Single neutral pion production by charged-current ν¯μ interactions on hydrocarbon at >Eν< = 3.6 GeV

Article

Reference

Single neutral pion production by charged-current ν¯μ interactions on hydrocarbon at >Eν< = 3.6 GeV

LE, T., PALOMINO, J.L. & Collaboration BRAVAR, Alessandro (Collab.)

Abstract

Single neutral pion production via muon antineutrino charged-current interactions in plastic scintillator (CH) is studied using the MINERvA detector exposed to the NuMI low-energy, wideband antineutrino beam at Fermilab. Measurement of this process constrains models of neutral pion production in nuclei, which is important because the neutral-current analog is a background for ν¯e appearance oscillation experiments. The differential cross sections for π0 momentum and production angle, for events with a single observed π0 and no charged pions, are presented and compared to model predictions. These results comprise the first measurement of the π0 kinematics for this process.

LE, T., PALOMINO, J.L. & Collaboration, BRAVAR, Alessandro (Collab.). Single neutral pion production by charged-current ν¯μ interactions on hydrocarbon at >EνPhysics Letters. B, 2015, vol. 749, p. 130-136

DOI : 10.1016/j.physletb.2015.07.039

Available at:

http://archive-ouverte.unige.ch/unige:74432

Disclaimer: layout of this document may differ from the published version.

1 / 1

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

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Single neutral pion production by charged-current ν ¯ _μ interactions on hydrocarbon at ^E ν = ³ . 6 GeV

T. Le

^a,∗,1

, J.L. Palomino

^b

, L. Aliaga

^c,k

, O. Altinok

^d

, A. Bercellie

^e

, A. Bodek

^e

, A. Bravar

^f

, W.K. Brooks

^g

, A. Butkevich

^h

, D.A. Martinez Caicedo

^b,o

, M.F. Carneiro

^b

, M.E. Christy

ⁱ

, J. Chvojka

^e

, H. da Motta

^b

, J. Devan

^c

, S.A. Dytman

^j

, G.A. Díaz

^k

, B. Eberly

^j

, J. Felix

^l

, L. Fields

^m

, R. Fine

^e

, A.M. Gago

^k

, H. Gallagher

^d

, R. Gran

ⁿ

, D.A. Harris

^o

, A. Higuera

^e,l

, K. Hurtado

^b,s

, M. Kordosky

^c

, E. Maher

^p

, S. Manly

^e

, W.A. Mann

^d

, C.M. Marshall

^e

,

K.S. McFarland

^e,o

, C.L. McGivern

^j

, A.M. McGowan

^e

, J. Miller

^g

, J.G. Morfín

^o

, J. Mousseau

^q

, J.K. Nelson

^c

, A. Norrick

^c

, J. Osta

^o

, V. Paolone

^j

, J. Park

^e

, C.E. Patrick

^m

, G.N. Perdue

^o,e

, L. Rakotondravohitra

^o,2

, R.D. Ransome

^a

, H. Ray

^q

, L. Ren

^j

, P.A. Rodrigues

^e

,

D. Ruterbories

^e

, H. Schellman

^m

, D.W. Schmitz

^r,o

, J.T. Sobczyk

^o,3

, C.J. Solano Salinas

^s

, N. Tagg

^t

, B.G. Tice

^a,4

, E. Valencia

^l

, T. Walton

ⁱ

, J. Wolcott

^e

, H. Yepes-Ramirez

^b

, G. Zavala

^l

, D. Zhang

^c

, B.P. Ziemer

^u

aRutgers,TheStateUniversityofNewJersey,Piscataway,NJ 08854,USA

bCentroBrasileirodePesquisasFísicas,RuaDr.XavierSigaud150,Urca,RiodeJaneiro,RJ,22290-180,Brazil cDepartmentofPhysics,CollegeofWilliam&Mary,Williamsburg,VA 23187,USA

dPhysicsDepartment,TuftsUniversity,Medford,MA 02155,USA eUniversityofRochester,Rochester,NY 14610USA

fUniversityofGeneva,Geneva,Switzerland

gDepartamentodeFísica,UniversidadTécnicaFedericoSantaMaría,AvenidaEspaña1680,Casilla110-V, Valparaíso,Chile hInstituteforNuclearResearchoftheRussianAcademyofSciences,117312Moscow,Russia

