ sample data. This choice
is made as the systematic uncertainties relating to infiducial events have been well-studied, 30% of the outof-fiducial events are on heavy targets (iron and lead)5
and 66% are from interaction channels on which there
are large uncertainties in the modeling (deep inelastic
scattering and neutral current interactions). The MC
prediction of events in the fiducial volume is subtracted
from the γ sample data, and the data/MC ratio of theout-of-fiducial events is then computed in (pe , cos(θe ))bins. The out-of-fiducial component of the νe sample
is re-weighted based on this data/MC ratio distribution.
The two-dimensional re-weighting scheme is chosen as
the νe and γ samples preferentially select photons fromdifferent origins: the γ sample requires both the e+ ande− to be reconstructed, so preferentially selects higherenergy and more forwards-going photons.
The effect of systematic uncertainties on the crosssection measurements are computed using the same covariance matrix method as in Ref. [6]. Separate covariance matrices are computed for the data statistics,
the MC statistics, detector systematics, flux and crosssection systematics, and out-of-fiducial systematics. One
thousand toy experiments are performed to generate eachmatrix, and each experiment simultaneously affects boththe νe and γ samples.
The data statistical uncertainty is evaluated by varying the contents of each data bin according to Poisson
statistics. The MC statistical uncertainty is evaluatedby separately varying the νe , the in-fiducial backgroundand the out-of-fiducial background components according to Poisson statistics. Detector systematics are studied by varying parameters such as the momentum resolution, and propagating the effect to the selection. The
TPC, FGD, ECal and external interaction uncertainties
are described in detail in Ref. [27]. The uncertainty on
the FGD mass is 0.67% [6]. The flux and cross-section
uncertainties are also described in Ref. [27]. The flux
uncertainties are based on beamline measurements andhadron production data. The cross-section uncertainties,
including neutrino-nucleon, nuclear modeling, pion production and final state interaction uncertainties are constrained using external data and comparisons between
different nuclear models [29]; these uncertainties affectsignal efficiencies and background spectra.
Due to the discrepancy between data and MC in theγ sample, conservatively an extra systematic is applied
to the out-of-fiducial re-weighting in addition to the statistical uncertainty of the γ sample. If the re-weighting
factor in a given bin is α, then the correction is modeled
as a Gaussian with mean α and width α/3.
Cross-section results—The signal for this analysis isall νe CC interactions occurring in the FGD1 fiducial
volume. FGD1 is composed of carbon (86.1% by mass),hydrogen (7.4%), oxygen (3.7%), titanium (1.7%), silicon(1.0%) and nitrogen (0.1%). The analysis measures theflux-averaged differential νe CC inclusive cross-section,and for bin tk of variable X, this is given by


Ntk
∂hσiφ
,
=
∂X tk
∆Xtk T φ(3)

where X is either pe , cos(θe ) or Q2 , ∆Xtk is the width of
the bin, Ntk is the total number of signal events in thebin, T is the number of target nucleons (5.5 × 1029 [6]), φ
is the total integrated flux (1.35 × 1011 cm−2 ), and h· · · iφindicates that the quantity is averaged over the flux.
The total flux averaged cross-section per nucleon iscomputed by summing over all X bins, asPnt
Nthσiφ = k=1 k .
(4)
Tφ
For comparison, differential and total flux-averaged
cross-section predictions are computed using the NEUT(version 5.1.4.2) and GENIE (version 2.6.4 [31]) generators.
Fig. 2 shows the unfolded differential cross-section results as a function of pe , cos(θe ) and Q2 . The data agrees
with both NEUT and GENIE, although a deficit is seen
at low Q2 compared to NEUT. The biggest differences
between NEUT and GENIE at low Q2 are caused by thedifferent values of MAQE chosen for CCQE interactions,and different CC coherent interaction models.
The total flux-averaged cross-section when unfolding
through Q2 is hσiφ = 1.11 ± 0.09 (stat) ± 0.18 (syst) ×
10−38 cm2 /nucleon, which agrees with both the NEUT
prediction of 1.23 × 10−38 cm2 /nucleon and the GENIE prediction of 1.08 × 10−38 cm2 /nucleon. The result is shown in Fig. 3, along with the Gargamelle datafrom 1978 [9]. The results when unfolding through theother variables agree at the percent level. The dominant systematic uncertainties on this result are the flux
(12.9%) and detector systematics (8.4%), with all othersystematics giving a 6.1% uncertainty when added inquadrature. The uncertainty from re-weighting the outof-fiducial background is 2.1%.
An important aspect of the Bayesian unfolding approach is that it allows a reconstructed distribution to
be unfolded into regions that it is not sensitive to. This
analysis has poor reconstruction efficiency for low momentum, backwards going, or high angle electrons. This
adds model dependency since the NEUT generator must
predict these poorly determined regions. For this reason,a second result is presented, in which only events withpe > 550 MeV and cos(θe ) > 0.72 are considered. In
this “reduced phase-space” result, no attempt is madeto unfold into regions of low detector efficiency. The unfolded Q2 differential cross-section result for this reduced
phase-space is shown in Fig. 4.
Conclusion—Understanding differences between νeand νµ cross-sections is vital as long baseline oscillation
experiments search for CP violation in the lepton sector. The T2K off-axis near detector, ND280, has been

