Measurement of the antineutrino to neutrino charged-current interaction cross sectionratio in MINERvA

L. Ren,1 L. Aliaga,2, 3 O. Altinok,4 L. Bellantoni,5 A. Bercellie,6 M. Betancourt,5 A. Bodek,6 A. Bravar,7 H. Budd,6

T. Cai,6 M.F. Carneiro,8 H. da Motta,9 J. Devan,2 S.A. Dytman,1 G.A. Dıaz,6, 3 B. Eberly,1, ∗ E. Endress,3

J. Felix,10 L. Fields,5, 11 R. Fine,6 A.M. Gago,3 R.Galindo,12 H. Gallagher,4 A. Ghosh,12, 9 T. Golan,6, 5 R. Gran,13

J.Y. Han,1 D.A. Harris,5 K. Hurtado,9, 14 M. Kiveni,5 J. Kleykamp,6 M. Kordosky,2 T. Le,4, 15 E. Maher,16

S. Manly,6 W.A. Mann,4 C.M. Marshall,6, † D.A. Martinez Caicedo,9, ‡ K.S. McFarland,6, 5 C.L. McGivern,1, §

A.M. McGowan,6 B. Messerly,1 J. Miller,12 A. Mislivec,6 J.G. Morfın,5 J. Mousseau,17, ¶ D. Naples,1 J.K. Nelson,2

A. Norrick,2 Nuruzzaman,15, 12 V. Paolone,1 J. Park,6 C.E. Patrick,11 G.N. Perdue,5, 6 M.A. Ramırez,10

R.D. Ransome,15 H. Ray,17 D. Rimal,17 P.A. Rodrigues,18, 6 D. Ruterbories,6 H. Schellman,8, 11 C.J. Solano Salinas,14

M. Sultana,6 S. Sanchez Falero,3 E. Valencia,2, 10 T. Walton,19, ∗∗ J. Wolcott,6, †† M.Wospakrik,17 and B. Yaeggy12

(The MINERνA Collaboration)1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

2Department of Physics, College of William & Mary, Williamsburg, Virginia 23187, USA3Seccion Fısica, Departamento de Ciencias, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima, Peru

4Physics Department, Tufts University, Medford, Massachusetts 02155, USA5Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

6University of Rochester, Rochester, New York 14627 USA7University of Geneva, 1211 Geneva 4, Switzerland

8Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA9Centro Brasileiro de Pesquisas Fısicas, Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, Rio de Janeiro, 22290-180, Brazil

10Campus Leon y Campus Guanajuato, Universidad de Guanajuato, Lascurainde Retana No. 5, Colonia Centro, Guanajuato 36000, Guanajuato Mexico.

11Northwestern University, Evanston, Illinois 6020812Departamento de Fısica, Universidad Tecnica Federico Santa Marıa, Avenida Espana 1680 Casilla 110-V, Valparaıso, Chile

13Department of Physics, University of Minnesota – Duluth, Duluth, Minnesota 55812, USA14Universidad Nacional de Ingenierıa, Apartado 31139, Lima, Peru

15Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA16Massachusetts College of Liberal Arts, 375 Church Street, North Adams, MA 01247

17University of Florida, Department of Physics, Gainesville, FL 3261118University of Mississippi, Oxford, Mississippi 38677, USA

19Hampton University, Dept. of Physics, Hampton, VA 23668, USA(Dated: April 8, 2017)

We present measurements of the neutrino and antineutrino total charged-current cross sectionson carbon and their ratio using the MINERvA scintillator-tracker. The measurements span theenergy range 2-22 GeV and were performed using forward and reversed horn focusing modes of theFermilab low-energy NuMI beam to obtain large neutrino and antineutrino samples. The flux isobtained using a sub-sample of charged-current events at low hadronic energy transfer along withprecise higher energy external neutrino cross section data overlapping with our energy range between12-22 GeV. We also report on the antineutrino-neutrino cross section ratio, RCC , which does notrely on external normalization information. Our ratio measurement, obtained within the sameexperiment using the same technique, benefits from the cancellation of common sample systematicuncertainties and reaches a precision of ∼5% at low energy. Our results for the antineutrino-nucleusscattering cross section and for RCC are the most precise to date in the energy range Eν < 6 GeV.

PACS numbers: 13.15.+g, 14.60.Lm

∗now at SLAC National Accelerator Laboratory, Stanford, CA94309, USA†now at Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA‡now at Illinois Institute of Technology, Chicago, IL 60616, USA§now at Fermi National Accelerator Laboratory, Batavia, IL 60510,USA

¶now at University of Michigan, Ann Arbor, MI 48109, USA∗∗now at Fermi National Accelerator Laboratory, Batavia, IL60510, USA††now at Tufts University, Medford, MA 02155, USA

FERMILAB-PUB-16-595-ND ACCEPTED

Operated by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the United States Department of Energy.

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I. INTRODUCTION

Long-baseline oscillation experiments [1] [2], which aimto precisely measure neutrino oscillation parameters andconstrain CP violation, will make use of neutrino and an-tineutrino beams in the few-GeV neutrino energy (Eν)range. For appropriate baselines and energies, neutrinooscillation phenomena produce distinct shape signatureson either νµ → νe or νµ → νe appearance proba-bilities, which, in matter, depend on the CP violatingphase (δCP ) and the (unknown) sign of the mass split-ting term, ∆m2

31. Variations of oscillation parametersover their allowed ranges produce degenerate effects onthe appearance probabilities, complicating these mea-surements. Uncertainties in poorly constrained cross sec-tion components in this energy range produce furthercompeting shape effects on the measured visible energyspectra used to extract the oscillation probabilities. Uti-lizing beams of both neutrinos and antineutrinos allowsa measurement of the CP asymmetry [3], ACP , definedas,

ACP =P (νµ → νe)− P (νµ → νe)P (νµ → νe) + P (νµ → νe)

, (1)

which can be written in terms of probability ratios. Re-ducing uncertainties on the cross sections, and in particu-lar their ratio, RCC = σν/σν , to which ACP is primarilysensitive, is essential to achieving ultimate sensitivity inoscillation measurements.

The results presented here use neutrino and antineu-trino events analyzed in the MINERvA scintillator (CH)detector exposed to the NuMI (Neutrinos at the MainInjector) beam. Total cross sections are extracted fromselected charged-current (CC) event samples, and inci-dent fluxes are measured in situ using a sub-sample ofthese events at low-ν (ν is the energy transfered to thehadronic system) as in our previous result [4]. The ratio,RCC , is obtained by forming ratios of measured eventrates in the two beam modes. Since the measurementsare performed using the same apparatus and flux mea-surement technique, common detector and model relatedsystematic uncertainties cancel in the ratio, resulting ina precise measurable quantity that can be leveraged totune models and improve knowledge of interaction crosssections.

While knowledge of neutrino cross sections has recentlybeen improved in the low-energy region, there is a dearthof precise antineutrino cross section measurements at lowenergies (below 10 GeV) [5]. The cross section ratio,RCC , has recently been measured by MINOS [6] on ironwith a precision of ∼7% at 6 GeV. At lower energies,only one dedicated measurement [7] (on CF3Br) has beenperformed, with a precision of ∼20%. Measurements on arange of nuclear targets are needed to constrain nucleardependence which currently contributes significantly tomodeling uncertainty. While much of the existing datais on an iron nucleus, this result provides data on a lightnuclear target (carbon). We improve on the precision of

both the antineutrino cross section and RCC (by nearlya factor of four) at low energies (2-6 GeV).

