arXiv:1407.4256v1 [hep-ex] 16 Jul 2014

Measurement of the inclusive νµ charged current cross section
on iron and hydrocarbon in the T2K on-axis neutrino beam
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 K. Koseki,14, ∗ Y. Koshio,33, ‡ I. Kreslo,2 W. Kropp,5 H. Kubo,25
Y. Kudenko,22, § R. Kurjata,53 T. Kutter,28 J. Lagoda,31 K. Laihem,41 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,18K. 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,7M. 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 M. Otani,25 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 F. Retiere,50 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,11M. 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 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 A. Vacheret,35 M. Vagins,23, 5 G. Vasseur,6 T. Wachala,13 A.V. Waldron,35
C.W. Walter,9, ‡ D. Wark,44, 35 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
5
University of California, Irvine, Department of Physics and Astronomy, Irvine, California, U.S.A.

2
6

IRFU, CEA Saclay, Gif-sur-Yvette, France
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: July 17, 2014)7

We report a measurement of the νµ inclusive charged current cross sections on iron and hydrocarbon in the T2K on-axis neutrino beam. The measured inclusive charged current cross sections oniron and hydrocarbon averaged over the T2K on-axis flux with a mean neutrino energy of 1.51 GeV−38
are (1.444 ± 0.002(stat.)+0.189
cm2 /nucleon, and (1.379 ± 0.009(stat.)+0.178−0.157 (syst.)) × 10
−0.147 (syst.)) ×−38
2
10cm /nucleon, respectively, and their cross section ratio is 1.047 ± 0.007(stat.) ± 0.035(syst.).
These results agree well with the predictions of neutrino interaction model and thus demonstrate
the correct treatment of the nuclear effect for iron and hydrocarbon targets in the model.

3
I.

INTRODUCTION

The T2K (Tokai-to-Kamioka) experiment is a long
baseline neutrino oscillation experiment [1] whose primary goals are precise measurements of the appearanceof electron neutrinos and the disappearance of muon neutrinos. An almost pure intense muon neutrino beam
is produced at J-PARC (Japan Proton Accelerator Research Complex) in Tokai. The proton beam impinges
on a graphite target to produce charged pions, which
are focused by three magnetic horns [2]. The pions decay mainly into muon - muon-neutrino pairs during theirpassage through the 96-meter decay volume. The neutrinos are measured by the near detectors (INGRID [3] andND280 [4–8]) in J-PARC and the far detector (SuperKamiokande [9]) in Kamioka, located 295km away from
J-PARC (Fig. 1).
A precise neutrino oscillation measurement requires
good knowledge of neutrino interaction cross sections.
The neutrino charged current (CC) interaction is especially important for neutrino oscillation measurements
because the neutrino flavor is identifiable via the CC interaction. Charged current neutrino-nucleon interactions
at neutrino energies around 1 GeV have been studied in
the past predominantly on deuterium targets [10, 11].
Many modern neutrino oscillation experiments use heavier targets like carbon, oxygen and iron. Nuclear effects
are large for those targets and, consequently, they cause
large systematic uncertainties for the neutrino oscillation measurement. Therefore, it is therefore important
to measure and understand these interactions to minimize systematic uncertainties for the neutrino oscillation
measurement.
In this paper, we present measurements of the inclusive muon neutrino charged current cross section on ironand hydrocarbon and their cross section ratio at neutrino energies around 1 GeV using the INGRID detector.
INGRID is located on the beam center axis and consists of 16 standard modules and an extra module called
Super-Kamiokande

Near Detector
1000 mKamioka

280 m

J-PARC

Neutrino Beam

295 kmTokai

the Proton Module. Iron (Fe) makes up 96.2% of thetarget mass in the standard module, and hydrocarbon(CH) makes up 98.6% of the target mass in the Proton
Module. Thus, the νµ CC inclusive cross sections on
Fe and CH are calculated from the number of selected
CC events in the standard module and the Proton Module respectively. The νµ CC inclusive cross section on
Fe at neutrino energies above 3.5GeV was measured by
the MINOS experiment [12], however that around 1 GeV
had never been measured. Although the νµ CC inclusive
cross section on CH around 1 GeV was already measured
by the T2K off-axis near detector ND280 [13] and otherexperiments[14, 15], the Proton Module can measure thecross section for higher energy neutrinos than the ND280
measurement, because the energy distribution of the onaxis neutrinos is higher than that of the off-axis neutrinos(the average energies of the on-axis and off-axis neutrinos
are 1.51 GeV and 0.85 GeV, respectively). We also measured the νµ CC inclusive cross section ratio on Fe to CH
using a central standard module and the Proton Module.
The central standard module and the Proton Module areon the central axis of the beam and are exposed to thesame neutrino beam. Thus, this cross section ratio canbe measured very precisely, since many of the large systematic errors from uncertainties on the neutrino fluxand neutrino interactions will be cancelled between thetwo detectors. Therefore, it can provide a good test of
the target dependence of the nuclear effect. Recently, the
MINERνA experiment measured the cross section ratio
at neutrino energies of 2–20 GeV [16]. We can provide a
result of the cross section ratio at a lower energy.
T2K collected data corresponding to 6.57 × 1020 protons on target (POT) during the four run periods listed
in Table I, with which νµ → νe appearance was observed[17]. During this time period, INGRID recorded morethan 99.5% of the delivered beam data. A subset of data
corresponding to 0.21 × 1020 POT from Run3 was collected with the magnetic horns operating at 205 kA instead of the nominal value of 250 kA. The Run3 periods
with the magnetic horns operating at 205 kA and 250
kA are referred to as Run3b and Run3c, respectively.
For the cross section measurement, data from Run1, in
which the Proton Module was not installed, and Run3b
are not used. The total data set for the cross section
measurement corresponds to 6.04 × 1020 POT.

FIG. 1. Overview of the T2K experiment.
TABLE I. T2K data-taking periods and integrated protons
on target (POT).
∗ 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.