Full phase-space

25

NEUT
20

GENIE
T2K data

15
10
5
0
0

0.2 0.4 0.6

0.81

1.2 1.4 1.6 1.8

2

8
40
6

30

T2K νe flux
NEUT prediction
GENIE prediction
NEUT average
GENIE average
Gargamelle data
T2K data

20
10
0
0

2.2 >

1

2

3

4

5

6

7

120

NEUT

100

GENIE

9

2
0
10

FIG. 3. Total νe CC inclusive cross-section when unfolding
through Q2 . The T2K data point is placed at the νe flux
mean energy. The vertical error represents the total uncertainty, and the horizontal bar represents 68% of the flux eachside of the mean. The T2K flux distribution is shown in grey.
The NEUT and GENIE predictions are the total νe CC inclusive predictions as a function of neutrino energy. The NEUT
and GENIE averages are the flux-averaged predictions. The
Gargamelle data is taken from Ref. [9].

T2K data

80
60
40
20
0
<

d σ /dQ2 (×10-39 cm2/nucleon/(GeV2/c2))

Full phase-space

84Eν (GeV)

0.5

0.6

0.7

0.8

35

0.9

1

cos(θ e)Full phase-space

30

NEUT

25

GENIE

20

T2K data

15
10

d σ /dQ2 (×10-39 cm2/nucleon/(GeV2/c2))d σ /dcos(θ ) (×10-39 cm2/nucleon)pe (GeV/c)
14010Full phase-space50

νe flux (×109 /cm2/50 MeV/1021 p.o.t.)

νe CC σ (×10-39 cm2/nucleon)d σ /dp (×10-39 cm2/nucleon/(GeV/c))6pe > 550MeV and cos(θ e) > 0.72

20
18

NEUT

16
14

GENIE

12

T2K data

10
8
6
4
2
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

>

Q2 (GeV2/c2)

5
0
0

0.2

0.4

0.6

0.8

1

Q

2

>
2

(GeV /c2)

FIG. 2. Unfolded νe CC inclusive differential cross-sections
as a function of pe (top), cos(θe ) (middle) and Q2 (bottom).
The inner (outer) error bars show the statistical (total) uncertainty on the data. The dashed (solid) line shows the NEUT
(GENIE) prediction. Overflow (underflow) bins are indicatedby > (<) labels, and are normalized to the width shown.

used to extract νe CC inclusive flux-averaged differential
cross-sections as a function of pe , cos(θe ) and Q2 , andthey are found to agree with both the NEUT and GENIE
neutrino interaction generator predictions. These are thefirst ever νe differential cross-section measurements at theGeV-scale. The total νe CC inclusive flux-averaged cross-

FIG. 4. Unfolded νe CC inclusive differential cross-section as
a function of Q2 , when only electrons with pe > 550 MeV
and cos(θe ) > 0.72 are considered. The inner (outer) error bars show the statistical (total) uncertainty on the data.
The dashed (solid) line shows the NEUT (GENIE) prediction.
Overflow (underflow) bins are indicated by > (<) labels, andare normalized to the width shown.

section is found to be 1.11 ± 0.20 × 10−38 cm2 /nucleon,
which is also in agreement with the NEUT and GENIE
predictions. The data related to the measurement can befound in [32].
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
CFI, Canada; CEA and CNRS/IN2P3, France; DFG,

7
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.

∗

also at J-PARC, Tokai, Japan
also at Institute of Particle Physics, Canada‡
affiliated member at Kavli IPMU (WPI), the Universityof Tokyo, 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.
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