Neutrino Scattering Uncertainties and their Role in Long Baseline Oscillation Experiments

theirRoleinLongBaselineOscillationExperiments

D.A.Harris4,G.Blazey10,A.Bodek13,D.Boehnlein4,S.Boyd12,W.K.Brooks11,A.Bruell11,H.Budd13,R.Burnstein6,D.Casper2,A.Chakravorty6,7,M.E.Christy5,J.Chvojka13,M.A.C.Cummings10,P.deBarbaro13,D.Drakoulakos1,J.Dunmore2,R.Ent11,H.Gallagher15,D.Gaskell11,R.Gilman14,C.Glashausser14,W.Hinton5,X.Jiang14,T.Kafka15,O.Kamaev6,C.E.Keppel5,11,M.Kostin4,S.Kulagin8,G.Kumbartzki14,S.Manly13,W.A.Mann15,K.McFarland13,W.Melnitchouk11,J.G.Morf´ın4,D.Naples12,J.K.Nelson16,G.Niculescu9,I.Niculescu9,W.Oliver15,V.Paolone12,E.Paschos3,A.Pla-Dalmau4,R.Ransome14,C.Regis2,P.Rubinov4,V.Rykalin10,W.Sakumoto13,P.Shanahan4,N.Solomey6,P.Spentzouris4,P.Stamoulis1,G.Tzanakos1,S.A.Wood11,F.X.Yumiceva16,B.Ziemer2,M.Zois1

1

UniversityofAthens;Athens,Greece

2

UniversityofCalifornia,Irvine;Irvine,California,USA

3

UniversityofDortmund,Dortmund,Germany

4

FermiNationalAcceleratorLaboratory;Batavia,Illinois,USA

5

HamptonUniversity;Hampton,Virginia,USA6

IllinoisInstituteofTechnology;Chicago,Illinois,USA7

SaintXavierUniversity;Chicago,Illinois,USA8

InstituteforNuclearResearch,Moscow,Russia9

JamesMadisonUniversity,Harrisonburg,Virginia,USA10

NorthernIllinoisUniversity;DeKalb,Illinois,USA

11

ThomasJeffersonNationalAcceleratorFacility;NewportNews,Virginia,USA

12

UniversityofPittsburgh;Pittsburgh,Pennsylvania,USA13

UniversityofRochester;Rochester,NewYork,USA

14

Rutgers,TheStateUniversityofNewJersey;Piscataway,NewJersey.USA

15

TuftsUniversity;Boston,Massachusetts,USA

16

WilliamandMaryCollege,Williamsburg,Virginia,USA

ABSTRACT

Thefieldofoscillationphysicsisabouttomakeanenormousleapforwardinstatisticalprecision:firstthroughtheMINOSexperimentinthecomingyear,andlaterthroughtheNOνAandT2Kexperiments.Becauseoftherelativelypoorunderstandingofneutrinointeractionsintheenergyrangesoftheseexperi-ments,therearesystematicsthatcanariseininterpretingfardetectordatathatcanbeaslargeasorevenlargerthantheexpectedstatisticaluncertainties.Wedescribehowthesesystematicerrorsarise,andhowspecificmeasurementsinadedicatedneutrinoscatteringexperimentlikeMINERνAcanreducethecrosssectionsystematicerrorstowellbelowthestatisticalerrors.

arXiv:hep-ex/0410005v1 2 Oct 20041.Introduction

Overthepast5yearsthefieldofneutrinooscillationshasmovedfromseeingdecade-oldanomaliesincosmicray1)andsolar2)neutrinodatatocrosschecksoftheseanomalies(SNOdata3)andangulardistributionsinatmosphericneutrino

data4))andmostrecentlytoterrestrialconfirmationsoftheoscillationhypothesis(Kamland5)andK2K6)).Thenextstepsinthisfieldareto1)movetotheprecisionrealmofmeasurementsofthemasssplittingsandthemixinganglesthathavebeenobserved,and2)toseeifanymoreoff-diagonalelementsintheneutrinomixingmatrixarenon-zero.