Systematic uncertainties in our measured cross sec-tions are dominated at the lowest energies by the lim-ited knowledge of cross-section model components at lowhadronic energy transfer (<∼1 GeV). The current suite ofneutrino generators [8–14] are known to be deficient inmodeling nuclear effects and detailed exclusive processrates at low energy transfer. To allow our measurementto be updated with future models, we also present themeasured rates (corrected for detector effects and back-grounds) with the primary model-dependent terms fac-torized.

We have previously reported an inclusive CC cross sec-tion measurement [4] using the same data sample andmethod to constrain the flux shape with energy. The re-sults presented here use an updated cross-section modelwhich has been tuned to improve agreement with ourdata in the low-ν region [15] as described in Sec. III. Thecurrent work also provides a precise measurement of theratio, RCC , as well as the measured model-independentrates for re-extracting cross sections with alternativegenerator-level models. In addition, the antineutrinoflux normalization method employed here improves theantineutrino cross section precision by a factor of 1.5-1.9, which for the previous result was dominated by thelarge uncertainty (∼10%) on the model-based antineu-trino normalization constraint.

II. MINERVA EXPERIMENT

Muon neutrinos and antineutrinos are produced inNuMI when 120 GeV protons from the Fermilab MainInjector strike a graphite target. Details of the NuMIbeamline can be found in Ref. [16]. A system of twomagnetic horns is used to focus emerging secondary pi-ons and kaons, which are allowed to decay in the 675 mspace immediately downstream of the target. We analyzeexposures in two low-energy NuMI beam modes. The for-ward horn current (FHC) mode sets the horn polarity tofocus positively-charged secondary beam particles, whichresults in a primarily muon neutrino beam (10.4% muonantineutrino component) with 3 GeV peak energy. If thepolarity of both horns is reversed (RHC mode) the result-ing beam has a large fraction of muon antineutrinos withthe same peak beam energy and a sizable muon neutrinocomponent (17.7%) that extends to high energies. Fig-ure 1 shows the simulated fluxes [17] for muon neutrinosand antineutrinos in each mode. We use samples col-lected between March 2010 and April 2012 correspond-ing to exposures of 3.20×1020 protons on target (POT)in FHC and 1.03×1020 POT in RHC beam modes.

The MINERvA fine-grained scintillator tracking detec-tor [18] is situated approximately 1 km downstream of theNuMI target. The active detector consists of triangularscintillator strips with height 1.7 cm and base 3.3 cm ar-ranged into hexagonal X, U and V planes (at 60 degrees

3

Neutrino Energy (GeV)0 5 10 15 20 25 30

PO

T6

/GeV

/10

2N

eutr

inos

/m

-210

-110

1

10

210 FHCNeutrino

Antineutrino

Neutrino Energy (GeV)0 5 10 15 20 25 30

PO

T6

/GeV

/10

2N

eutr

inos

/m

-210

-110

1

10

210 RHCAntineutrino

Neutrino

FIG. 1: Predicted incident neutrino fluxes at the MINERvA detector in FHC (left) and RHC (right) beam modes from Ref. [17].

with respect to one another) and giving single-plane po-sition resolution of about 2.5 mm. We use events orig-inating in the 6 ton fully-active scintillator region thatis primarily composed of carbon nuclei (88.5% carbon,8.2% hydrogen, 2.5% oxygen and a number of other nu-clei that make up the remaining fraction, by mass). Wereport results on a carbon target by correcting for theMINERvA target proton excess (see Sec. VI).

The downstream most plane of MINERvA is posi-tioned 2 m upstream of the magnetized MINOS NearDetector [19] (MINOS ND), which is used to contain andmomentum analyze muons exiting the MINERvA activedetector volume. The detector geometry changes fromsampling after every iron plane (2.54 cm thickness) tosampling every five iron-scintillator units after the first7.2 m. This produces features in the measured muon mo-mentum distribution and acceptance which will be dis-cussed below. For FHC (RHC) beam mode the MINOSND toroidal magnetic field is set to focus negatively (pos-itively) charged muons. Measurement of the direction oftrack curvature is used to tag the charge-sign of tracks,which is crucial to reducing the large wrong-sign beambackground in RHC mode.

III. MONTE CARLO SIMULATION

We use a custom MINERvA-tuned modification of GE-NIE 2.8.4 [20, 21] referred to here as “GENIE-Hybrid” asinput to simulated event samples as well as for the modelcorrection terms needed to obtain our default cross sec-tion results. This model incorporates improved model-ing of low-ν cross section components and is similar tothat described in Ref. [15]. GENIE 2.8.4 uses a mod-ified version of the relativistic Fermi gas model of thenucleus, which is inadequate to precisely describe neu-

trino scattering data at low three-momentum transfersuch as quasi-elastic (QE) and ∆(1232) resonance pro-duction. For QE events, we use the Random Phase Ap-proximation (RPA) [22] model, which includes long-rangenucleon-nucleon correlations to more accurately charac-terize scattering from a nucleon bound in a nucleus. Wealso include the Valencia “2p2h” model contribution [23]of the neutrino interacting with a correlated nucleon pairthat populates the energy transfer region between theQE and ∆-resonance events. Since even this does notadequately cover the observed signal excess in this re-gion [15], we include additional modeling uncertaintiesfrom this contribution. In addition, we reduce the GE-NIE single pion non-resonant component1 with initialstate ν + n (or ν + p) by 57%, which has been shown toimprove agreement with observed deuterium data [24].

IV. TECHNIQUE OVERVIEW

Events studied in this analysis are categorized ascharged-current events by the presence of a long trackoriginating from the primary interaction vertex whichextrapolates into the MINOS ND. The inclusive sample,Nν(ν)CC (E), is the number of measured charged current

events in neutrino energy bin E. We define Rν(ν)(E),which is related to the fiducial cross section, as

Rν(ν)(E) =(Nν(ν)

CC (E)−Bν(ν)CC (E))×Aν(ν),DET

CC (E)

(F ν(ν)(E)−Bν(ν)Φ (E))×Aν(ν)

Φ (E),

(2)

1 The corresponding GENIE parameter is RνnCC1πbkg for neutrino

and RνpCC1πbkg for antineutrino [21].

4

where superscript ν (ν) refers to neutrino (antineutrino).F ν(ν)(E) is the “flux sample” obtained from a subset ofNν(ν)CC (E) with low hadronic energy (discussed below).

The terms Bν(ν)CC (E) and B

ν(ν)Φ (E) are backgrounds due

to neutral current and wrong-sign beam contaminationin the inclusive and flux samples, respectively. TermsAν(ν),DETCC (E) and Aν(ν)

Φ (E) correct the cross section andflux respective samples for detector resolution and bin-migration effects. The numerator of Eq. (2), Γν(ν)

CC (E),

Γν(ν)CC (E) = (Nν(ν)

CC (E)−Bν(ν)CC (E))×Aν(ν),DET

CC (E), (3)

is the fiducial event rate and is tabulated below. Toobtain the incident beam flux, we employ the “low-ν”method described previously [4, 6, 25, 26]. In brief, thedifferential dependence of the cross section in terms of νis expanded in ν/E as

dσν,ν

dν= A

(1 +

Bν,ν

A

ν

E− Cν,ν

A

ν2

2E2

), (4)

where E is the incident neutrino energy. The coefficientsA, Bν,ν , and Cν,ν depend on integrals over structurefunctions (or form factors, in the low energy limit).