Run period
Dates
Integrated POT
Run 1
Jan. 2010 − Jun. 2010
0.32 × 1020
Run 2
Nov. 2010 − Mar. 20111.11 × 1020
Run 3bMar. 2012
0.22 × 1020
Run 3cApr. 2012 − Jun. 20121.37 × 1020
Run 4
Oct. 2012 − May. 2013
3.56 × 1020

The remainder of this paper is organized as follows:
Details of the INGRID detector and Monte Carlo sim-

4
ulations are explained in Sec. II and III, respectively.
Section IV summarizes the CC-inclusive event selection.
The analysis method of the cross section measurement is
described in Sec. V. Section VI describes the systematic
errors. The results and conclusions are given in Sec. VII
and VIII, respectively.

II.

beam pulse structure. For the cross section measurement,
only the horizontal central module was used because it
is on the same beam axis as the Proton Module and provides a good cancellation of the systematic errors with
the Proton Module. Details of the components and thebasic performance of the INGRID standard modules aredescribed in Ref [3].

DETECTOR CONFIGURATIONThe INGRID (Interactive Neutrino GRID) detector isan on-axis neutrino near detector located 280m downstream of the proton target. It consists of 16 identicalstandard modules and an extra module called Proton
Module.

~10m
1.5m

Beam centerA.

Y

INGRID standard modules
X~10m

FIG. 2. Overview of the 16 INGRID standard modules viewed
from beam upstream.

Electronics boxes

Veto planes

1.24m

The main purpose of the INGRID standard modules
is to monitor the neutrino beam direction with a precision better than 1 mrad. The spatial width (1σ) of
the neutrino beam at the location of INGRID is about
5 m. In order to cover a large enough region to see a full
beam profile, INGRID is designed to sample the beamin a transverse section of 10 m×10 m, with 14 identical modules arranged in two identical groups along thehorizontal and vertical axes, as shown in Fig. 2. Two separate modules are placed off the main cross to monitor
the asymmetry of the beam. Each of the modules consistsof nine iron target plates and eleven tracking scintillator
planes, as shown in Fig. 3 left. They are surrounded byveto scintillator planes (Fig. 3 right) to reject charged
particles coming from outside of the modules. The dimensions of each iron target plate are 124×124cm2 in thehorizontal and vertical directions and 6.5 cm along thebeam direction. The total iron mass serving as a neutrino
interaction target is 7.1 tons per module. Each tracking scintillator plane consists of two scintillator layers.
Each layer has 24 scintillator bars whose dimensions are
5cm×1cm×120cm, making a plane of 120×120cm2 in thehorizontal and vertical directions and 1.0 cm along thebeam direction. One layer is placed perpendicular to theother layer in a tracking scintillator plane so that it is sensitive to both horizontal and vertical positions. The vetoscintillator plane consists of one scintillator layer which
is made up of 22 scintillator bars segmented along thebeam direction, in order to identify the incoming charged
particles produced by neutrino interactions in the wallsof the detector hall. Scintillation light is collected andtransported to a photodetector with a wavelength shifting fiber (WLS fiber) which is inserted in a hole at thecenter of the scintillator strip. The light is read out bya Multi-Pixel Photon Counter (MPPC) [18, 19] attached
to one end of the WLS fiber. The electrical signal fromeach MPPC is digitalized to integrated charge and timing information by the Trip-t front-end board (TFB) [20].
The integration cycle is synchronized with the neutrino

Y
X

Tracking planes
Iron platesZ

FIG. 3. Exploded view of an INGRID standard module. It
consists of iron target plates and tracking scintillator planes(left), and it is surrounded by veto scintillator planes (right).

B.

INGRID Proton Module

The Proton Module is an extra module located at thebeam center between the horizontal and vertical standard modules (Fig. 4). It is a fully-active tracking detector which consists of only scintillator bars. It wasconstructed and additionally installed between Run1 andRun2. The purpose of this Proton Module is to separate
the neutrino interaction channels by detecting the protons and pions together with the muons from the neutrino interactions, and to measure the neutrino cross section for each interaction channel.
It consists of 36 tracking layers surrounded by vetoplanes, where each tracking layer is an array of two

5

MONTE CARLO SIMULATIONThe INGRID Monte Carlo (MC) simulation consistsof three main parts. The first is a simulation of the neutrino beam production, which predicts the neutrino fluxand energy spectrum of each neutrino flavor. The second is a neutrino interaction simulation, which is used to
calculate the neutrino interaction cross sections and thekinematics of the final state particles taking into accountthe intranuclear interactions of hadrons. The third stepis a detector response simulation which reproduces the
final-state particles’ motion and interaction with material, scintillator light yield, and the response of the WLS
fibers, MPPCs, and front-end electronics.

n

n

X

n

n

n

n

n

INGRID
verticalmodulesZ

Proton Module

INGRID horizontal modules

FIG. 4.
above.

Veto planes

Y

Z

X

Tracking planes

Shading panels

FIG. 5. Exploded view of the Proton Module.

A.

Neutrino beam prediction

To predict the neutrino fluxes and energy spectra, a neutrino beam Monte Carlo simulation, called
JNUBEAM [22], was developed based on the GEANT3
framework [23].
We compute the neutrino beam
fluxes starting from models (FLUKA2008 [24, 25] andGCALOR [26]) and tune them using existing hadron production data (NA61/SHINE [27, 28], Eichten et al. [29]and Allaby et al. [30]). The predicted neutrino energy
spectra at the center of INGRID are shown in Fig. 6.
Energy spectra 10 m upstream of INGRID are predictedwith the same procedure in order to simulate the background events from neutrino interactions in the walls of
the experimental hall.
Flux (/cm2/1021POT/50MeV)

III.