Newextremelyintensebeamlinesarebeingbuiltorplannedthatwillgreatlyin-creasethestatisticalreachandultimateprecisiononoscillationparameters.However,withsuchlargeimprovementsinthestatisticalaccuracycomenewconcernsaboutsystematicuncertaintiesthathaveuntilnowbeennegligible.Inparticular,uncertain-tiesinneutrinocrosssectionsandnucleareffectscanproducesystematicuncertaintiesintheextractionofmixingparameters.Althoughneardetectorsareacriticalpartofprecisionlong-baselineoscillationmeasurements,theyarenotoftenwell-suitedtomakealltheneededcrosssectionmeasurements,duetothefactthattheytendtobeverysimilartothemassivefardetectors.Furthermore,aneardetectorcanatbestbeaconstraintontheproductofthenearflux,crosssectionanddetectionef-ficiency.Uncertaintiesonallofthesequantitiesmustbeincorporatedinultimateneardetectoranalyses.Thestudiesdescribedinthisdocumentdonotaddresstheseotheruncertainties,butwhentakenintoaccountclearlyworsenthepredictionfromtheneardetectordatabeyondwhatisdescribedhere.

Thisarticleisdividedintotwosections.Thefirstsectionaddressesthekindsofuncertaintiesthataremostrelevantforνµdisappearanceexperiments,whoseaimistopreciselymeasurethemasssplitting∆m223,andthemixinganglewhichhasalreadybeendeterminedtobelarge,θ23.Inordertoachievethesegoalstheexperimentsmustmeasureoscillationprobabilitiesasafunctionofneutrinoenergy.Twoimpor-tantconcernshereareuncertaintiesinchargedcurrentnon-quasi-elasticprocesses,andthescaleofnucleareffects.Bothnon-quasi-elasticchannelsandthenuclearenvi-ronmentaltertherelationshipbetweenthemeasuredandtrueneutrinoenergy.Thesecondsectionaddressesexperimentssearchingforνeappearance,whichifseenwouldindicateanon-zerovalueofθ13.Becausethesizeofthesignalisunknown,thefinaleventsamplemaybedominatedbybothsignal(chargedcurrent)crosssections,orbybackground(neutralandchargedcurrent)processes.Eitherway,theexperimentsofthepastarenotpreciseenoughtoprovideaccuratepredictionsforthefardetectoreventsamples.

Afterdiscussingthewaysneutrinointeractionuncertaintiesapplytoeachofthesemeasurements,adescriptionisgivenofthekindofneutrinoscatteringmeasurementsthatareneeded.AsanexamplewegivetheexpectedprecisionoftheMINERνAexperiment,whichhasbeenproposedtorunparasiticallyintheNuMIbeamline8).2.νµDisappearance

Inordertopreciselymeasurethemasssplittingbetweentwoeigenstatesonemustmeasuretheoscillationprobabilityasafunctionofneutrinoenergy(Eν)dividedbybaseline(L).Themuonneutrinodisappearanceprobability(inthestandard3-generationoscillationparameterization7))isexpressedas

P(νµ→νµ)=1−cosθ13sin2θ23sin

422

󰀄

2

1.27∆m223(eV)L(km)

ized,butatthetimeofthiswritingawaterCerenkovneardetectorisnotforseenaspartofthefirstphaseoftheexperiment.2.1.KinematicRecontructionofNeutrinoEnergy

Inkinematicreconstructiononeassumesthattheeventisofaparticularprocess(forexample,quasi-elastic)andonecalculatestheenergyassumingthekinematicsofthatreaction.ThisisthetechniquethatisusedpredominantlyinwaterCerenkovdetectors,whichoperatebestinregimeswherethequasi-elasticprocessdominatesthecrosssection.IntheSuper-Kamiokandedetector,forexample,theνµchargedcurrentsignalsampleconsistsofsingleringmuon-likeevents,whicharethenassumedtobequasi-elasticevents.Theenergyoftheincomingneutrinocaninthatcasebecalculatedusingonlytheoutgoingmuonmomentum(pµ)anddirection(θµ),asfollows:

Eν=

mNEµ−m2µ/2

Figure1:TheneutrinoenergydistributionforeventsatT2K,brokenupintovariousprocesses:quasi-elastic,singlepion(Resonance),multi-pion(DIS),andneutralcurrents,for(left)nooscillationsand(right)oscillations

Asisshowninfigure2,thequasi-elasticcrosssectionsthemselvesareknowntoatbestthe10%level,andworseatenergiesofafewGeV17).Currentmeasurementsofthechargedcurrentsinglepionandmultipioncrosssectionscomefromexperimentsdoneinthe80’s18,19),andareknowntoatbestthe20%level20).However,someofthesemeasurementshavecentralvalueswhichdifferbymuchmorethanthetotalerrorbars,andthecrosssectionsweremeasuredonavarietyofneutrinotargets.TheK2Kexperimenthasafine-grainedneardetectorwhichcantrytomeasurethenon-quasi-elastictoquasi-elasticratio.Inreference6)thisratiowasassignedanerrorof20%basedonconsideringdifferentcrosssectionmodelswhichwereallinagreementwiththeirneardetectordata.Onecanseethatthestatisticalerrorforthefinaleventsamplewillbewellabove100eventsintotal,sofutureconstraintsofthisratiowillbeextremelyimportant.