A =G2FM

π

∫F2(x)dx, (5)

Bν,ν = −G2FM

π

∫(F2(x)∓ xF3(x))dx, (6)

and

Cν,ν = Bν,ν−G2FM

π

∫F2(x)

(1 + 2Mx

ν

1 +RL− Mx

ν− 1

)dx.

(7)

In the limit of ν/E → 0, the B and C terms vanishand both cross sections approach A (defined in Eq. (5)),which is the same for neutrino and antineutrino probesscattering off an isoscalar target (up to a small correctionfor quark mixing). We count events below a maximum νvalue (ν0) and apply a model-based correction

Sν(ν),ν0(E) =σν(ν)(ν0, E)

σν(ν)(ν0, E →∞), (8)

to account for ν/E and (ν/E)2 terms in Eq. (4). Thenumerator in Eq. (8) is the value of the integrated crosssection below our chosen ν0 cut at energy E, and thedenominator is its value in the high energy limit. Forantineutrinos, the structure functions in Eq. (6) add, re-sulting in a larger energy dependent correction term thanfor the neutrino case where they are subtracted and par-tially cancel. The flux is then proportional to the cor-rected low-ν rate

Φν(ν)(E) ∝(F ν(ν)(E)−Bν(ν)

Φ (E))×Aν(ν)Φ (E)

Sν(ν)(ν0, E). (9)

We obtain a quantity that is proportional to the totalCC cross section,

σν(ν)CC (E) ∝ Rν(ν) × Sν(ν)(ν0, E)×Aν(ν),KIN

CC (E), (10)

by applying a correction, Aν(ν),KIN, for regions outside ofour experimental acceptance. The term Aν(ν),KIN (dis-cussed in Sec. V A) is computed from a generator levelMonte Carlo model. The rates, Rν andRν , in each beammode are used to obtain the ratio

RCC(E) =σνCC(E)σνCC(E)

=Rν

Rν

(Aν,KINCC (E)× Sν(ν0, E)×H ν(ν0)

Aν,KINCC (E)× Sν(ν0, E)×Hν(ν0)

). (11)

The terms H ν(ν0) and Hν(ν0), which supply the abso-lute flux normalization in the low-ν method for neutrinosand antineutrinos, respectively, are related in the Stan-dard Model and nearly cancel in this ratio. The mea-surements are performed using the same detector andbeamline, which reduces the effect of some experimentaluncertainties. The ratio measured in this technique alsobenefits from cancellation of correlated model terms; thiscancellation reduces the modeling component of the sys-tematic uncertainty relative to that for either neutrino or

antineutrino measured cross section.

V. EVENT RECONSTRUCTION ANDSELECTION

Neutrino events are reconstructed using timing andspatial information of energy deposited in the MINERvAscintillator. Hits are grouped in time into “slices” andwithin a slice, spatially into “clusters” which are used

5

along with pattern recognition to identify tracks. TheCC-inclusive event sample, denoted Nν(ν)

CC (E), is selectedby requiring a primary track matched into the MINOSND. MINOS-matched track momentum, Eµ, is recon-structed using either range, for tracks that stop and de-posit all of their energy in the MINOS ND, or the mea-sured curvature of the trajectory, for tracks which exitthe MINOS ND. Tracks measured from range in MI-NOS have a momentum resolution of order 5% whilethose measured from curvature typically have a reso-lution of order 10%. Clusters not associated with theMINOS-matched muon track form the recoil system andare calorimetrically summed to obtain the hadronic en-ergy, ν. Neutrino energy is constructed from the sumEν = Eµ + ν. An event vertex is assigned by trackingthe muon upstream through the interaction region untilno energy is seen in an upstream cone around the track.The vertex is required to be within the fiducial region ofthe scintillator.

Additional track requirements are applied to improveenergy resolution and acceptance. The track fitting pro-cedure in the MINOS spectrometer yields a measure-ment of the momentum with an associated fractional un-certainty, which is required to be less than 30%. Thecharge-sign is determined by measuring the track curva-ture and is required to be negative for tracks in FHCmode and positive for those in RHC mode. We also re-quire the muon track candidate to have a minimum en-ergy Eµ > 1.8 GeV and a maximum angle θµ < 0.35 rad(20 deg) with respect to the beam direction in the labframe. The portion of the track in MINOS is requiredto not pass through the uninstrumented coil hole region.Events in which the muon track ends less than 80 cmfrom the center of the coil hole are also removed. Thisremoves 0.8% (0.4%) events from the neutrino (antineu-trino) CC-inclusive sample.

The flux-extraction technique uses F ν(ν)(E), the num-ber of CC-inclusive events in an energy bin below a max-imum ν value. We choose this maximum value (ν0) tovary with energy, keeping the energy dependent contri-butions in Eq. (4) small (<∼0.1 for neutrinos and <∼0.2for antineutrinos) in the region where modeling uncer-tainties are sizable (Eν < 7 GeV), while at higher ener-gies where we normalize to external data (12-22 GeV), itis increased to improve statistical precision. The valuesare ν0 = 0.3 GeV for Eν < 3 GeV, ν0 = 0.5 GeV for3 < Eν < 7 GeV, ν0 = 1 GeV for 7 < Eν < 12 GeVand ν0 = 2 GeV for Eν > 12 GeV. The inclusive andflux sample overlap is less than 50% (60%) for neutrinos(antineutrinos).

A. Event Rates

Figure 2 shows the measured inclusive and flux samplerates in the two beam modes. The fiducial event rate,Γν(ν)

CC (E), (Eq. (3)) is determined by removing samplebackgrounds and applying corrections for experimental

acceptance. The components are described below andtabulated in Table I.

Backgrounds are dominated by the contribution fromtracks with misidentified charge-sign which arise fromthe wrong-sign beam flux component (wrong-sign con-tamination). The background peaks at high energiesin RHC mode (about 4% above 10 GeV in the inclu-sive sample). The charge-sign and track quality require-ments effectively reduce the wrong-sign contamination.The remaining background is estimated using the simu-lated wrong-sign beam flux shown in Fig. 1. The neutralcurrent contribution is negligible (� 1%) in both beammodes.

We correct for the experimental acceptance effects us-ing a full detector simulation along with a tuned ver-sion of GENIE Monte Carlo (GENIE-Hybrid) which isdescribed in Sec. III. We separate experimental accep-tance terms into two contributions. The term A

ν(ν),DETCC ,

which represents the ratio of the number of events gen-erated in a given neutrino energy bin to the numberreconstructed in our event sample, accounts for detec-tor resolution smearing and bin migration effects. Finalstate interaction (FSI) effects, which arise from reinter-actions of emerging final state particles in the target nu-cleus, change the measured hadronic energy and also af-fect Aν(ν),DET

CC . This bin migration effect is included inour Monte Carlo simulation model. The term A

ν(ν)Φ (E) is

defined similarly with an additional maximum ν require-ment. The fiducial event rate depends only on Aν(ν),DET

CC

and Aν(ν)Φ (E) and is nearly generator model independent.