Power supply
Electronics box

1.2m

types of scintillator bars (Fig. 5). The 16 bars in the
inner region have dimensions of 2.5cm×1.3cm×120cm
while the 16 bars in the outer region have dimensions of
5cm×1cm×120cm, making a layer of 120×120cm2 in thehorizontal and vertical directions. The former is the scintillator produced for the K2K SciBar detector [21] andthe latter was produced for INGRID. The tracking layers are placed perpendicular to the beam axis at 23mm
intervals. Since the bars are aligned in one direction,a tracking layer is sensitive to either the horizontal orvertical position of the tracks. The tracking layers are
therefore placed alternating in perpendicular directions
so that three-dimensional tracks can be reconstructed.
The tracking layers also serve as the neutrino interaction
target. As with the standard modules, scintillation lightis read out by a WLS fiber and MPPC, and electricalsignal from MPPC is digitalized by TFB. The INGRID
horizontal modules which lie downstream of the Proton
Module are used to identify muons from the neutrino interactions in the Proton Module.

νµ
νµ
νe
νe

1012
1011
1010
109
108
107
0

1

2

3

4

5

6

7

8

9

10

Eν (GeV)

FIG. 6. Neutrino energy spectrum for each neutrino species
at the central module predicted by JNUBEAM.

B.

Neutrino interaction simulation

The position of the Proton Module viewed from

Neutrino interactions with nuclear targets are simulated with the NEUT program library [31] which has

6been used in the Kamiokande, Super-Kamiokande, K2K,
SciBooNE, and T2K experiments. NEUT simulates neutrino interactions with nuclear targets such as protons,
oxygen, carbon, and iron, in the neutrino energy range
from 100 MeV to 100 TeV. Both the primary neutrino
interactions in nuclei and the secondary interactions of
the hadrons in the nuclear medium are simulated. Additionally, a cross section prediction by a different neutrino
interaction simulation package, GENIE [32], is used forcomparison. In both NEUT and GENIE, the following
neutrino interactions in both charged current (CC) andneutral current (NC) are simulated:• quasi-elastic scattering (ν + N → ` + N 0 )• resonant π production (ν + N → ` + π + N 0 )• coherent π production (ν + A → ` + π + A0 )• deep inelastic scattering (ν +N → `+N 0 +hadrons)
where N and N 0 are the nucleons (proton or neutron), `is the lepton, m is the meson and A is the nucleus. Bothsimulators use the Llewellyn Smith formalism [33] for
quasi-elastic scattering, the Rein-Sehgal model [34, 35]
for single meson production and coherent π production
and GRV98 (Glück-Reya-Vogt-1998) [36] parton distributions with Bodek-Yang modifications [37, 38] for deep
inelastic scattering. However, the actual models used inour simulation have many differences from above originalmodels, such as set values of the axial mass, the treatment of nuclear effects, descriptions of the non-resonant
inelastic scattering, etc. More details about the simulators used are described in Ref [13]. Figure 7 shows theneutrino-nucleus cross sections per nucleon divided by
the neutrino energy predicted by NEUT.
σ / Eν (cm2 / GeV)

-39

18 ×10CCQE
CC resonant π
CC coherent π
CC DIS

Total (CC+NC)
CC total
NC total

16
14
12
10
8
6
4

tector structures (geometries, materials). The structureof the walls of the experimental hall is also modeled tosimulate background events from neutrino interactionsin the walls. The particles’ motion and physics interactions with the materials are simulated, and the energy
deposit of each particle inside the scintillator is stored.
Simulations of hadronic interactions are performed with
the QGSP BERT physics list [40]. The energy deposit
is converted into the number of photons. Quenching effects of the scintillation are modeled based on Birks’ law[41, 42]. The effect of collection and attenuation of thelight in the scintillator and the WLS fiber is modeled
based on the results of electron beam irradiation tests.
The non-linearity of the MPPC response is also taken
into account, since the number of detectable photoelectrons is limited by the number of MPPC pixels. The
number of photoelectrons is smeared according to statistical fluctuations and electrical noise. The dark count of
the MPPCs is added with a probability calculated fromthe measured dark rate. Because the response of the
ADCs on front-end electronics is not linear, its response
is modeled based on the results of a charge injection test.

IV.
A.

EVENT SELECTION

Event selection for the Proton Module

A neutrino charged current interaction in the Proton
Module is identified by a track from the fiducial volumeof the Proton Module to the standard horizontal modules
located behind the Proton Module, where the standard
modules are used to identify a long muon track. First,
hits are clustered by timing. A pre-selection is applied
to reject accidental noise events. Then, tracks are reconstructed using hit information. Next, tracks matchedbetween the Proton Module and the standard module aresearched to select long muon tracks. If matched tracks
are found, vertexing is applied to identify event pileup.
After that, charged particles from outside the module arerejected with veto planes, and the reconstructed event
vertex is required to be inside the fiducial volume (FV).
The event selection criteria are described in the following
subsections.

2
0

0

1

2

3

4

5

6

7

8

9

10

Eν (GeV)

FIG. 7. Neutrino-nucleus cross sections per nucleon of carbon
nucleus divided by the neutrino energy predicted by NEUT.

C.

INGRID detector response simulation

The INGRID detector simulation was developed using the Geant4 framework [39]. It models the real de-

1.

Time clustering

When there are four or more hits in a 100 nsec time
window, all hits within ±50 nsec of the average time makeup a timing cluster.

2.

Pre-selection

A tracking plane with at least one hit in both the horizontal and vertical layers is defined as an active plane.

7

Number of events

The timing clusters with three or more active planes are
selected as shown in Fig. 8.
107

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

106

Figure 9 shows an example of a merged track. This track
matching is applied to select long muon tracks from CCinteractions and reject short tracks caused by neutral particles from outside, like neutrons and gammas which cannot be rejected by a VETO cut, or NC interactions.

105

ν

104

ν

103

ν

0

2

4

6

8

10

12

14

16

18

Number of active planes

FIG. 8. Number of active planes for the Proton Module.
Events with more than two active planes are selected. The
background events from the walls of the detector hall is normalized with beam induced muon backgrounds, as describedin Sec. IV A 9

3.

Two-dimensional track reconstruction

Tracks are reconstructed in the XZ and YZ planes independently. We developed a track reconstruction algorithm based on a cellular automaton. The cellular automaton is the dynamical system which was used for the
track reconstruction for the K2K SciBar detector [43],and our track reconstruction algorithm is analogous with
it. This algorithm can reconstruct one or more tracks ina timing cluster.