Whatwouldbestreducethisuncertaintyforfutureexperimentsareprecisemea-surementsofboththedifferentialsingle-pionandmultipionchargedcurrentcrosssections,asafunctionofneutrinoenergy.Clearlybecausetheeventsamplesaresodifferentbetweennearandfardetectors,andbecausethewaterCerenkovtechnologyisnotenoughtoconstrainthisratio,additionalmeasurementswithfine-graineddetec-torsarerequired.Ideally,therewouldbemeasurementsofexclusivenon-quasi-elasticfinalstatesidentifiedwithawell-modeledefficiencyrelativetothatofquasi-elasticevents.Becausethereconstructedenergyfortheseeventsislowerthanthetrueneu-trinoenergy,itisimportanttomeasurethechargedcurrentsingleandmulti-pion(resonance)crosssectionsbothatandabovetheT2Kneutrinoenergy.

Byidentifyingboththeoutgoingmuonandprotoninaquasi-elasticevent,andbyrequiringtheretobenootheroutgoingtrack,afine-graineddetectorsuchastheoneproposedbyMINERνAcancleanlyseparatequasielasticeventsinabroadenergyrange,andtheexpectedpurityisabove70%8).In4yearsofparasiticNuMIrunning

ν + n → p + µ, BBA-2003 Form Factors, mA=1.00cm2 )1.41.210.80.60.40.20ν FNAL 83, D2ν ANL 77, D2ν BNL 81, D2ν ANL 73, D2ν SKAT 90, CF3Brν GGM 79, C3H8Fermi Gas,C12,EB=25 MeVν Minerva, C12ν Serpukov 85, Alν GGM 77, CF3Br-38-σ( 10110Eν (GeV)Figure2:CurrentandexpectedMINERνAstatisticalsensitivityforquasi-elasticcrosssection(left)andformfactor(right)measurements,fora4yearparasiticMINOSrun.Left:theopenredtrianglesareinmanyenergybinslargerthanthestatisticalerrorexpectedinMINERνAtakingintoaccountdetectoracceptanceandresolution.

MINERνAhopestocollectabout105Quasielasticeventsperton,andtheexpectedstatisticalerroronthecrosssectionprecisionasafunctionofenergy(aftertakingintoaccountdetectoracceptance,backgrounds,andresolution)isshowninfigure2(left).Figure2(right)showshowMINERνAwouldalsohaveadequatestatisticsandresolutiontodiscriminatebetweentwodifferentmodelsfortheQ2dependenceofthequasi-elasticformfactor,whichagainwillhaverelevanceforthequasi-elastictonon-quasielasticratio.Thesystematicerrorintheenergydependencewouldmostlikelybedominatedbythefluxuncertainty,comingfromtheMIPPdataonhadronproduction21),butisexpectedtobeatthe5%levelatlowenergies.2.3.CalorimetricEnergyReconstruction

Atneutrinoenergieshigherthan1GeV,calorimetricenergyreconstructionisamuchmoreusefultechniquethankinematicreconstruction.Inacalorimetricdevicethereconstructedorvisibleneutrinoenergyissimplythesumofallthesecondaryparticles’energiesthatarevisibleintheevent.Foraνµchargedcurrentevent,themuonenergycanbedeterminedbyfirstmeasuringitsmomentumusingeitherrangeorcurvature(ifthecalorimeterismagnetized),andthentheremainingsignalintheeventissummedtobethehadronenergy.BecausemostcalorimetershaveamuchlowerpionthresholdthanCerenkovdetectors,muchmoreofthetotalkineticenergyisvisibleformulti-pionevents,whichdominatethecrosssectionaboveafewGeV.Asaresult,theneutrinoenergyreconstructionisnotasbiasedfornon-quasi-elasticeventsasitisforwaterCerenkovdetectors.