The kinematic acceptance, AKINCC , defined as the ratio ofall generated events in a given bin to those with muonenergy Eµ >1.8 GeV and angle θµ < 0.35 rad, mustbe applied to obtain a total cross section from the fidu-cial event rate. This term is computed directly from agenerator level model. It is tabulated for our defaultmodel along with other model-dependent corrections inTable III. Nearly all muons in the selected flux sampleautomatically pass the kinematic cuts (except for a smallfraction in the first energy bin which is computed to be5.1% using the GENIE-Hybrid model and 4.9% usingNuWro [14]). We therefore only report one acceptance,AΦ, which includes the kinematic contribution in the fluxsample.

Figure 3 shows the size of the acceptance correctionterms for each sample. Kinematic acceptance is mostimportant at lowest energies (primarily below 3 GeV),which have the largest fraction of events below muonenergy threshold. The kinematic thresholds result inpoorer overall acceptance at all energies for neutrinoscompared with antineutrinos. This is a consequence ofthe different inelasticity (y = ν/Eν) dependence of thetwo cross sections, which produce a harder muon energydistribution for antineutrinos with correspondingly moreforward-going muons. The flux sample with the ν < ν0

requirement also selects a harder muon spectrum and re-sults in better corresponding acceptance relative to the

6

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Eve

nts

/ GeV

0

10000

20000

30000

40000

50000

Inclusive sample

Flux sample

FHC Neutrino

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Eve

nts

/ GeV

0

2000

4000

6000

8000

10000

12000

Inclusive sample

Flux sample

RHC Antineutrino

FIG. 2: Neutrino inclusive (Nν(ν)CC ) and low-ν flux sample (F ν(ν)) yields for FHC neutrino (left) and RHC antineutrino (right)

modes. The dashed lines are plotted at the values where the flux sample ν0 is changed. Statistical errors are too small to bevisible on the points.

ν0(GeV) E(GeV) NνCC BνCC Aν,DET

CC F ν BνΦ Aνφ N νCC BνCC Aν,DET

CC F ν BνΦ Aνφ

0.3 2-3 20660 53 2.38 11493 29 1.94 5359 18 1.99 3673 6 1.60

3-4 44360 61 2.30 25530 19 1.76 10133 25 1.94 6560 4 1.56

0.5 4-5 29586 65 1.92 11765 13 1.45 5955 24 1.65 2871 2 1.36

5-7 32026 170 1.70 8046 29 1.34 5284 74 1.47 1764 4 1.27

1.0 7-9 23750 171 1.86 6980 32 1.59 3261 102 1.58 1224 6 1.50

9-12 29161 207 1.95 6165 31 1.60 3400 141 1.66 1007 9 1.53

12-15 24093 158 1.94 7438 39 1.42 2496 115 1.63 1033 9 1.42

2.0 15-18 19011 104 1.85 5041 17 1.28 1690 77 1.48 595 6 1.23

18-22 18475 98 1.78 3826 14 1.25 1418 72 1.44 427 5 1.23

TABLE I: Neutrino and antineutrino inclusive, Nν(ν)CC , and flux sample, F ν(ν), yields along with corresponding background

contributions (Bν(ν)CC and B

ν(ν)Φ , respectively). The acceptance term, A

ν(ν),DETCC , is applied to obtain the fiducial event rate,

Γν(ν)CC (E), from Eq. (3).

inclusive sample in both modes. The detector acceptanceis above 50% for neutrino energies greater than 5 GeV.The shapes of 1/ADET

CC and 1/AΦ are affected by the MI-NOS ND sampling geometry as well as the two methodsof measuring momentum (from range and from curva-ture), which have different resolution. The dip in the6-10 GeV region results from the contained (range) mo-mentum sample decreasing while the curvature sample,which has poorer resolution, is becoming dominant.

VI. LOW-ν FLUX EXTRACTION

We obtain the shape of the flux with energy from thecorrected flux yield using Eq. (9). The low-ν correctionterm is computed from Eq. (8) using the GENIE-Hybridmodel as shown in Fig. 4 (also in Table III).

The neutrino flux is normalized using external neu-trino cross section data overlapping our sample in thenormalization bin, EN , (neutrino energies 12-22 GeV).The NOMAD [27] measurement is singled out becauseit is the only independent result on the same nucleartarget (carbon) in this range. The weighted averagevalue of the NOMAD from 12-22 GeV is σνN/EN =(0.699±0.025)×10−38cm2/GeV. We compute a weightedaverage value for our measured unnormalized neutrinocross section, σν,ν0(EN), from our points (E = 13.5, 16.5,and 20 GeV) in the normalization bin from Eq. (10). Weobtain a normalization constant for each ν0 sub-sample,Hν(ν0), using

Hν(ν0) =σν,ν0(EN )× Iνiso(EN )

σνN, (12)

where the isoscalar correction, Iiso, accounts for the pro-ton excess (fp = 54%, fn = 1 − fp) in the MINERvA

7

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

1/A

0

0.2

0.4

0.6

0.8

1

CCDET 1/A

CCKIN 1/A φ 1/A

FHC Neutrino

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

1/A

0

0.2

0.4

0.6

0.8

1

CCDET 1/A

CCKIN 1/A φ 1/A

RHC Antineutrino

FIG. 3: Reciprocal of acceptance components (1/ADETCC ,1/AKIN) for cross section and (1/AΦ) for flux samples of FHC neutrinos

(left) and RHC antineutrinos (right).

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

(E)

νS

0.95

1.00

1.05

1.10

1.15Neutrino

<0.3 GeVν<0.5 GeVν<1 GeVν<2 GeVν

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

(E)

νS

0.7

0.8

0.9

1

Antineutrino

<0.3 GeVν<0.5 GeVν<1 GeVν<2 GeVν

FIG. 4: GENIE-hybrid based low-ν corrections, Sν(ν)(ν0, E), for neutrinos (left) and antineutrinos (right).

target material obtained from

Iν(ν)iso (E) =

(σν(ν)p (E) + σ

ν(ν)n (E)

fpσν(ν)p (E) + fnσ

ν(ν)n (E)

)(fpσ

ν(ν)p (ν0, E) + fnσ

ν(ν)n (ν0, E)

σν(ν)p (ν0, E) + σ

ν(ν)n (ν0, E)

). (13)

Here, σν(ν)p(n)(E) is the neutrino (antineutrino) cross sec-

tion on a proton (neutron) in carbon and σν(ν)p(n)(ν0, E) is

its value for ν < ν0. This correction, (see Table III), is

negligible above 6 GeV and increases up to 4.2% in thelowest energy bin.