iHamptonUniversity,Dept.ofPhysics,Hampton,VA 23668,USA

jDepartmentofPhysicsandAstronomy,UniversityofPittsburgh,Pittsburgh,PA 15260,USA

kSecciónFísica,DepartamentodeCiencias,PontificiaUniversidadCatólicadelPerú,Apartado1761,Lima,Peru

lCampusLeónyCampusGuanajuato,UniversidaddeGuanajuato,LascuraindeRetanaNo.5,Col.Centro, Guanajuato36000,Guanajuato,Mexico mNorthwesternUniversity,Evanston,IL 60208,USA

nDepartmentofPhysics,UniversityofMinnesota–Duluth,Duluth,MN 55812,USA oFermiNationalAcceleratorLaboratory,Batavia,IL 60510,USA

pMassachusettsCollegeofLiberalArts,375ChurchStreet,NorthAdams,MA 01247,USA qUniversityofFlorida,DepartmentofPhysics,Gainesville,FL32611,USA

rEnricoFermiInstitute,UniversityofChicago,Chicago,IL 60637USA sUniversidadNacionaldeIngeniería,Apartado31139,Lima,Peru

tDepartmentofPhysics,OtterbeinUniversity,1SouthGroveStreet,Westerville,OH43081, USA uDepartmentofPhysicsandAstronomy,UniversityofCalifornia,Irvine,Irvine,CA 92697-4575,USA

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received7March2015

Receivedinrevisedform10May2015 Accepted17July2015

Availableonlinexxxx Editor:D.F.Geesaman

Singleneutralpionproductionviamuonantineutrinocharged-currentinteractionsinplasticscintillator (CH) is studiedusingthe MINERvAdetector exposedtothe NuMIlow-energy,widebandantineutrino beamatFermilab.Measurementofthisprocessconstrainsmodelsofneutralpionproductioninnuclei, whichis important becausethe neutral-current analogis abackground for ν¯e appearanceoscillation experiments.The differentialcross sections forπ⁰momentumand production angle,for events with

*

Correspondingauthor.Tel.:+16313719595.

E-mailaddress:[email protected](T. Le).

1 NowatSLACNationalAcceleratorLaboratory,Stanford,CA94309, USA.

2 AlsoatDepartmentofPhysics,UniversityofAntananarivo,Madagascar.

3 AlsoatInstituteofTheoreticalPhysics,WrocławUniversity,Wrocław,Poland.

4 NowatArgonneNationalLaboratory,Argonne,IL 60439,USA.

http://dx.doi.org/10.1016/j.physletb.2015.07.039

0370-2693/©^{2015PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

JID:PLB AID:31194 /SCO Doctopic: Experiments [m5Gv1.3; v1.159; Prn:22/07/2015; 8:58] P.2 (1-7)

2 Le et al. / Physics Letters B•••⁽••••⁾•••^–•••

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Keywords:

Neutrino-nucleusscattering Finalstateinteraction

asingle observedπ⁰ andnocharged pions,are presented andcomparedtomodel predictions.These resultscomprisethefirstmeasurementoftheπ⁰kinematicsforthisprocess.

©^{2015PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Neutrino- andantineutrino-induced interactions atenergies of afewGeVareaprovinggroundforweakinteractionphenomenol- ogy in nuclei [1]. Measurements in this energy range are im- portant because neutrino oscillation experiments [2,3] need de- tailed understanding of the large variety of processes allowed.

As a result, there is a growing body of new high-quality mea- surements for neutrino-nucleus interactions [4–7]. In particular, neutrinocharged-current neutralpionproduction hasbecome an important benchmark providing new challenges to theories de- scribingthisprocess[8–11].

Most of the published data for pion production in nuclei uses neutrinobeams. Neutral pion productionin nucleifor anti- neutrinos,however,ismuchlessstudied.Onlyonedatapoint for thischannelinthefew-GeVenergyrangeexists intheliterature:

a measurement of

ν

¯_μp→

μ

⁺n

π

⁰ from SKAT in a heavy liquid (CF₃Br)bubblechamberbasedon20eventsatanaverageneutrino energyof7 GeV[12].Measurementsof

π

⁰ productionby neutri- nos havebeenmade indeuteriumbubble chambers[13–16] and more recently on nuclear targets inthe 0.1–1 GeV energy range usingtheMiniBooNEdetector[17]withamineraloil(CH2)target, andusing the SciBar detector inK2K andSciBooNE experiments [18,19]withplastic scintillator(CH). Theserecentmeasurements, as well as data on charged pion production [7,20] and neutral pionproduction[21] havebeendifficultforeventgenerators and theoreticalcalculationstodescribeaccurately[8–11].Everypredic- tionmusthavea modelfor

π

⁰ productionfromnucleons;all use isospindecompositionswithinahelicityformalismthataretuned toavailabledata[22].