FortheMINOSdetector,theabsoluteenergyscaleofthemuonsissetbyknowingthethicknessofthesteelplatesandbyunderstandingtheprocessofmuonenergyloss.Thethicknessofeachoftheplateshasbeenmeasuredtobetterthan0.1%andtheyvarywithanRMSof0.4%22).AmuontestbeamwasusedatCERNwherea2%absolutescalecalibrationwasachieved23).ThehadronicandelectromagneticenergyscaleshavebeencalibratedusingtestbeamsonaprototypedetectoratCERN,andhavebeenmeasuredrelativetothemuonscaletobetterthan5%24,25).However,onemusttranslatefromtheresponsefrompionsandmuonstothatofinteracted

neutrinos.

AtneutrinoenergiesofafewGeVandbelow,therearethreeeffectsthatbecomesignificantinthetranslationbetweenbetweenvisibleenergyandneutrinoenergy.Uncertaintiesintheseeffectsmustbeunderstoodandincludedinanyprecisemea-surementof∆m223.Oneeffect,whichisindependentofthetargetnucleus,isthefactthatoftherestmassesthesecondarychargedpionsbecomeimportant.SinceMINOScannotmeasurethemultiplicityoffinalstateparticles,amultiplicitydistributionasafunctionofhadronenergymustbeassumed.Thesecondandthirdeffectsareduetothefactthatsecondaryparticlescaneitherscatterinthenucleusorbecompletelyabsorbed.Allthreeoftheseeffectsresultinareductioninthevisiblehadronenergyinanevent,whichthereforeresultsinalowerreconstructedneutrinoenergy.Asisdescribedinreference26),thesizeoftheseeffectscanbequitelargeastheparentneutrinoenergydecreases,sincethereisapeakinthepionabsorptioncrosssectionforpionsatseveralhundredMeV27).

Inordertoevaluatetheextenttowhichnucleareffectswillaltera∆m223mea-surementinaMINOS-likedetector,acrudedetectorsimulationcombinedwiththeNEUGENeventgenerator28)andNuMIfluxesat735km29)wasused.Inthissimulationthevisibleenergyisdefinedsimplyasthesumofthekineticenergiesofallthechargedfinalstateparticles,plusthetotalenergyfortheneutralpions,andpho-tons,sinceitisassumedtheydepositalltheirenergyintheformofelectromagneticshowers.

Figure3showsthechangesintheratioofvisibletototalneutrinoenergyforchangesinabsorptionandscatteringseparately.Fortheplotontheleftthetargetisassumedtobesteel,andtheparameterintheeventgeneratorthatdescribespionabsorptionissettozeroordoubled.Fortheplotontherightallpionabsorptionisturnedoff,andthedifferencesthatremainareduetotherescatteringeffectsbetweensteel,carbon,andlead.Becausetheνµdisappearanceprobabilityisexpectedtobelarge,thefarandneardetectorenergyspectrawillbeverydifferent,andthereforetheseeffectswillonlypartiallycancelbetweenthenearandfardetector.Theextenttowhichtheydonotcancelresultsinasystematicerroron∆m223.

Ifwetakethetwodifferencesdescribedaboveastheuncertaintiesinpionab-sorptionandrescattering,wecandeterminehowthiswouldcomparetotheMINOSstatisticalerror.Inamorecompleteanalysis,thedetectoracceptancemustalsobetakenintoaccount.Themostimportantcutthatwillreducethesizeofnuclearef-fectscomesfromrequiringthemuontotakeupaminimumenergyintheevent.Thesmallertheneutrinoenergythatcomesfromthehadroncontribution,thesmallerthechangeswhichthenucleareffectuncertaintieswillbringtothetotalneutrinoen-ergymeasurement.However,byrequiringthemuontotakeupmostoftheneutrinoenergy,onewillbelosingpreciousfardetectorstatistics.Intheevaluationofthesystematicerrorsshownhere,aminimummuonenergycutof0.5GeVwasmadetotrytotakeintoaccounttheacceptanceinarealanalysis.Iftheuncertaintiesonnu-cleareffectsareassignedtobethedifferencesshowninfigure3,thenwitha0.5GeVmuonmomentumcuttheyinduceanerrorin∆m223thatisonlyslightlysmallerthanthestatisticalerrorexpectedbyMINOSfor7.6×1020protonsontarget(POT),asshowninfigure4.