4.

INGRID

Proton Modulepµ−νFIG. 9. MC event display of a charged current neutrino eventin the Proton Module. Red circles and black lines represent
observed hits and reconstructed tracks, respectively. Areas of
red circles correspond to light yields.

5.

Three-dimensional tracking

Three-dimensional tracks are searched for among pairsof two-dimensional merged tracks in the XZ-plane (Xtrack) and YZ-plane (Y track) according to the following rules. If the difference of the upstream Z point of
an X track and a Y track is smaller than three layers,
they are combined into a three-dimensional track. If a
two-dimensional X or Y track meets the above condition
with more than one two-dimensional Y or X track, thepair of tracks with the smallest difference in the upstream
Z point is combined.

Track matching

When two-dimensional tracks are reconstructed inboth horizontal central standard module and the Proton
Module in the same integration cycle, they are merged ifthey meet the following four requirements:
1. The upstream edge of the standard module track isin either of the most upstream two layers.
2. The downstream edge of the Proton Module trackis in either of the most downstream two layers.
3. The difference between the reconstructed angles ofthe standard module and Proton Module tracks
with respect to z axis is less than 35◦ .
4. At the halfway point between standard module and
the Proton Module, the distance between the extrapolated standard module track and the Proton
Module track is less than 85mm.

6.

Vertexing

After the reconstruction of a three-dimensional track,
the upstream edge of the three-dimensional track is identified as a reconstructed vertex. If a pair of threedimensional tracks meet the following conditions, they
are identified as tracks coming from a common vertex:
1. The sum of the Z position differences between the
upstream edges of the two tracks in XZ and YX
planes is less than two planes.
2. The distance between the upstream edges of thetwo tracks in the XY-plane is less than 150mm.
This vertexing is performed for all combinations of threedimensional tracks, allowing more than two tracks to be
associated with the same reconstructed vertex. The following event selection cuts are applied to every vertex,

Number of events

8
since each one is expected to correspond to a single neutrino interaction. This means that, as long as the vertices
are distinguishable, events with multiple neutrino interactions (event pileup) are handled correctly.

7.

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

106
105
104

Timing cut
103

The T2K neutrino beam is pulsed. Each pulse hasan eight-bunch structure and each bunch has a width of
58 nsec. To reject off-timing events, such as cosmic-ray
events, only events within ±100 nsec from the expected
timing in each bunch are selected (Fig.10). The expected
timing is calculated from the primary proton beam timing, the time of flight of the particles from the target
to INGRID, and the delay of the electronics and cables.
The event time is defined by the time of the hit at thestart point of the track.

102
0

4

6

8

10

12

14

16

18

Vertex Z (plane)

FIG. 11. Vertex Z distribution for the Proton Module before
applying the veto and fiducial volume cuts.

9.

Number of events

2

Summary of the event selection for the Proton Module

5

10

104
103
102
10
1
-200 -150 -100

-50

0

50

100

150

200

Time residual (nsec)

FIG. 10. Time difference between the measured event timing and the expected neutrino event timing for the Proton
Module. Events within ±100 nsec are selected.

8.

Veto and fiducial volume (FV) cuts

Two selections are applied to reject incoming particles
produced by neutrino interactions in upstream materials,
such as the walls of the experimental hall. First, theupstream veto cut is applied. The first tracker plane isused as the front veto plane, and events which have avertex in the plane are rejected as shown in Fig. 11. The
events rejected by this front veto cut are identified asbeam induced muon backgrounds. Furthermore, events
which have a hit in a side veto plane at the upstream
position extrapolated from the reconstructed track arerejected. After the veto cut, a fiducial volume (FV) cut
is applied. The FV of each module is defined as a volume
within ±50 cm from the module center in the X and Y
directions, and from the third to the sixteenth tracker
plane in the Z direction. The ratio of the FV to the total
target volume is 58.1%. Events having a vertex inside
the FV are selected as shown in Fig. 12.

The results of the event selection for the Proton Module are summarized in Table II. Figure 13 shows the vertex distributions in the X, Y and Z directions after all
cuts. The MC simulation includes neutrino interactions
on the wall of the detector hall. The MC prediction of
the beam induced muon backgrounds is 35% smaller thanthe observation. This is likely due to the uncertainties ofthe density of the walls, the neutrino flux and the neutrino interaction model. Thus, the number of neutrino
interactions on the walls in the MC simulation is normalized by the observed number of the beam induced
muon backgrounds.
TABLE II. Number of events passing each selection step for
the Proton Module. The MC assumes 6.04 × 1020 POT anduses the nominal NEUT model. The efficiency is defined as
the number of selected CC events divided by the number of
CC interactions in the FV. The purity is defined as the fraction of the νµ CC events on CH among the selected events.
Selection
Data
MC Efficiency Purity
Vertexing 1.296×106 1.317×106
65.6% 3.9%
Timing cut 1.294×106 1.317×106
65.6% 3.9%
Veto cut
1.281×105 1.380×105
53.0% 29.9%
FV cut3.618×104 3.585×104
41.2% 89.4%

B.

Event selection for the standard module

The event selection for the standard module is thesame as that for the Proton Module except for two differences. One is that track matching is not applied for the
standard module, and the other is an additional acceptance cut. The event selection for the standard module is
as follows. First, time clustering, pre-selection (Fig. 14)
and two-dimensional track reconstruction are applied as93

Number of events

Number of events

3

25 ×10Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

20
15

25 ×10

15

10

10

5

5

0
-60

-40

-20

0

20

40

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

20

0
-60

60

Vertex X (cm)

-40

-20

0

20

40

60

Vertex Y (cm)Dataνµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

3000
2500
2000

3000
2500
2000
1500

1000

1000

500

500
-40

-20

0

20

40

60

Vertex X (cm)Dataνµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

3500

1500

0
-60

Number of events

3500

Number of events

Number of events

FIG. 12. Vertex X and Y distributions for the Proton Module after applying the veto cut. A volume within ±50 cm in the X
and Y directions from the module center is defined as fiducial volume (FV). Most of the background events which pass the FV
cut in one direction (X or Y) are actually rejected by the FV cut in the other direction (Y or X).