Charged-current single

π

⁰ (1

π

⁰) production in the few-GeV region is modeled both as decays of nucleon resonances (most strongly the (1232)) and non-resonant processes. The produc- tion in nuclei can be either direct, through the reaction

ν

¯_μp→

μ

⁺n

π

⁰,orindirect,forexample,throughchargeexchange(CEX)of achargedpioninthenucleus, p

π

⁻_→n

π

⁰ orn

π

⁺_→p

π

⁰.New datawillprovideusefultestsofbothneutrino-inducedresonance productionandfinalstateinteraction(FSI)models.

Neutrino interaction measurements are also important to the analysisofneutrinooscillationexperiments [2,3,23,24]. Theseex- periments requirethe neutrino flavor be identified and the neu- trino energy to be reconstructed on an event-by-event basis. An accurate modeling of theseparticles requires knowledge of both theunderlyingneutrino-nucleoninteractionsandofthefinal-state modifications that arise within the target nuclei (such as car- bon) of which the massive oscillation detectors are comprised.

Pion production is a source of backgrounds and systematic un- certaintiesinneutrinooscillationexperiments.Neutral-current

π

⁰

production,forexample,isadominantbackgroundin

ν

e (

ν

¯e)ap- pearance experiments because the

π

⁰ can mimic a final state electron(positron).Inaddition,experimentsthatreconstructneu- trino energyby identifying quasielastic events,

ν

N(n)→⁻p or

¯

ν

N(p)→⁺n,interactions inwhichapionisproduced butthen absorbedinthetargetnucleuscanbemistakenforquasielasticsig- nalandyieldanincorrectestimateoftheincidentneutrinoenergy.

Newmeasurements of 1

π

⁰ productionby charged-current

ν

¯μ interactionsinplasticscintillator(CH)usingtheMINERvAdetector are presented.Flux-integratedsingle differentialcross sectionsas afunctionof

π

⁰ momentumandproductionangleforeventswith

a single observed

π

⁰ and no

π

^± exitingthe interaction nucleus have been measured and are compared to predictions from the GENIE[25],NuWro[26,27],andNEUT[28]eventgenerators.

2. Experiment

ThedatapresentedhereweretakenusingtheMINERvAdetec- tor and the widebandantineutrino beam produced by the NuMI beamline in the low-energy mode [29] with a mean energy of 3.6 GeV. The antineutrino flux is estimated from a simulation of the neutrino beamline based on Geant4 [30,31], with hadron production inthesimulation constrainedby proton-carbonexter- nal data[32–34].The MINERvA detectorconsistsofafullyactive region of scintillator strips surrounded on the sides and down- stream endby electromagnetic andhadroniccalorimeters, andis describedindetailinRef.[35].Therearethreeorientations(views) forthe strips(X, U,V), offsetby 60^◦ fromeach other,whichen- able three-dimensionalreconstruction of particletrajectories. The X view issampledtwice asoften astheother views. The down- streamedge oftheMINERvA detectorislocated 2 mupstreamof the MINOS Near Detector, a magnetized iron spectrometer [36]

used in this analysis to reconstruct the momentum and charge ofmuons. Thetransportofparticlesfromneutrinointeractionsin thedetectorissimulatedbyaGeant4-basedprogram.Thereadout simulationistunedsothatboththephotostatisticsandtherecon- structed energydeposited by momentum-analyzedthrough-going muonsagreebetweendataandthesimulation.Thedetectorsimu- lationofsingleparticleresponsesisvalidatedusingtestbeamdata takenwithascaled-downversionoftheMINERvAdetector[37].

NeutrinointeractionsaresimulatedusingtheGENIE2.6.2neu- trinoeventgenerator.DetailsconcerningGENIEanditsassociated parameters are described inRef. [25].For baryon resonancepro- duction, the formalism of Rein–Sehgal [22] is used withmodern resonanceproperties[38].Non-resonantpionproductionissimu- latedusing theBodek–Yang model[39] andisconstrainedbelow W=¹.7 GeV byneutrino-deuteriumbubblechamberdata[40,41].