Figure3:Ratioofvisible(reconstructed)totrueneutrinoenergyforseveraldifferentmodelsofnucleareffects.Theleftplotshowstheratioforsteel(solid)withthenominalpionabsorption,aswellasthesameratioforthepionabsorptionturnedoffordoubledabovewhatisexpected.Therightplotshowsthedifferencestheratioforthreedifferenttargetnuclei,wherethepionabsorptioneffectsareturnedofftoisolatetheeffectsofpionrescattering.

Figure4:Fractionalsizeofthe90%confidencelevelregionatsin22θ23=1fromstatisticsfortheMINOSexperiment.Alsoshownarepossiblesystematicuncertaintiesduetouncertaintiesinnucleareffects:thedot-dashedlinearethoseeffectsdescribedinthetext,andthedottedlineassumesuncertaintiesafterdedicatednucleareffectmeasurementswherepionrescatteringandabsorptionaremeasuredonthetargetnucleus(steel).Detectoracceptanceismodelledbyrequiringmuonstobeabove0.5GeV.Alsoshownarethestatisticalerrorsfortwodifferentintegratedprotonintensities.

2.4.CurrentandFutureMeasurementsofNuclearEffectsinNeutrinoScatteringEvaluatingtheappropriateuncertaintyinthesizeofnucleareffectsinneutrinoscatteringisnottrivial,becausetheonlydataontheseeffectsinheavynucleicomefromchargedleptonscattering30),andonehastousetheoreticalmodelstotranslatetheeffectsfromthechargedleptonstotheneutralleptons.TheonlyneutrinodatameasuringnucleareffectswithneutrinoscomesfrompionrescatteringmeasurementsonNeandD231).

Inordertomakeaprecisemeasurementofnucleareffectsinneutrinoscatter-ingoneshouldmeasureinteractionsonseveraldifferenttargetnucleisimultaneously,whereoneofthenucleiisthesameasthefardetector,andtheothertargetsspanabroadrangeofatomicnumber.Adetectorwhichcanpreciselyidentifythetargetnucleusevent-by-eventiscritical.Inthiswaythenucleareffectsandtheirenergydependencecanbemeasuredatleastinchargedcurrentinteractions,andgivenadetectorwithgoodenoughxandQ2resolution,thesekinematicdependencescanalsobemeasured.

TheMINERνAexperimenthasproposedafine-graineddetectorwhichwouldmeasureneutrinointeractionsonsteel,carbon,andlead.ByrunningparasiticallyintheNuMIbeamlineforfouryears,theexperimentwouldbeabletocollectabout940keventson8ironandlead,and2.8Meventsoncarbonwithinthefiducialvolumeofthescintillator).Thisenormousimprovementinbothstatisticsandrangeoftargetnucleiwouldchangeourlevelofunderstandingofnucleareffectsinafundamentalway,andgiverealconstraintsonneutrinointeractionmodels.Theuncertaintiesin∆m2error,23effectswiththisnewdatainhandwouldbesmallcomparedtothestatisticalevenforhigherlevelsofintegratedprotonsontarget,asisshowninfigure4.3.νeAppearance

Thegoalofthenextgenerationofneutrinooscillationexperimentsistodeterminewhetherornotthelastunmeasuredneutrinomixingmatrixelement,(called|Ue3|orsinθ13)isnon-zero.Ifθ13isinfactnon-zerothenthereisachancethatfutureexperimentscansearchforCPviolationintheleptonsector.Ifitisnon-zerothenthepossibilityofmeasuringtheneutrinomasshierarchyalsoarises.ForT2KandNOνAprobingthismatrixelementisdonebymeasuringtheνµ→νeoscillationprobabilityata“frequency”correspondingto∆m223.Theoscillationprobabilityforνµ→νeinvacuumcanbeexpressedas7)

P(νµ→νe)=sin2

θ23sin2

2θ13sin

2

󰀄

1.27∆m223(eV2

)L(km)