0
-60

5000

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

4500
4000
3500
3000
2500
2000
1500
1000
500

-40

-20

0

20

40

60

Vertex Y (cm)

0
0

2

4

6

8

10

12

14

16

18

Vertex Z (plane)

FIG. 13. Vertex X, Y and Z distributions for the Proton Module following event selection. There are jumps at X or Y = ±20cm
because the Proton Module uses thicker scintillators in the inner region (−20cm ∼ +20cm).

with the Proton Module. When the tracks are reconstructed, three-dimensional tracking is done for all reconstructed tracks, while it is done only for the merged
tracks in the case of the Proton Module. Then, the vertexing, timing cut (Fig. 15), and veto and fiducial volume cuts (Fig. 16) are applied as with the Proton Module. The ratio of the FV to the total target volume is61.7% for the standard modules. CC interactions in thestandard module can be selected with sufficiently highpurity by the above event selection. However, there arelarge differences in the selection efficiency between thestandard module and the Proton Module, as shown in
Fig. 17. This is because the acceptance of the Proton
Module is limited by the required track matching withthe standard module. These differences enlarge the systematic error on the measurement of the CC-inclusive
cross section ratio on Fe to CH. To minimize this difference, the following acceptance cut is added to the event
selection for the standard module. First, an imaginary
standard module is defined directly behind the standard
module. The distance between the standard module andthe imaginary module is the same as that between the
Proton Module and the standard module. The reconstructed tracks are then extended further downstream,even if the track has stopped in the module. If no tracks

from the vertex reach the imaginary module, the eventis rejected as shown in Fig.18. After applying this acceptance cut, the difference in the selection efficiencies
between the standard module and the Proton Module isgreatly reduced, as shown in Fig. 17. The results of theevent selection are summarized in Table III. Figure 19
shows the vertex distributions in the X, Y and Z directions after all cuts. As with the Proton Module, thenumber of neutrino interactions on the walls in the MC
simulation is normalized with the beam induced muon
backgrounds.

C.

Event pileup correction

When a track from a neutrino event piles up witha track from another neutrino event, vertices may failto be reconstructed. Because this results in the loss of
events, this event-pileup effect needs to be corrected for.
The event-pileup effect is proportional to the beam intensity. Hence, the correction factor is estimated as alinear function of the beam intensity. The slope of thelinear function is estimated from beam data as follows.
First, the beam data is categorized into sub-samples according to the beam intensity. In each sub-sample, allNumber of events

10
×103
Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

1000
800
600

Selection
Data
MC Efficiency Purity
Vertexing
3.179×106 3.194×106
96.7% 35.9%
Timing cut
3.179×106 3.194×106
96.7% 35.9%
Veto cut
1.369×106 1.418×106
88.8% 74.2%
FV cut8.875×105 9.169×105
74.4% 86.6%
Acceptance cut 5.185×105 5.130×105
42.7% 88.8%

400
200
0
0

2

4

6

8

TABLE III. Number of events passing each selection step forthe standard module. The MC assumes 6.04 × 1020 POT
and uses the nominal NEUT model. The efficiency is definedas the number of selected CC events divided by the numberof CC interactions in the FV. The purity is defined as thefraction of the νµ CC events on Fe among the selected events.

10

Number of active planes

FIG. 14. Number of active planes for the standard module.
Events with more than two active planes are selected.

background subtraction and efficiency correction:
σCC =

105
104
103
102
10
1
-200 -150 -100

-50

0

50

100

150

200

Time residual (nsec)

FIG. 15. Time difference between the measured event timing
and expected neutrino event timing for the standard module.
Events within ±100 nsec are selected.

hits in INGRID from two beam bunches are summed together to make one new pseudo beam bunch. This procedure effectively doubles the beam intensity observedby INGRID. A slope is estimated from the number of selected events in an original beam bunch and the a pseudo
beam bunch for each sub-sample. The slopes estimatedfrom all sub-samples are consistent with each other, andthe average value of this slope is used for the correction.
This event pileup correction is applied module-by-moduleand bunch-by-bunch using the slope and POT per bunchwhich corresponds to the relevant beam intensity. The
event pileup correction gives 0.85% and 0.40% differencesin the number of selected events in the standard moduleand the Proton Module respectively.

V.

ANALYSIS METHOD

The flux-averaged νµ CC inclusive cross section is calculated from the number of selected events using theNsel − NBG
,
φT ε

(1)

where Nsel is the number of selected events from realdata, NBG is the number of selected background events
predicted by MC simulation, φ is the integrated νµ flux,
T is the number of target nucleons, and ε is the detection efficiency for CC events predicted by MC simulation.
The νµ CC inclusive cross sections on Fe and CH are measured from the number of selected events in the standard
module and the Proton Module, respectively. The νµ
CC inclusive cross section ratio on Fe to CH is measured
using the results from both detectors. The background
events for this analysis consist of NC events, ν̄µ events, νeevents, interactions on elements other than the measuring
elements in the detector (Ti or O for the Proton Module, C or H for the standard module), and background
events created by neutrino interactions in the material
surrounding the detector. The expected breakout of theselected events are summarized in Table IV. The rateof the background events from outside for the Proton
Module is much larger than that for the standard module. It is because the number of neutrino interactionsin the Proton Module is much smaller than that in thestandard module while the number of background eventsfrom outside is comparable level. NBG , φ, and ε are estimated using MC simulation and T is calculated from thetarget mass measured prior to detector assembly. These
quantities are summarized in Table V.

VI.

SYSTEMATIC ERRORS

Uncertainties on NBG , φ, T , and ε are sources of systematic errors on the cross section results. The sourcesof systematic error can be categorized into three groups:
those from the neutrino flux prediction, the neutrino interaction model including intra-nuclear interactions, andthe detector response.