Pion and nucleon FSI are modeled in GENIE using a parameter- ized intranuclearcascademodel,withthefull cascadebeingrep- resentedbyasingleinteraction.Forallmodelsfittingdataforlight nucleisuchascarbon,thepionmostoftenhasoneinteractionasit propagatesthroughthenucleus.Foreachinteraction,choiceofthe channel(e.g.chargeexchange)isbasedontotalcrosssectiondata andcalculations[42,43]andthekinematicsandmultiplicityofthe final state are taken from fits to more detailed data. At the en- ergies importantfor thismeasurement, the hadron-nucleuscross sections have large uncertainties. For example, the cross section of

π

⁻→

π

⁰ CEXoncarbonhasanuncertaintyofabout50%. Re- action cross sections for

π

⁰ are estimated from measured cross sections for

π

^± scattering usingisospin symmetry or theoretical models. The mostsignificant advantages of thesingle interaction usedinGENIE’sFSImodelare theabilitytoexactlyreweightand tocharacterizeeacheventwithasinglefinalstatechannel.Theun- certainties intheFSI modelare evaluated byvarying its strength within previously measured hadron-nucleus cross-section uncer- tainties.

ThisanalysisusesdatatakenbetweenOctober2009andFebru- ary 2012with2.01×^{1020protonsontarget(POT)inthe}

ν

¯μmode.

About half of the exposure (0.945×^{1020 POT) was taken dur-} ingconstruction withthedownstreamhalfofthedetector.Inthis

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periodtheArgoNeuTdetector[44]wassituatedbetweentheMIN- ERvAandMINOSNear detectors.Because thetwosub-samplesof thedatahavedifferentefficiencies,theywere analyzedseparately andtheirresultscombined.

3. Eventreconstructionandselection

TheMINERvA detector recordsthe charge andtime ofenergy depositions(hits)ineachscintillatorstrip.Hitsarefirstgroupedin timeandthenclustersofenergyareformedbyspatiallygrouping adjacenthitsineachscintillatorplane.Clusterswithenergymore than1 MeVare thenmatchedamongthethreeviewstocreatea track.Theper-planepositionresolutionis2.7 mmandtheangular resolutionofthemuon trackis betterthan10 mrad [35] ineach view.The

μ

⁺isidentifiedbymatchingatrackthatexitstheback ofMINERvA witha positively-chargedtrackentering thefront of MINOS.The reconstruction ofthe muon inthe MINOSspectrom- eter gives a typical momentum resolution of 11%. Event pile-up causesadecreaseinthemuontrackreconstructionefficiency.This effectisstudiedinbothMINERvAandMINOSbyprojectingtracks foundinoneofthedetectorstotheotherandmeasuringthemis- reconstructionrate. Thisresultsina −⁴.4% (−¹.1%)correction to thesimulatedefficiencyformuonsbelow(above)3 GeV/c.

Theeventvertex, definedasthemostupstreamclusteronthe muon track, is restricted to be within the central 108planes of the scintillator tracking region andno closer than 22 cm to any edge of the planes.These requirements define a fiducial volume withamassof5.47 metrictons.Duetotherequirementthatthe

μ

⁺istrackedinMINOSforchargeandmomentummeasurement, thedetection efficiencyhas astrong dependence onmuon angle θ_μ andmomentum |^pμ|^{,whichdrops tozeroforeventswith}θ_μ greaterthan 20 degreesor |^pμ|^{lessthan 1}.0 GeV/c.The correc- tionsforthe angleandmomentum efficiencyareestimatedfrom theeventsimulation. Onlyevents witha single trackat thever- tex,the

μ

⁺ matchedtoMINOS,areusedinordertorejectevents includingchargedpionproduction.Acceptedeventsarepassed to the

π

⁰ reconstruction.

The neutralpion has a lifetimeof 8.52×^{10−17s and decays} intotwophotonswithabranchingratioof98.8%[38],sothetwo photonsappeartocomefromtheeventvertex.Plastic scintillator hasaradiationlength X0∼^{40 cm,whichallowsthetwophotons} toconvertbye⁺e⁻pairproductionorComptonscatteringfaraway fromthevertex,thusproducingisolatedenergydeposits.Thepho- tonscanalsohavesignificantenergyleakageorescapethedetec- torwithoutconversion.Furthermore,energydepositsproducedby neutronsfromthesameneutrinointeraction canbe mistakenfor low-energyphotonconversions,furthercomplicatingthepatternof energydeposits.The

π

⁰reconstructionmustcorrectlygroupthese energydepositsintothetwophotons.