probabilitymustbelessthanabout5%atthe90%confidencelevel.Also,thereisanintrinsicνecomponentthatcanbeaslargeasafewpercent.Finally,neutralcurrentorhigh-ychargedcurrentνµinteractionscanproduceenergeticneutralpions,whichcaninturnproduceelectromagneticshowersthatfakeaνechargedcurrentevent.TheT2KandNOνAexperimentswillreducethesebackgroundssignificantlybe-lowthatofthecurrentgenerationoflongbaselineexperimentsbyusingdetectorsoptimizedforelectronappearance,andbyplacingthosedetectorsoffthebeamlineaxis.Becauseofthetwobodydecayofthechargedpion,theenergyspectraatsmallangleswithrespecttothebeamlineaxiscanbemorepeakedthanthespectrumonthebeamlineaxis.Also,atthesesmallanglesthepeakenergyitselfisreduced.Thenarrowestneutrinoenergyspectrumoccurswhenthefardetectorisplacedatananglecorrespondingto90◦inthepioncenterofmass.Inthisconfiguration,theνefluxcomesfromthethree-bodydecaysofthemuon,sotheintrinsicνefluxatlowerenergiesdoesnotincreaseathigheranglesliketheνµfluxdoes.Also,theneutralcurrentbackgroundisalwaysasteeplyfallingfunctionofvisibleenergybecausetheoutgoingneutrinoalwaystakessomefractionoftheincomingneutrino’senergy.Withthis“off-axis”strategy,theNOνAandT2Kexperimentsstillexpecttheretobesomebackgroundeventsafteralltheanalysiscutsaremade,evenintheabsenceofνµ→νeoscillations.Themeasurementoftheνµ→νeprobabilityrequiresknowingtheleveloftheremainingbackground,andthecrosssectionanddetectionefficienciesforνeinteractions.

3.1.Quantifyingtheeffectsduetocrosssectionuncertainties

Inordertounderstandwhyprecisecrosssectionmeasurementsareneededforaνeappearanceexperiment,itishelpfultorevisithowexperimentswillmeasuretheνµ→νeoscillationprobability.Thenumberofeventsinthefardetectorcanbedescribedas

Nfar=ΦµP(νµ→νe)σeǫeMfar+Bfar

(4)

whereΦµisthemuonneutrinofluxatthefardetector,Pistheoscillationprobability,σeandǫearetheelectronneutrinocrosssectionandefficiency,respectively,andMfaristhefardetectormass.Thebackgroundatthefardetector,Bfar,canbeexpressedas

Bfar=Σi=e,µΦiP(νi→νi)σiǫiMfar

(5)

Thenotationisthesameasequation4,butǫiistheefficiencyforaneutrinooftypeitobemisreconstructedasanelectronneutrino.Backgroundscomefrombothmuonandelectronneutrinos,andfromseveraldifferentneutrinointeractionchannels.Bothequation4and5mustbesummedoverthosechannels(quasi-elastic,resonance,etc.),aswellasintegratedoverneutrinoenergy.

Theerrorontheoscillationprobability,inthissimplifiednotation,isexpressedas

󰀄

δP

(ΦµσeǫeMfar)2

(δBfar)2

+

󰀂

ΦµσeǫeMfar

(

dΦµ

σe

)2+(

δǫe

abouthowtheeventsamplesarelikelytochangebetweennearandfar.Ataneardetector,thefluxofmuonneutrinoswillhaveaverystrongpeakataparticularenergy,whileatthefardetectorthatpeakwillhaveoscillatedmostlytoντ’s.Attheseenergies,ντ’swillnotproducechargedcurrentevents,onlyneutralcurrentevents.Theneutralcurrenteventsamplesarelikelytobesimilarfromneartofar,providedtheneardetectorisatasimilaroff-axisangle.Theelectronneutrinoeventsatthepeakareprimarilyfrommuondecaysinthebeamline,whichoccuronaveragesubstantiallyfartherdownstreamthanthepiondecays.Therefore,theextrapolationfromtheneartofardetectortendstobedifferentforallthreeeventsamples.Ifonecannotpredictfortheneareventsamplehowmanybackgroundeventsbelongtoeachcategory(duetoanyoftheaboveuncertainties),thefardetectorextrapolationcanbewrong.

Asaquantitativeexampleofhowcrosssectionuncertaintieswouldnotcompletelycancelbetweennearandfardetectors,astudywasdoneusingasimulationforanearlydesign32)oftheNOνAdetector.AlthoughthefinaldesignoftheNOνAdetectorwillbedifferent,thefundamentalargumentswillstillbetrue:therewillbeamixofcontributingcrosssectionsatthefardetectorthatbydefinitioncannotbethesamemixasthatattheneardetector.