×106

3

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

1.6
1.4
1.2
1
0.8

3

100 ×10

Number of events

1.8

Number of events

Number of events

11Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

90
80
70
60
50

100 ×10
80
70
60
50

40

40

30

0.4

30

20

20

0.2

10

0.6

0
0

2

4

6

8

10

0-60

10

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

90

-40

-20

0

20

40

0
-60

60

-40

-20

0

20

Vertex X (cm)Vertex Z (plane)

40

60Vertex Y (cm)

0.9

70

0.8

60

0.7
0.6

50

Standard module
w/o acceptance cut
Standard module
w/ acceptance cut
Proton Module
Energy spectrum

0.5
0.4
0.3
0.2
0.1
0
0

1

2

3

4

5

6

7

8

9

40
30
20
10
0
10

Eν (GeV)×103 50

1

Proton Module
Angle distribution

0.9
0.8

Number of CC interactions / deg.

×10380

Selection efficiency

1

Number of CC interactions / 50MeV

Selection efficiency

FIG. 16. Vertex Z distribution for the standard module before applying the veto and fiducial volume cuts (left) and vertex X
and Y distributions after applying the veto cut (center and right).

45
40

0.7

35

0.6

30

0.5

25

0.4

20

0.3
0.2
0.1
0
0

15

Standard module
w/o acceptance cut
Standard module
w/ acceptance cut
10

20

30

10
5

40

50

60

70

80

0
90

Muon angle (deg.)

FIG. 17. Event selection efficiency of CC interactions for the standard module and the Proton Module as a function of true
neutrino energy (left) and true muon scattering angle (right). The energy spectrum and angle distribution of the CC interactionsin the standard module are overlaid.

Standard module

ν
ν
ν
ν

Imaginary module

Rejected

Selected

FIG. 18. MC event display of a selected event and a rejected
event by the acceptance cut.

A.

Neutrino flux uncertainties

The neutrino flux uncertainty sources can be separated into two categories: hadron production uncertainties and T2K beamline uncertainties. The uncertainties on hadron production are mainly driven by theNA61/SHINE measurements [27, 28] and the Eichten andAllaby data [29, 30], and constitute the dominant component of the flux uncertainty. They include the uncertainties on the production cross section, the secondary nu-

TABLE IV. Expected breakout of the selected events. The
CCQE and CCnonQE events are signal events and others arebackground events for this measurement.

CCQE events
CCnonQE events
NC eventsν̄µ events
νe events
Other target element
Backgrounds from outside

Standard module Proton Module
35.34%
34.90%
51.70%
50.53%
6.44%
4.19%
2.04%
2.39%
0.99%
0.73%
2.67%
1.39%
0.82%
5.87%

TABLE V. Summary of the inputs for the cross section calculation.
Nsel
NBG
φ
T
ε
Fe
σCC
523045 67838 2.999×1013 cm−2 2.461×1030 0.4270
CH
σCC36330 5385.5 3.025×1013 cm−2 1.799×1029 0.4122

cleon production, the pion production multiplicity, andthe kaon production multiplicity. The second categoryof flux uncertainties is associated with inherent uncer-

×103

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

40
35
30
25
20

45
35
30
25
20

15

15
10

5

5
-40

-20

0

20

40

60

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

40

10
0-60

×103

Number of events

45

Number of events

Number of events

12

0-60

×103
100
80

Data
νµ CCQE
νµ CCnonQE
νµ NC
νµ + νe
B.G. from outside

60
40
20

-40

-20

Vertex X (cm)

0

20

40

60

Vertex Y (cm)

0
0

2

4

6

8

10

Vertex Z (plane)

FIG. 19. Vertex X, Y and Z distributions for the standard module following event selection.

tainties and operational variations in the beamline conditions. They include uncertainties in the proton beam
position, the off-axis angle, the absolute horn current,
the horn angular alignment, the horn field asymmetry,
the target alignment, and the proton beam intensity. The
method of estimating these flux uncertainties is describedin Ref [22]. To evaluate the systematic error from theflux uncertainties, the flux is fluctuated using a covariance matrix produced based on the flux uncertainty. Thisis repeated for many toy data sets, and the ±1σ of thechange in the cross section result is taken as the systematic error associated with the neutrino flux.

B.

Neutrino interaction uncertainties

We use a data-driven method to calculate the neutrino
interaction uncertainties, where the NEUT predictions
are compared to available external neutrino-nucleus datain the energy region relevant for T2K. We fit some parameters of the models implemented in NEUT, and introduce
ad hoc parameters, often with large uncertainties, to take
into account remaining discrepancies between NEUT and
the external data like [12, 44–55]. The model parameters
include axial mass values for quasi-elastic scattering andmeson production via baryon resonances, the Fermi momentum, the binding energy, a spectral function parameter, and a π-less ∆ decay parameter. NEUT uses the relativistic Fermi gas model as a nuclear model. The spectral function model is more sophisticated, and is known
to be a better representation of the nuclear model. A
spectral function parameter is introduced to take into account the difference between the two nuclear models. In
the resonant pion production process, baryon resonances,
mainly ∆, can interact with other nucleons and disappear
without pion emissions. The π-less ∆ decay parameteris introduced to take into account uncertainties on thisprocess. The implemented ad hoc parameters include
cross section normalizations. In addition, uncertainties
on the secondary interactions of the pions with the nuclear medium are included. Table VI shows the nominal values and uncertainties on these parameters. The
method used to estimate these uncertainties is describedin Ref [13]. Systematic errors due to these parameters
are estimated from variations of the cross section results
when these parameters are varied within their uncertainties. For the measurement of the CC-inclusive cross section ratio on Fe to CH, we assume that the uncertainties of MARES , CC1π normalizations, NC normalizations,Fermi gas parameters and pion secondary interactions
are fully correlated between the Fe target and the CH
target cases because these uncertainties are understoodas independent of the target nucleus. By contrast, theuncertainties of MAQE , CCQE normalizations, CC coherent pion normalization and spectral function parameterare assumed to be uncorrelated because nuclear dependences of these uncertainties are not well understood. In
addition, the uncertainty of CC other shape is left outof the cross section ratio measurement because there isno evidence for a large nuclear modification in the deep
inelastic scattering regime.