The reconstruction can be separated into two steps: pattern recognitionandkinematicreconstruction.Thepatternrecognition buildsupon theknowledgeofthevertexlocationoftheevent.In theX view,clustersthat are closeinpolarangle withrespectto thevertex butcan be separatedin radial distance fromthe ver- texaregroupedintophotoncandidates.Then,foreach candidate, clustersintheUandVviewsconsistentwiththestereocondition areadded.Photoncandidatesmusthaveclustersfromatleasttwo viewsforthree-dimensionaldirectionreconstruction.

Inthe second step,photon position, direction,and energyare determined from the clusters that have been assigned to the photons. The photon direction is reconstructed from the cluster energy-weightedslopesineachview.Thephotonvertexisdefined bytheclosestcluster totheeventvertexonthephoton direction axis.The photon energies are reconstructed by calorimetryusing calibrationconstants determinedfromthesimulation.The overall

calibration constant that sets the absoluteenergy scale is deter- minedbymatchingthepeakinthe

γ γ

invariantmassdistribution tothe

π

⁰ nominalmassof134.97 MeV/c²[38].Thisprocedureis done separatelyfordataandsimulationwhichenablescorrection foradifferenceinenergyscalesof5%betweenthedataandsimu- lation. Finally,the

π

⁰ momentum is calculated frommomentum conservation, pπ⁰ = ^k1+ ^k2, where ki are reconstructed photon momenta. The

π

⁰ is reconstructed witha 25% energy resolution and 3.5 degrees angular resolution in each view. The incoming neutrinoenergyisreconstructedfromthe

μ

⁺ and

π

⁰ 4-momenta using

E^rec_ν

=

E_μ

+

E_π0

+

Tn

T_n

=

¹ 2

[(

^Eμ

−

^pμ

) + (

E_π0

−

^p_π0

)]

²

+ (

^p⊥_μ

+

^p⊥_π0

)

²

mN

− (

E_μ

−

p_μ

) − (

E_π0

−

p_π0

) ,

(1) where ^{p⊥, p are thetransverse and}longitudinalcomponents of momentum, respectively.It isassumedthat theinitial nucleon is atrestandthat the

π

⁰ isproducedtogether withanucleon.The neutrinoenergyisreconstructedwith10%resolution.The

γ γ

in- variantmassmγ γ isreconstructedfromthephotonenergies E1,2 andtheseparationangleθγ γ betweenthetwophotonsusing

m²_{γ γ}

=

^2E1E2

(

1

−

^cos

θ

_{γ γ}

).

(2) Thetworeconstructedphotonsare requiredtoconvertatleast 15 cm (0.36X₀) away fromthe vertex to further reject charged- pionbackgrounds. Inaddition, itis requiredthat E^recν isbetween 1.5 and 20 GeV. The lower energy cut is needed due to MI- NOSacceptance whilethe uppercut is to reduce flux uncertain- ties. Finally, it is required that mγ γ is between 75 MeV/c² and 195 MeV/c².Theselectedsamplehas1304events.Thetotalselec- tion efficiencyis6% andpurity 55%,according tothe simulation.

The background is dominated (70% of the total background) by events with at least one

π

⁰ in the detector. Half of this is due tomulti-pionproduction,

π

⁰+

π

^±,wherethe

π

^± isnottracked, while theother halfhas a secondary

π

⁰ produced by

π

⁻_→

π

⁰

CEXornucleonscatteringinthedetectorbutoutsidetheprimary interactionnucleus. Thenon-

π

⁰ backgroundismostly duetoen- ergydepositsby

π

⁻andneutronswhicharemistakenlyidentified asphotons, andaccountsfortheremaining30%ofthetotalback- ground.