In the low-ν flux extraction method, neutrino andantineutrino cross sections in the low inelasticity limit

8

ν0(GeV) E(GeV) F ν(E) BνΦ(E) Aνφ(E) Hν(ν0) F ν(E) BνΦ(E) Aνφ(E) α(ν0)

13.50 1315 10 1.18 247 1 1.04

0.3 16.50 863 4 1.12 3.83±0.091 147 1 0.94 1.126±0.067

20.00 662 4 1.05 110 1 0.96

13.50 2415 15 1.28 385 2 1.21

0.5 16.50 1613 7 1.19 1.96±0.035 224 1 1.09 1.056±0.051

20.00 1190 4 1.16 159 2 1.12

13.50 4419 25 1.36 636 5 1.33

1.0 16.50 2967 12 1.25 1.02±0.014 373 3 1.18 1.005±0.039

20.00 2235 8 1.21 260 3 1.19

13.50 7438 39 1.42 1033 9 1.42

2.0 16.50 5041 17 1.28 0.574±0.006 595 6 1.23 1

20.00 3826 14 1.25 427 5 1.23

TABLE II: Neutrino and antineutrino flux data and corrections needed to apply the normalization technique described in the

text. The flux sample yield, F ν(ν), along with corresponding background contribution, Bν(ν)Φ , and acceptance correction, A

ν(ν)φ ,

are ν0 dependent and are used to compute the unnormalized cross section.

E(GeV) Aν,KINCC (E) Sν(ν0, E) Iνiso(ν0, E) Aν,KINCC (E) Sν(ν0, E) I νiso(ν0, E)

2.5 3.094 1.096 0.954 1.883 0.801 1.042

3.5 1.981 1.040 0.982 1.293 0.809 1.016

4.5 1.746 1.032 0.983 1.185 0.850 1.016

6 1.559 1.023 0.984 1.118 0.884 1.016

8 1.423 1.007 0.998 1.076 0.869 1.005

10.5 1.326 1.005 0.998 1.060 0.899 1.005

13.5 1.253 0.995 0.999 1.044 0.875 1.004

16.5 1.207 0.992 0.999 1.035 0.893 1.004

20 1.171 0.995 0.999 1.032 0.912 1.004

TABLE III: Neutrino and antineutrino cross section model dependent corrections computed using the GENIE-Hybrid model.

Sν(ν)(ν0, E) is defined in Eq. (8) and Iν(ν)iso (ν0, E) is defined in Eq. (13).

y → 0 are related, and approach the same constantvalue (Eq. (4)) for an isoscalar target in the absenceof quark mixing. We make use of this to link the nor-malization of our low-ν antineutrino flux sample to thatfor neutrinos and therefore do not require external an-tineutrino cross section values. The weighted average(isoscalar corrected) unnormalized antineutrino cross sec-tion, σν,ν0(EN ) × I νiso(EN ), is computed in the normal-ization bin for each ν0 value. It is linked to that forneutrinos by applying a small correction due to quarkmixing, which is computed from a generator model

G(ν0) =σν(ν0, E →∞)σν(ν0, E →∞)

. (14)

This correction, which is dominated by a term that is pro-portional to V 2

us ≈ 0.05, is negligible for ν0 < 0.5 GeV,1.5% for ν0 < 1 GeV and 2.6% for ν0 < 2 GeV. We obtaina normalization factor for the ν0 = 2 GeV sub-samplefrom the corrected neutrino normalization, H ν = Hν/G.Rather than treating each low-ν sub-sample indepen-dently, we take the ν0 = 2 GeV value as a standardand relatively normalize among different flux samples to

make them match the same value in the normalizationbin. We obtain the normalization for each ν0 samplefrom H ν(ν0) = Hν(ν0)/G(ν0)/α(ν0), where α(ν0) is thefactor needed to adjust the measured antineutrino crosssection at EN to our measured value for ν0 = 2 GeV.This technique makes use of additional information inour low-ν data to compensate for unmodeled cross sec-tion contributions or energy dependent systematic uncer-tainties in that region. The values of α (given in Table II)range from 1.0 to 1.126. The size of the correction in thelowest energy bin is comparable to the size of the 1σ sys-tematic error in the bin (9%). The additional statisticalerror from α is included in the result and it dominates thestatistical error in the antineutrino flux and RCC below7 GeV.

VII. SYSTEMATIC UNCERTAINTIES

We consider systematic uncertainties that arise frommany sources including muon and hadron energy scales,reconstruction-related effects, cross section modeling,

9

backgrounds, and normalization uncertainties. In eachcase, we evaluate the effect by propagating it throughall the steps of the analysis, including a recalculation ofthe absolute normalization. The normalization techniquemakes the results insensitive to effects that change theoverall rates.

The muon energy scale uncertainty is evaluated byadding the 2% range uncertainty [19] in quadrature withthe uncertainty in momentum measured from curvature(2.5% for Pµ < 1 GeV and 0.6% for Pµ > 1 GeV), whichis dominated by knowledge of the MINOS ND magneticfield [18]. A small component of energy loss uncertaintyin MINERvA is also taken into account. The hadronicresponse uncertainty is studied by incorporating an in-dividual response uncertainty for each final state parti-cle produced at the hadronic vertex in the neutrino in-teraction. A small-scale functionally-equivalent detectorin a test beam [28] was used to assess energy responsesand their uncertainties, which are found to be 3.5% forprotons, and 5% for π± and K. In addition to thetest beam study, information from in situ Michel elec-tron and π0 samples is used to determine the 3% uncer-tainty in electromagnetic response. Low-energy neutronshave the largest uncertainties (25% for kinetic energies< 50 MeV and 10-20% for > 50 MeV), which are es-timated by benchmarking GEANT4 [29] neutron crosssections against nA → pX measurements in this energyrange. The energy scale uncertainties are the most im-portant components of the flux shape measurement, butthese largely cancel in cross sections and RCC , resultingin a smaller overall effect.

Two reconstruction-related sources of uncertainty thataffect measured shower energies were considered. The ef-fect of PMT channel cross-talk is studied by injectingcross-talk noise into the simulation and its uncertainty isestimated by varying the amount by 20%. The resultinguncertainty is small and is added in quadrature with thehadronic energy scale uncertainty. Muon track-relatedenergy depositions (from δ-rays or bremsstrahlung) aredifficult to isolate within the shower region. We use dataand simulation samples of beam-associated muons pass-ing through the detector to model these and tune ourhadron energy distribution in data and simulation. Wecompare two algorithms to separate muon-associated en-ergy from the shower region and take their difference asthe uncertainty from this source, which is also found tobe small.

The effect of accidental activity from beam-associatedmuons is simulated by overlaying events from data withinour reconstruction timing windows. We study overall re-construction efficiency as a function of neutrino energyby projecting track segments reconstructed using onlythe MINERvA detector and searching for the track inMINOS ND, and vice versa. Track reconstruction effi-ciency, which agrees well between data and Monte Carlo,is above 99.5% for MINERvA and above 96% for MINOSND and is found to be nearly constant with energy. Weadjust the simulated efficiency accordingly, although the

normalization procedure makes the results insensitive tothese effects.

Cross section model uncertainties enter into the mea-surement directly through the model-dependent correc-tion as well as through bin migration effects at the bound-aries of our experimental acceptance. Our default model(GENIE-Hybrid) is based on GENIE 2.8.4, we thereforeuse the prescription in Ref. [21] to evaluate uncertain-ties on all of the corresponding model parameters. Thelargest GENIE model uncertainties arise from final stateinteractions (FSI) and the resonance model parameters.We account for uncertainties in the resonance contribu-tion by varying the axial mass parameters, MRES

A andMRESV , in our model by ±20% and ±10%, respectively.