C.

Detector response uncertainties

The uncertainty of the target mass measurement,
0.13% for the standard module and 0.25% for Proton
Module, is taken as the systematic error on the target
mass. Variation of the measured MPPC dark rate during
data acquisition, 5.84 hits/cycle for the standard moduleand 11.52 hits/cycle for the Proton Module, is taken as
the uncertainty on the MPPC dark rate, where the cycle denotes the integration cycle synchronized with theneutrino beam pulse structure. The discrepancy between
the hit detection efficiency measured with beam induced
muon backgrounds and that of the MC simulation, 0.17%
for the standard module and 0.21% for the Proton Module, is assigned as the uncertainty in the hit detection
efficiency. The relation between these quantities andthe cross section results are estimated by MC simulation, and variations on the calculated cross section results
due to these uncertainties are assigned as systematic errors. The event pileup correction factor has uncertainties
which come from the statistics of the beam data and the
MPPC dark count in the estimation of the correction
factor. The systematic error from these uncertainties is

13
TABLE VI. The nominal values of and the uncertainties on
the neutrino interaction model parameters. First, second,
and third groups represent the model parameters, the ad hoc
parameters, and the pion secondary interaction parameters.
Nominal values of 0 or 1 mean that the effect or the normalization is not implemented or is implemented by default,
respectively.
Parameter
Nominal value Error
QE
MA
1.21GeV
16.53%RES
MA
1.21GeV
16.53%
π less ∆ decay
0.2
20%Spectral function
0100%
Fermi momentum for Fe
250 MeV/c
12%
Fermi momentum for CH
217 MeV/c 13.83%
Binding energy for Fe
33MeV
27.27%
Binding energy for CH
25MeV
36%
CCQE norm. (Eν <1.5GeV)
1
11%
CCQE norm. (1.5< Eν <3.5GeV)
1
10%
CCQE norm. (Eν >3.5GeV)
1
10%CC1π norm. (Eν <2.5GeV)
121%
CC1π norm. (Eν >2.5GeV)
1
21%
CC coherent π norm.
1100%
CC other shape040%NC1π 0 norm.
1
31%
NC coherent π norm.
130%NC1π ± norm.
130%
NC other norm.
130%
Pion absorption
1
50%
Pion charge exchange (low energy)
150%Pion charge exchange (high energy)
130%
Pion QE scattering (low energy)
150%Pion QE scattering (high energy)
130%
Pion inelastic scattering
150%

estimated assuming the highest beam intensity achievedin beam operation so far. There is about a 35% discrepancy between the beam induced muon background rateestimated by the MC simulation and that measured fromthe data. The change in the background contamination
fraction from this discrepancy is taken as the systematic
error for the beam-related background. The cosmic-ray
background was found to be very small from the out-ofbeam timing data. The systematic error on the trackreconstruction efficiency is estimated by comparing theefficiency for several sub-samples between the data andthe MC simulation. The standard deviation of the data
− MC of the track reconstruction efficiency for the subsamples is taken as the systematic error. The systematic
errors from all event selections are evaluated by varying
each selection threshold. The maximum difference between the data and MC for each selection threshold istaken as the value of each systematic error.

D.

Summary of the systematic errors

Table VII summarizes the systematic errors on eachmeasurement. The total systematic error on the measurements of the CC inclusive cross section on Fe, that
+12.91%+3.32%
on CH, and their ratio are +13.11%−10.84% , −10.69% , and −3.33% ,respectively. The neutrino flux error is the dominantsystematic error for the measurement of the CC inclusive cross section on Fe and CH. However, it is small forthe measurement of the cross section ratio on Fe to CH,
since this error mostly cancels between two detectors, as
expected.

VII.

RESULTS

The measured flux-averaged CC inclusive cross sections on Fe and CH and their ratio areFe= (1.444 ± 0.002(stat.)+0.189
σCC−0.157 (syst.))×10−38 cm2 /nucleon,
CHσCC= (1.379 ± 0.009(stat.)+0.178−0.147 (syst.))
−38
2

×10

cm /nucleon, andFe
σCC= 1.047 ± 0.007(stat.) ± 0.035(syst.),
CH
σCC

(2)
(3)
(4)

at a mean neutrino energy of 1.51 GeV. These are purecross sections per nucleon for each atom, and isoscalarcorrections are not applied. They agree well with thepredicted values from NEUT and GENIE shown in Table VIII. The cross-section results are shown in Fig. 20
and 21 together with the predictions and measurementsfrom other experiments. Our result of the cross section
ratio on Fe to CH is very precise in 3% level. Hence, itsconsistency with the neutrino interaction models demonstrates that the target dependence of the nuclear effectis well understood and correctly treated in the models in
3% level.
In Table IX, the measured CC inclusive cross section on
CH and the ratios to the predictions by NEUT and GENIE are compared to those for the T2K off-axis neutrinos
measured by the ND280 detector. Here, it requires attention that the fluxes for these two detectors are highly
correlated. Both the ND280 and INGRID data are ingood agreement with both the NEUT and GENIE models.

VIII.