Fig. 1 showsthe mγ γ distributions forboth dataand simula- tionoftheselectedsamplebeforetheinvariantmasscut.Thereis a clearpeak centered around the

π

⁰ nominalmassin both data andsimulation. Thedistribution fromsimulation isbrokendown into signal andbackground components.The signal is definedas antineutrinocharged-currenteventswithsingle

π

⁰andno

π

^±es- caping the nucleus. The background is anythingelse that is not signal. By this definition, it is possible for signal events to have the

π

⁰s mis-reconstructedfromnon-

π

⁰ energydeposits.Thesig- nalevents athighmγ γ,outsidethesignal masswidth, haveone orbothcandidatephotonsreconstructedfromneutronenergyde- posits. The same mis-reconstruction happens to signal events in theselected sample butatasmallerrate(14%). The

π

⁰ momen- tumandangularshapesoftheseeventsarefoundtobesimilarto therestofthesignalevents.Theenhancementinthebackground distributionaroundthe

π

⁰massisduetobackgroundeventswith atleastone

π

⁰inthedetector.

Afterevent selection,the selected sample still hassubstantial background to be subtracted statistically fromthe total distribu- tion for each observable. The background distribution for each observable is estimatedfrom thesimulation withthe total back- groundrateconstrainedbydata.Thissignificantlyreducestheun- certainties in the estimated background. The background rate is

JID:PLB AID:31194 /SCO Doctopic: Experiments [m5Gv1.3; v1.159; Prn:22/07/2015; 8:58] P.4 (1-7)

4 Le et al. / Physics Letters B•••⁽••••⁾•••^–•••

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Fig. 1.Distributionoftheinvariantmassoftheγ γ pair.Dataareshownassolid circleswithstatisticalerrorbars.TheshadedhistogramsshowtheMonte Carlopre- dictionsforCC1π⁰signal(top)andforbackground(bottom).Thesignalisdefined asantineutrinocharged-currenteventswithsingleπ⁰andnoπ^±escapingthenu- cleus.Thebackgroundisanythingelsethatisnotsignal.Theverticallinesindicate theinvariantmasscut,75 MeV/c²<mγ γ<195 MeV/c².

determined fromabinnedextendedmaximumlikelihoodfitofan invariant massmodeltothe data[45].Theinvariant mass model M(mγ γ) is a two-component model constructed from the mγ γ distributionsofsignalandbackgroundevents,

M

(

m_{γ γ}

) =

^NsigM_sig

(

m_{γ γ}

) +

^NbkgM_bkg

(

m_{γ γ}

),

(3) where Msig(mγ γ), M_bkg(mγ γ) are the shapes of the signal and background mγ γ distributions from the simulation, respectively.

Theexpectednumbersofsignalandbackgroundevents N_sig,N_bkg inthe range 0–500 MeV/c² are the parameters determined from thefit. Afterthe fit,a backgroundrateof541±^{37 eventsis ob-} tainedbyintegratingthecurveN_bkgM_bkg(mγ γ)overthemasspeak regionfrom75 MeV/c²to195 MeV/c²,thesamerangeasrequired bytheeventselection.The fitreducesthebackgroundnormaliza- tionbyafactorof0.8comparedtothesimulationprediction.

The estimated backgroundis subtracted fromthe total distri- bution. This background-subtracted data distribution is unfolded toaccountfordetectorresolutioneffectsusingaBayesianunfold- ing method [46] withtwo iterations. The migration matrix used intheunfolding isobtainedfromthe simulation.Thereconstruc- tionefficiencyandacceptancecorrectionsaremadebydividingby anefficiencycurvederivedfromthesimulation.Dividingthiscor- recteddistributionbytheintegratedflux(2.5×¹⁰⁻⁸

ν

¯μ/cm²/POT) of antineutrinos withenergies in the range1.5–20 GeV, andthe numberofnucleonsinthefiducialvolume(3.30×^{1030)givesthe} differentialcrosssection.

The total uncertainties on the measured cross sections are 20–25% with comparable contributions from statistical and sys- tematicuncertainties. Thelargestsystematicuncertaintyisdueto theintegratedfluxuncertaintyat10%.Adetaileddiscussionofthe fluxsystematicuncertaintyispresentedinRef.[6].Thenextlargest contributiontothesystematicuncertaintyisthe8%normalization uncertaintyfrom the backgroundfit. The other smaller contribu- tions include the neutrino cross-section models, FSI models, and detectorsimulationsystematics.Thesesystematicuncertaintiesen- terthe measured crosssections through background subtraction, detectorresolution,andefficiencycorrections.Theneutrinocross- sectionmodelandFSImodeluncertaintiesareevaluatedbyGENIE.