The resulting effect on the cross section is up to 4%. TheGENIE parameters that control FSI effects include meanfree path, reaction probabilities, nuclear size, formationtime and hadronization model variation. The largest FSIuncertainty, due to the pion mean free path within thenucleus, is up to 2% (3%) for cross sections (fluxes).We separately evaluate the uncertainties from the tunedmodel components (RPA, single pion non-resonant, and2p2h) discussed in Sec. III. We include half the differ-ence between the default GENIE 2.8.4 and the imple-mented RPA model in quadrature into the total modeluncertainty. We assume a 15% uncertainty in the re-tuned non-resonant single pion production component.After incorporating the 2p2h model, a sizable discrep-ancy in the hadronic energy distribution with the dataremains. To assess an additional uncertainty from thisunmodeled contribution, we fit the data excess at lowhadronic energy described in Ref. [15] in the neutrinoenergy range 2 < Eν < 6 GeV (taking into account sep-arately proton-proton and proton-neutron initial states)to obtain a corrected model [30, 31]. We take the uncer-tainty as the difference of the result obtained with thisdata-driven model, from the nominal result. The MIN-ERvA antineutrino data also show an excess in the sameregion. We apply the corrected model from neutrino de-scribed above and then fit the remaining antineutrinoexcess to obtain a data-driven antineutrino 2p2h modeluncertainty. The primary effect of varying the size of thiscontribution is to shift the overall level of the cross sec-tion. The normalization procedure removes most of theeffect and the remaining uncertainty is less than 1.5%(2%) on the cross section (flux).

The contamination from wrong-sign events is signifi-cant only for the antineutrino sample (about 4% above15 GeV). To evaluate the uncertainty from this sourcewe recompute the antineutrino cross section with wrong-sign events in RHC mode reweighted by the extractedneutrino low-ν flux. The difference is taken as the wrong-sign contamination uncertainty, which is less than 0.5%(0.2%) for the extracted antineutrino cross section (flux).

The overall 3.6% normalization uncertainty arises fromthe precision of the NOMAD data set in the energy range12-22 GeV. We have assumed NOMAD data points inthis region to have 100% correlated point-to-point sys-

10

tematic uncertainties in computing the weighted aver-age error from their data. For antineutrinos and RCCwe study an additional contribution to the uncertaintyfrom the correction term, G(ν0), by varying the GENIE-Hybrid cross section model parameters within their un-certainties prescribed by GENIE. The resulting uncer-tainty is negligible (less than 0.5% for all energies).

An error summary for the fluxes is shown in Fig. 5.The dominant systematic uncertainties on the shape forboth the neutrino and antineutrino fluxes arise from lim-ited knowledge of muon and hadron energy scales. Thisuncertainty peaks at low energies and has a nontrivialenergy dependence that is due to the combined effectsfrom sub-components having different precisions, as wellas to the flux shape itself. The FSI uncertainty gives aneffect that is also important, 3.5%, and nearly constantwith energy. For antineutrinos, the statistical precisionis poorer and is comparable to the systematic precisionover most of the energy range. The statistical error in thedata-based cross normalization factor α(ν0) (Table II),dominates the statistical precision below 12 GeV and isresponsible for the detailed shape features in the uncer-tainty band2.

Neutrino and antineutrino cross section uncertaintycomponents are summarized in Fig. 6. Many system-atic effects cause changes that are similar in the crosssection and flux samples and partially cancel in the mea-sured cross section. The dominant uncertainty is fromthe cross section model at low energy, while normaliza-tion dominates at high energies. Neutrino and antineu-trino cross sections have comparable systematic errorsbut the statistical precision is poorer for antineutrinosand it dominates the error in all but the lowest energybin.

The uncertainties on the cross section ratio, RCC , aresummarized in Fig. 7. Energy scale uncertainties nearlycancel in this ratio, and the sizes of effects from FSI andmany model uncertainties are reduced. The dominant re-maining uncertainties are from the MRES

A cross sectionmodel parameter and the effect of implementing the RPAmodel in GENIE 2.8.4. The corresponding cross sectioncomponents produce sizable shape effects in the visibleenergy in the low-ν region. Different final states in neu-trino versus antineutrino interactions reduce cancellationeffects in these components for the ratio. The overall un-certainty in RCC is dominated by statistical uncertaintyin the antineutrino sample.

VIII. FLUX AND CROSS SECTION RESULTS

The extracted low-ν flux (Table IX) is shown in Fig. 8where it is compared to the MINERvA simulated flux

2 Features occur where the ν0 cut value changes at 3, 7, and12 GeV.

of Ref. [17]. The latter flux is constrained using hadronproduction data and a detailed GEANT4 [29] beamlinesimulation. The extracted flux low-ν is in reasonableagreement with the simulation for both modes3. Thelow-ν measurement prefers a smaller neutrino flux below7 GeV (approximately 5%) while a larger flux is pre-ferred for both neutrinos and antineutrinos (2-12% forneutrinos, up to 16% for antineutrinos) in the >7 GeVrange. The low-ν flux compared to the flux of the tunedproduction-based simulation achieves better precision forneutrinos (by 30% for Eν above 3 GeV) and comparablefor antineutrinos.

The measured cross sections (Table IX) are shown inFig. 9 compared with the GENIE-Hybrid model. Thedata (red points), extracted using GENIE-Hybrid formodel corrections, favor a lower total cross section inthe region 2-9 GeV, where data lie below the curves (byup to ∼2σ) for neutrinos. Antineutrino data also fa-vor a lower cross section in the same region, but agreewith models within the precison of the data, which havelarger statistical uncertainties. For comparison, we alsoextract results using Eqs. (10) and (11) and NuWro(squares) to compute explicit model correction terms4.We omit error bars from NuWro-based points, whichuse the same raw binned data, and therefore have thesame (correlated) statistical and detector-related system-atic uncertainties. The shaded band shows the size ofthe estimated model systematic uncertainty (computedfrom the GENIE-Hybrid model) which spans the differ-ences between the extracted cross section values. TheNuWro model has a different treatment of the low-ν re-gion than GENIE, including a different axial mass pa-rameter (MA = 1.2 GeV), a transverse enhancementmodel (TEM) [32]) to account for the meson exchangecurrent (MEC) scattering contribution, and a duality-based treatment in the resonance region [33]. The twosets of extracted cross sections show significant differ-ences at low energies that reflect different modeling ofthe kinematic acceptance correction (AKINCC ), which islarger for Eν < 7 GeV. QE and MEC components, whichdominate the lowest energy bin, have a harder muon spec-trum resulting in better acceptance in the NuWro model.GENIE kinematic acceptance is better in the 3-7 GeVenergy range for the resonance and deep inelastic scat-tering (DIS) components, which become dominant above3 GeV. At high energies, the normalization method re-moves the effect of correction differences between the twomodels for the neutrino data points. For antineutrinos,the GENIE-Hybrid results are systematically above thosefor the NuWro model by a few percent at high energies.

3 Our previous measurement uses an earlier version of the simu-lated flux as described in [4].

4 GENIE 2.8.4 with FSI turned on is used to simulate the fullyreconstructed MINERvA samples, and to correct for detectoreffects we deliberately turn the FSI processes off in NuWro, toavoid double counting them.