CONCLUSIONS

We have reported the first neutrino cross section measurement with the T2K on-axis near neutrino detector,
INGRID. We have selected a sample of inclusive νµ CC
interactions in an INGRID standard module and the Proton Module. From the number of selected events, theflux-averaged CC inclusive cross sections on Fe and CH
and their ratio at a mean neutrino energy of 1.51 GeV

14
TABLE VII. Summary of the systematic errors.
Fe
CH
Fe
CH
Item
σCC
σCC
σCC
/σCC
Neutrino flux
−10.34%+12.74% −10.12%+12.48% −0.31%+0.31%
QE
MA−1.44%+1.42% −0.60%+0.72% −1.61%+1.55%
RES
MA−0.35%+0.20% −0.61%+0.45% −0.25%+0.27%
CCQE normalization (Eν <1.5GeV)−0.82%+0.79% −0.52%+0.50% −0.95%+0.94%
CCQE normalization (1.5< Eν <3.5GeV) −0.45%+0.50% −0.67%+0.76% −0.88%+0.83%
CCQE normalization (Eν >3.5GeV)−0.11%+0.11% −0.10%+0.11% −0.15%+0.15%CC1π normalization (Eν <2.5GeV)−1.50%+1.37% −1.72%+1.66% −0.28%+0.22%CC1π normalization (Eν >2.5GeV)−0.50%+0.52% −0.54%+0.56% −0.04%+0.04%
CC coherent π normalization−0.48%+0.49% −1.03%+1.10% −1.20%+1.14%
CC other shape−0.82%+0.77% −1.07%+1.02%−
NC1π 0 normalization−0.30%+0.31% −0.18%+0.18% −0.13%+0.13%
NC coherent π normalization−0.02%+0.02% −0.01%+0.01% −0.01%+0.01%NC1π ± normalization−0.31%+0.31% −0.23%+0.23% −0.07%+0.07%
NC other normalization−1.21%+1.23% −0.71%+0.72% −0.51%+0.51%
π less ∆ decay−0.50%+0.54% −0.35%+0.39% −0.15%+0.15%
Spectral function−0.76%+0.00% −0.98%+0.00% −0.76%+0.98%
Fermi momentum−0.43%+0.49% −0.39%+0.41% −0.04%+0.08%
Binding energy−0.31%+0.32% −0.22%+0.25% −0.09%+0.07%
Pion absorption−0.15%+0.13% −0.09%+0.08% −0.05%+0.04%
Pion charge exchange (low energy)−0.06%+0.09% −0.07%+0.10% −0.16%+0.17%
Pion charge exchange (high energy)−0.09%+0.08% −0.08%+0.08% −0.02%+0.00%
Pion QE scattering (low energy)−0.14%+0.15% −0.18%+0.13% −0.00%+0.06%
Pion QE scattering (high energy)−0.16%+0.11% −0.23%+0.21% −0.10%+0.08%
Pion inelastic scattering−0.24%+0.20% −0.26%+0.23% −0.03%+0.02%
Target mass
±0.14%±0.27%±0.30%MPPC dark count±0.23%±0.12%±0.26%
Hit efficiency±0.44%±0.44%±0.62%
Event pileup±0.05%±0.03%±0.06%
Beam-related background±0.10%±0.93%±0.94%
Cosmic-ray background±0.01%±0.02%±0.02%
2D track reconstruction±0.50%±0.58%±0.77%
Track matching−±0.31%±0.31%
3D tracking±0.15%±0.97%±0.98%
Vertexing±0.31%±0.12%±0.33%
Beam timing cut±0.01%±0.01%±0.01%
Veto cut±0.53%±0.58%±0.79%
Fiducial volume cut±0.40%±0.18%±0.44%
Acceptance cut±0.36%−±0.36%
Total−10.84%+13.11% −10.69%+12.91% −3.33%+3.32%

TABLE VIII. CC-inclusive cross sections on Fe and CH andtheir ratio predicted by NEUT and GENIE.
Fe
CH
Fe
CH
σCC
σCC
σCC
/σCC
−38
2
−38
2
NEUT 1.3977×10
cm 1.3477×10
cm 1.03712
GENIE 1.2407×10−38 cm2 1.1883×10−38 cm2 1.04407

TABLE IX. The CC-inclusive cross section on CH measured
with the T2K on-axis and off-axis fluxes and the ratios to thepredictions by NEUT and GENIE. The errors represent the
total (statistical and systematic) uncertainties.
On-axisOff-axis
Average energy
1.51GeV
0.85GeV
Data (×10−38 cm2 ) 1.379+0.178−0.147 0.691 ± 0.085
Data/NEUT
1.023+0.132−0.109 0.950 ± 0.117
Data/GENIE
1.160+0.150−0.124 1.057 ± 0.130

ACKNOWLEDGEMENTS

have been measured. These results agree well with themodel predictions.

It is a pleasure to thank Mr. Taino from Mechanical Support Co. for helping with the construction of

×109
2000

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SciBooNE
NOMAD

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νµ flux (/cm2/50MeV/1021POT)

×10-392
σCH
CC (cm /nucleon)50νµ flux (/cm2/50MeV/1021POT)

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CC(cm /nucleon)

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0.9
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νµ flux (/cm2/50MeV/1021POT)CHσFe
CC/ σCC (per nucleon)

FIG. 20. The inclusive νµ charged current cross section on Fe (left) and that on CH (right) with predictions by NEUT and
GENIE. The isoscalar corrections are not applied to our data or predictions. Our data point is placed at the flux mean energy.
The vertical error bar represents the total (statistical and systematic) uncertainty, and the horizontal bar represents 68% of
the flux at each side of the mean energy. The MINOS, T2K ND280, SciBooNE and NOMAD results are also plotted[12–15].
Because the isoscalar correction is applied to the MINOS data, it is expected to be shifted by about −2%.

1

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Eν (GeV)

INGRID. 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, Germany; INFN, Italy; Ministry of Science andHigher Education, Poland; RAS, RFBR and MES, Russia; MICINN and CPAN, Spain; SNSF and SER, Switzerland; STFC, U.K.; and DOE, U.S.A. We also thank
CERN for the UA1/NOMAD magnet, DESY for the
HERA-B magnet mover system, and NII for SINET4.
In addition participation of individual researchers andinstitutions has been further supported by funds from:
ERC (FP7), EU; JSPS, Japan; Royal Society, UK; DOE
Early Career program, U.S.A.

FIG. 21. The inclusive νµ charged current cross section ratio on Fe to CH with predictions by NEUT and GENIE. The
isoscalar corrections are not applied to our data or predictions. Our data point is placed at the flux mean energy. The
vertical error bar represents the total (statistical and systematic) uncertainty, and the horizontal bar represents 68% of theflux at each side of the mean energy. The MINERνA result
is also plotted[16].

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