The systematic uncertainties on the estimated background are smallsincethebackgroundrateisconstrainedbydata.Systematic errorsinthedetectorresponsemustbe independentlyestimated.

Fig. 2.Differentialcrosssectionfor1π⁰productionasfunctionofπ⁰momentum.

Dataareshownassolidcircles.Theinner(outer)errorbarscorrespondtostatis- tical(total)uncertainties.Thesolid(dashed)histogramsareGENIEpredictionwith (without)FSI,thelong-dashedhistogramisthepredictionfromtheNuWrogenera- tor,andthedot-dashedhistogramisthepredictionfromNEUT.

Fig. 3.Differentialcrosssection for1π⁰ production asfunctionofthe π⁰ polar angle.Dataareshownassolidcircles.Theinner(outer)errorbarscorrespondto statistical(total)uncertainties.Thesolid(dashed)histogramsareGENIEprediction with(without)FSI,thelong-dashedhistogramisthepredictionfromtheNuWro generator,andthedot-dashedhistogramisthepredictionfromNEUT.

The uncertaintyinneutronresponseisevaluatedby changingthe neutron inelastic cross section within experimental uncertainties [47–54] througheventreweighting.The reweightingisapplied to theleadingneutronintheevent.Alargefractionofthesecondary

π

⁰ in the backgroundis estimatedto arise from

π

⁻_→

π

⁰ CEX, forwhich thecross sectionsare poorly known.The effectofthis uncertaintyonourmeasurementisevaluatedbychangingtheCEX cross sectionwithin its uncertaintyof ±^50% [43,55,56], andthen re-measuring the cross sections. Finally, the electromagnetic en- ergyscaleuncertainty(2.2%)istakenfromthefittedmeanuncer- tainty ofthe datamγ γ distribution. Flux-integratedsingle differ- ential crosssectionsin

π

⁰ momentumandanglewithstatistical, systematic,andtotaluncertaintiesaresummarizedintables.⁵ 4. Resultsanddiscussion

Themeasureddifferentialcrosssectionsasfunctionof

π

⁰ mo- mentum andanglewithrespecttothebeamdirectionareshown in Figs. 2 and 3, respectively. The data are compared to the

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Fig. 4.Samecross sectiondataas inFig. 2.Thestackedhistogramsshow ade- compositionofthe1π⁰ signalintodifferentFSIchannelsaspredictedbyGENIE.

Descriptionofthe FSIchannelsfollows(fromtoptobottom):1) Multi-π→π⁰: multi-pionproducedbytheprimaryinteractionandallotherpionsarere-absorbed insidethenucleus,exceptaπ⁰,2)π⁻→π⁰:aπ⁻producedbytheprimaryinter- action,thenchargeexchangesinsidethenucleus,3)π⁰producedbytheprimary interactionandthenundergoinginelasticscatteringinsidethenucleus,4)π⁰pro- ducedbytheprimaryinteractionandthenundergoingelasticscatteringinsidethe nucleus,and 5)π⁰producedbytheprimaryinteractionandexitingthenucleus withoutinteracting.

predictions from GENIE with and without FSI. Above 0.7 GeV/c, FSI effects have little influence on the

π

⁰ momentum distribu- tion,and both predictions are in good agreement withthe data.

Formomentabelow0.3 GeV/c,inclusionofFSIgivesanincreased and shifted cross section relative to the no FSI case. This trend isexhibitedby thedata;GENIEcalculationswithandwithoutFSI give a

χ

² of 25.4 and 50.0 for 11 degreesof freedom (dof), re- spectively. For the distribution of

π

⁰ productionangle in Fig. 3, inclusion ofFSI into the GENIE simulation resultsin a mild flat- teningofthedistributionwithnosignificant improvementinthe

χ

²comparedtothenoFSIcase,16.7versus16.0for11degreesof freedom.ThustheeffectsofFSIaremorepronouncedwithrespect to

π

⁰ momenta than with

π

⁰ production angle. This situation likelyreflectstheinfluenceofthe(1232)resonance,whichgives aparticularly strongmomentum dependencetothe pion-nucleus interactionforpπ≈⁰.26 GeV/c wherethepion-carboncrosssec- tionismaximum.