11

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Fra

ctio

nal U

ncer

tain

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12TotalEnergy scalesNormalizationCross section modelFSI

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Fra

ctio

nal U

ncer

tain

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12TotalEnergy scalesNormalizationCross section modelFSI

FIG. 5: Measurement uncertainties for neutrino (left) and antineutrino (right) low-ν fluxes. The total uncertainty (sys. + stat.)is the solid line. Components from cross section model (dashed red), FSI (dot-dash blue), and energy scales (dotted) are shown.The 3.6% uncertainty in the external normalization (dashed black) is the error of the NOMAD data in the normalization region.

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Fra

ctio

nal U

ncer

tain

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12TotalCross section model NormalizationEnergy scalesFSI

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Fra

ctio

nal U

ncer

tain

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12TotalCross section model NormalizationEnergy scalesFSI

FIG. 6: Measurement uncertainties for neutrino (left) and antineutrino (right) total cross sections. The total uncertainty(sys. + stat.) is the solid line. Components from the cross-section model (dashed red), FSI (dot-dash blue), and energy scales(dotted) are shown. The 3.6% uncertainty in the external normalization (dashed black) is the error of the NOMAD data in thenormalization region. Statistical error dominates the measurement in the antineutrino result.

We have applied the GENIE-Hybrid quark mixing cor-rection G(ν0) to the NuWro data points, which does notinclude quark mixing by default. Figure 10 shows a com-parison of the measured charged-current total cross sec-tions with world neutrino data [6, 7, 27, 34–46]. We applya non-isoscalarity correction5 to other data sets to com-

5 Corrections for SciBooNE CH target points with energies in the

pare with our isoscalar-corrected carbon measurement.The neutrino cross section is in good agreement withother measurements that overlap in this energy range and

range 0.38-2.47 GeV are 1.085, 1.06, 1.038, 1.033, 1.028, 1.028,respectively. We correct T2K 2013 (CH target at E=0.85 GeV)by 1.04, T2K 2014 (iron at E=1.5 GeV) by 0.977, T2K 2015(iron at E=1 GeV, 2 GeV, and 3 GeV) by 0.971, 0.976 and0.977, respectively.

12

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Fra

ctio

nal U

ncer

tain

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12TotalCross section model Energy scalesFSI

FIG. 7: Measurement uncertainties for the cross section ra-tio, RCC . The total uncertainty (sys. + stat.) is the solidline. Components from cross section model (dashed red), FSI(dot-dash blue), and energy scales (dotted) are shown. Nor-malization uncertainty is very small (<1%) and is included inthe total error curve. The uncertainty is dominated by thestatistical precision of the antineutrino sample.

is among the most precise in the resonance-dominatedregion (2-7 GeV). Comparisons with world antineutrinodata [6, 40, 47, 48] are also shown. Our data add informa-tion in the region below 10 GeV where previous antineu-trino data are sparse and improve precision and coverage,especially in the region below 6 GeV. Our results are inagreement with precise data on other nuclei [6] in theneutrino energy region of overlap (> 6 GeV) and providethe most precise measurement of the antineutrino crosssection below 5 GeV to date.

The measured cross section ratio, RCC , is shownin Fig. 11 compared with GENIE and NuWro mod-els and with world data [6], [7], [40]. Measured pointsare extracted using GENIE-Hybrid (circles) and NuWro(squares) for model corrections. The measured RCClies above the model predictions at low energies andfavors a flatter extrapolation into that region than dothe models, which fall off below 5 GeV. The NuWroresults are systematically below the GENIE-Hybrid re-sults by a few percent, tracking the differences seenin the antineutrino cross section level in the numera-tor (discussed above). The differences between GENIE-Hybrid-based and NuWro-based RCC measurements atlower energies are less significant than differences seenin the cross sections from the two models. The shadedband, which spans the NuWro versus GENIE-Hybridpoint differences, shows the size of the estimated sys-tematic uncertainty from model sources. Our result is ingood agreement with the recent measurement from MI-NOS on an iron target in the region where they overlap(Eν > 6 GeV). This measurement is the only precise

determination of RCC in the Eν < 6 GeV region. Itspans neutrino energies from 2 to 22 GeV, a range whichis highly relevant to ongoing and future oscillation exper-iments.

IX. CONCLUSION

We present the first precise measurement of the ra-tio of antineutrino to neutrino cross sections, RCC , inthe region below 6 GeV, which is important for futurelong baseline neutrino oscillation experiments. Our mea-surement, with precision in the range of 5.0-7.5%, rep-resents an improvement by nearly a factor of four overthe previous measurements in this region [7]. We mea-sure neutrino and antineutrino cross sections that extendthe reach for antineutrino data to low energies and areamong the most precise in the few GeV energy range.Two leading neutrino generators, GENIE and NuWro,both overestimate the measured inclusive CC cross sec-tions at the level of 4-10% as energy decreases from 9 GeVto 2 GeV. We also present measured total and low-ν fidu-cial rates that can be used to obtain the cross sectionsand their ratio with other models. In the near future,this will allow our data to be used with new models thatwill have improved treatments of nuclear effects and lowenergy scattering processes.

The cross section ratio RCC is found to have system-atic uncertainties that are significantly smaller than thoseassociated with either of the CC inclusive cross sections,due to cancellation of common systematic uncertainties.We demonstrate the robustness of RCC by comparingresults using two different models (GENIE-Hybrid andNuWro). The differences are found to be smaller than inthe individual cross section measurements and are com-parable with the size of estimated model systematic un-certainties.

X. ACKNOWLEDGMENTS

This work was supported by the Fermi National Ac-celerator Laboratory under US Department of Energycontract No. DE-AC02-07CH11359 which included theMINERvA construction project. Construction supportwas also granted by the United States National Sci-ence Foundation under Award PHY-0619727 and bythe University of Rochester. Support for participatingscientists was provided by NSF and DOE (USA), byCAPES and CNPq (Brazil), by CoNaCyT (Mexico), byCONICYT programs including FONDECYT (Chile), byCONCYTEC, DGI-PUCP and IDI/IGI-UNI (Peru). Wethank the MINOS Collaboration for use of its near de-tector data. We acknowledge the dedicated work of theFermilab staff responsible for the operation and main-tenance of the beamline and detector and the FermilabComputing Division for support of data processing.

13

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FHC Neutrino

10 15 200

2

4

6

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

PO

T6

/GeV

/10

2N

eutr

inos

/m

0

20

40

60

80Simulation

Data

RHC Antineutrino

Neutrino Energy (GeV)10 15 20

0

1

2

3

FIG. 8: Extracted low-ν flux (points) for FHC neutrino (left) and RHC antineutrino (right). The histogram shows the MonteCarlo simulated fluxes from Ref. [17] and one sigma error band (shaded bars). The insets show a zoom-in of the 7-22 GeVenergy range.

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Rat

io to

Mod

elν σ

0.8

0.9

1

1.1

1.2 FHC Neutrino

Data (GENIE Hybrid)

Data (NuWro)

NuWro model

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Rat

io to

Mod

elν σ

0.8

0.9

1

1.1

1.2

Data (GENIE Hybrid)

Data (NuWro)

NuWro model

RHC Antineutrino

FIG. 9: Ratio of the measured neutrino (left) and antineutrino (right) cross sections to the GENIE-Hybrid model. Points areMINERvA data with default GENIE-Hybrid (circles) and alternative NuWro model (squares) used to compute model-basedcorrection terms. GENIE-Hybrid data points are plotted with total error (sys. + stat.). The dashed line shows the NuWromodel. The shaded band give the size of the cross section model systematic uncertainty.

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2 4 6 8 10 12 14 16 18 20 22

0.6

0.8

1

1.2Neutrino

Neutrino energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

0.25

0.3

0.35

0.4

Antineutrino

MINERvA 2017

MINERvA 2016

T2K 2015

T2K 2014

T2K 2013

ArgoNeuT 2012, 2014

SciBooNE 2011

MINOS 2009

NOMAD 2008

JINR 1996

BNL 1980

SKAT 1979

GGM 1979

BEBC 1979

ITEP 1979

/GeV

)2

cm-3

8/E

(10

σ

FIG. 10: MINERvA measured neutrino and antineutrino charged-current inclusive cross sections (red circles and previous resultfrom Ref. [4] shown with blue squares) compared with other measurements for neutrinos [6, 7, 27, 34–46] (upper plot), andantineutrinos [6, 40, 47, 48] (lower plot), on various nuclei in the same energy range. The reference curve shows the predictionof GENIE 2.8.4.

Neutrino Energy (GeV)0 2 4 6 8 10 12 14 16 18 20 22

Rat

io to

Mod

elν σ/ν σ

0.8

0.9

1

1.1

1.2

Data (GENIE Hybrid)

Data (NuWro)

NuWro model

Neutrino energy (GeV)2 4 6 8 10 12 14 16 18 20 22

ν σ/ν σ

0.2

0.3

0.4

0.5

0.6

GENIE 2.8.4MINERvA GGM 1973ITEP 1979MINOS 2009

FIG. 11: (Left) Ratio of measured RCC to GENIE-Hybrid. Points are MINERvA data with default GENIE-Hybrid (circles) andalternative NuWro model (squares) used to compute model-based correction terms. GENIE-Hybrid data points are plotted withtotal error (sys. + stat). The dashed line shows the NuWro model. The shaded band shows the size of the cross section modelsystematic uncertainty. (Right) Comparison of MINERvA RCC (corrected to an isoscalar target) with world measurements( [7],[40] and [6]).

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17

Supplemental materials

18

Neu

trin

oA

nti

neu

trin

o

E(G

eV)

2-3

3-4

4-5

5-7

7-9

9-1

212-1

515-1

818-2

22-3

3-4

4-5

5-7

7-9

9-1

212-1

515-1

818-2

2

5.6

71.6

71.3

51.3

51.1

31.0

30.8

30.7

80.8

11.3

10.7

00.5

00.4

50.4

50.4

50.4

10.4

50.4

1

2-3

1.5

00.8

80.8

40.8

00.7

80.7

20.6

30.6

40.6

70.4

70.3

70.3

40.3

50.3

60.3

40.3

30.3

1

3-4

1.1

90.8

10.7

40.7

10.6

50.6

60.6

90.5

40.3

90.3

40.3

20.3

20.3

20.3

10.3

40.3

2

5-7

1.2

60.7

70.7

60.6

50.6

80.7

00.5

40.3

70.3

30.3

50.3

30.3

30.3

20.3

50.3

3

Neu

trin

o7-9

1.0

40.7

60.7

00.6

60.6

60.4

70.3

60.3

20.3

20.3

40.3

40.3

30.3

30.3

0

9-1

21.0

60.7

30.6

60.6

50.4

50.3

60.3

20.3

30.3

50.3

70.3

40.3

20.3

0

12-1

50.9

30.6

30.6

20.3

80.3

40.3

10.3

00.3

30.3

40.3

30.3

00.2

9

15-1

80.8

90.6

80.3

30.2

90.2

90.3

00.2

90.3

00.2

90.3

20.3

1

18-2

21.0

20.3

40.2

90.3

00.3

00.2

90.2

80.2

90.3

40.3

3

2-3

1.2

00.3

00.2

10.2

00.2

00.1

90.1

90.1

80.1

7

3-4

0.5

50.1

70.1

60.1

70.1

70.1

60.1

50.1

4

4-5

0.4

80.1

50.1

50.1

40.1

50.1

40.1

4

5-7

0.5

20.1

40.1

40.1

40.1

50.1

4

Anti

neu

trin

o7-9

0.5

10.1

60.1

50.1

40.1

3

9-1

20.5

40.1

60.1

40.1

3

12-1

50.3

90.1

40.1

4

15-1

80.5

60.1

5

18-2

20.6

5

TA

BL

EV

:C

ovari

ance

matr

ixco

rres

pondin

gto

tota

ler

ror

for

the

extr

act

edneu

trin

ocr

oss

sect

ion

inth

eF

HC

and

anti

neu

trin

ocr

oss

sect

ion

inth

eR

HC

bea

mm

ode.

The

cova

riance

elem

ents

are

inunit

sof

(σ/E

)2,

whic

his

(10−

38cm

2/G

eV)2

,and

scale

dby

afa

ctor

of

1000.

19

E(GeV) 2-3 3-4 4-5 5-7 7-9 9-12 12-15 15-18 18-22

2-3 1.080 0.088 0.021 0.002 -0.024 -0.018 -0.030 -0.019 -0.010

3-4 0.718 0.119 0.106 0.056 0.039 0.010 0.015 0.019

4-5 0.816 0.150 0.103 0.065 0.032 0.031 0.024

5-7 0.919 0.107 0.083 0.046 0.045 0.038

7-9 0.796 0.060 0.033 0.033 0.030

9-12 0.788 0.030 0.031 0.027

12-15 0.507 0.031 0.015

15-18 0.872 0.017

18-22 1.053

TABLE VI: Covariance matrix of extracted cross section ratio, RCC , scaled by 1000.

E(GeV) 2-3 3-4 4-5 5-7 7-9 9-12 12-15 15-18 18-22

2-3 44.869 21.466 -0.026 0.475 0.832 0.629 0.421 0.109 0.017

3-4 22.823 3.814 1.333 0.847 0.548 0.337 0.160 0.075

4-5 3.784 0.815 0.295 0.152 0.078 0.076 0.050

5-7 0.348 0.099 0.055 0.029 0.023 0.015

7-9 0.077 0.032 0.019 0.011 0.006

9-12 0.029 0.012 0.006 0.003

12-15 0.011 0.004 0.002

15-18 0.004 0.002

18-22 0.001

TABLE VII: Covariance matrix for the extracted neutrino flux in the FHC beam mode. The covariance elements are in unitsof (νµ/m

2/GeV/106POT)2.

E(GeV) 2-3 3-4 4-5 5-7 7-9 9-12 12-15 15-18 18-22

2-3 58.944 17.011 -0.415 0.032 0.386 0.250 0.137 -0.003 -0.004

3-4 26.699 2.211 0.623 0.370 0.216 0.117 0.037 0.020

4-5 4.166 0.488 0.140 0.069 0.038 0.030 0.017

5-7 0.302 0.038 0.019 0.010 0.008 0.004

7-9 0.046 0.009 0.005 0.002 0.001

9-12 0.014 0.003 0.001 0.001

12-15 0.003 0.001 0.000

15-18 0.001 0.000

18-22 0.000

TABLE VIII: Covariance matrix for the extracted antineutrino flux in the RHC beam mode. The covariance elements are inunits of (νµ/m

2/GeV/106POT)2.