Figs. 2 and 3 also show predictions including FSI from the NuWroandNEUTeventgenerators.Anypredictionrequiresknowl- edgeof

ν

¯μN→

μ

⁺

π

⁰N reactions. Because ofthe dearth ofdata forthesechannels,thecalculationsuseisospinrelationstoextrap- olate from other pion production channels [22,57]. Both NuWro andNEUTusefullcascademodels[58]fortheFSIdescription.The

χ

²/dof valuesforthe NuWroandNEUT comparisonsare25.0/11 and24.9/11forthe

π

⁰momentumand11.8/11and14.0/11forthe

π

⁰ productionangle,respectively.These

χ

² valuesindicatethata commonlevelofagreementisachievedbyallthreegeneratorsfor

π

⁰ momentum,andthatmodestdifferenceswithpredictionsver- susdataareobservedfor

π

⁰ productionangle.

ThereareuncertaintiesintheFSIusedinallcalculations.Each assumesthe pion FSI afterproduction in the nuclear medium is thesameasforpionbeams;thisassumesnomedium effectsbe- yond Fermi momentum and a simple binding energy. Since

π

⁰

beamsarenotpossible,isospinrelationsmustbeusedfor

π

⁰ FSI.

Experimentslike theseare valuable fortesting theseapproxima- tions.Inspiteoftheseuncertainties,thecalculationsgiveadequate descriptionsofthesenewdata.

Figs. 4 and5show decompositionsofthe

π

⁰ momentum and angle spectra of Figs. 2 and 3 according to the FSI channels as

Fig. 5.SamecrosssectiondataasinFig. 3andsamedecompositionaswithFig. 4.

Thestackedhistogramsshowadecompositionofthe1π⁰signalintodifferentFSI channelsaspredictedbyGENIE.

predicted by the GENIE simulation, allowing for a more detailed interpretation.ThisshowshoweachFSIprocesschangesthespec- trumandgivesan indicationofwhat refinementsare neededfor betteragreementwithdata.GENIE predictsthatabout80%ofthe events undergo some FSI. In the momentum spectrum, absorp- tion events(not shownin the spectrumbecause the piondisap- pears in the nucleus) preferentially deplete the region centered at pπ ≈⁰.26 GeV/c, the momentum where the pion-carbon to- tal reactioncrosssection isa maximum[42].Ontheother hand, pion inelastic scatteringandCEX interactions shiftthe pion mo- mentum fromhighvaluesto lower values,thereforecontributing tothebuildupofeventsat pπ≈⁰.2 GeV/c seeninthe data.The contributions frommulti-pionproduction followedby absorption, elasticscattering,andthenon-interactingcomponenthavenono- ticeableeffectonshape.

For the angle spectrum FSI decomposition (Fig. 5) the effects are very different. The interactions displayed in the figure have a small influence on shape and the angular distribution of the (1232)decaybecomesimportant.TheinelasticandCEXinterac- tionsarelargelyresponsibleforthebuildupofeventsatbackward angles.

Comparison of the observed spectral shape in Fig. 4 to the GENIE prediction suggeststhat an increase ininelastic scattering together withcompensating reductionin elastic and/or multiple- pion production with absorption, could improve the agreement withdata.Ontheotherhand,Fig. 5indicatessuchchangeswould worsentheagreementwiththedataforpionproductionatback- wards angles. Thus it appears that a refined description might requireseparate,independentadjustmentstothetwospectra.

Whilethepreviouslyreportedinformationonthereactionstud- iedhereistoolimitedtoenable comparisons,itisusefultocom- pare withtherecentlyreported MINERvAobservations on

ν

μ in- ducedchargedpionproduction[20].Thelatterdatawasobtained usingalow-energyexposureinthesamebeamline,andthecross section normalizations are carried out in a similar way forboth analyses. Existence of both results provides stronger constraints on the calculations. The

π

⁰ momentum range inthis analysis is wider than the range shown for the charged pions of Ref. [20]

(0–1.5 GeV/cversus0.1–0.5 GeV/c)becausethe

π

⁺dataislimited by trackingandparticleidentificationrequirements.Nevertheless, both analyses show that GENIE predictions are significantly im- proved when FSI are accounted for.Both resultsshow a peak in the momentum distribution at pπ≈⁰.2 GeV/c which is seen in the GENIE calculations, but do not have the correct distribution atenergiesnearthispeak.TheGENIEpredictionsfortheabsolute