Thesignalandbackgroundstatisticsforthenominal5yearrunaregivenintable1.Alsogivenintable1arethefractionsthateachneutrinointeractionprocesscontributestotheeventsofthattypethatpassallcuts,aswellasthecrosssectionuncertaintyonthatprocess,astabulatedinreference20).Withoutaneardetector,thetotalerroronthebackgroundpredictionfromcrosssectionuncertainties,forthecasethattherearenoνµoscillations,is16%,whichisequivalenttothestatisticalerrorforthatcase.Forthecaseofmixingatthelevelindicatedinthetable,thestatisticalerrorontheprobabilitywouldbe8%,whiletheerrorsfromcrosssectionuncertaintiesalonewouldbe31%.

QE20%

Statistics

175(sin22θ13=0.1)

15.43.619.1

COH100%

infardetector35%10%50%30%65%35%40%10%

Table1:ListofthesignalandbackgroundprocessesthancancontributeeventsintheNOνAfar

detector,fora50ktondetectorlocated12kmfromtheNuMIaxis,820kmfromFermilab,assuming

−3

a∆m2eV2.Alsogivenarethecurrentcrosssectionuncertaintiesonthoseprocesses.23of2.5×10

“n/I”indicatesthatthechargedcurrentcoherentprocesswasnotincluded,sinceitisexpectedtobesmallcomparedtootherchargedcurrentprocesses.

Figure5showsthefractionalerroronthefardetectorpredictionasafunctionoftheanglebetweenthebeamlineandtheneardetector,fortwodifferentextremes:

Figure5:Thefractionalerrorintheeventratesatthefardetectorfromuncertaintiesineachprocess(Quasi-elastic,resonance,deepinelasticscattering,andneutralcurrentcoherentπ0production),addedinquadratureforeachsource(neutralcurrent,νµchargedcurrent,beamνe),plottedasafunctionoftheanglebetweentheneardetectorandthebeamlineaxis,for(left)background-dominatedexperimentand(right)signal-dominatedexperiment.

theleftplotshowsthecasewheretheνµ→νeprobabilityiszero(correspondingtothebackground-limitedexperiment),andtherightplotshowsthecasewheretheprobabilityisatabout5%(orsin22θ13=0.1,correspondingtothesignal-dominatedexperiment).Forlowanglestheerrorduetothehighyνµchargedcurrentuncertain-tiesissmallest.Forhighanglestheerrorsduetoneutralcurrentuncertaintiesandlowyνechargedcurrentuncertaintiesarethesmallest.

Theerrorsforeachofthethreebackgroundcontributionsareshown,wheretheerrorsduetoquasi-elastic,resonance,DIS,andcoherentcrosssectionuncertaintiesareaddedinquadrature.Inthecaseofthebackground-dominatedexperiment,thecrosssectionerrorsalonearecomparablenolessthanhalftheexpectedstatisticalerrorofabout15%.Forthesignal-dominatedexperiment,thecrosssectionatbestafactoroftwoworsethantheexpectedstatisticalerrorof7%.3.3.FutureMeasurementsofLowEnergyCrossSections

Giventhelowstatistics,discrepantdata,andlimitedreachintargetnucleiforchargedandneutralcurrentcrosssectionmeasurements,thereisclearlymuchworktobedone.Sectiondescribedthecrosssectionuncertaintiesforquasi-elasticandresonancechargedcurrentprocesses,anddescribedhowMINERνAcouldprovideanaccuratequasi-elasticcrosssectionmeasurement.Forνeappearancemeasurementsthechargedcurrentcrosssectionsareimportantincaseofalargesignal.Regardlessofsignalsize,however,theneutralcurrentcrosssectionsareimportantsincetheyareverypoorlyknownnow.Insomecasesthebeststrategywillbetomeasurethechargedcurrentanalogasafunctionofneutrinoenergy,anddependontheorycombinedwithanaverageneutralcurrentmeasurementtopredicttheneutralcurrentcrosssectionasafunctionofneutrinoenergy.Recentneutralcurrentmeasurementshavebeennormalizedtodifferentchargedcurrentchannels:forexample,theratioofsingleπ0productioninneutralcurrentstothetotalνµchargedcurrentcrosssection

Figure6:Thefractionalerrorinthetotaleventrateatthefardetectorfrompost-MINERνAuncertaintiesineachprocessasafunctionoftheanglebetweentheneardetectorandthebeamlineaxis,forthecasewheretheνµ→νeprobabilityis0(left)or5%(right).

hasbeenmeasuredtoabout11%bytheK2Kcollaboration33).

Withanappropriatedesignthatwouldincludebothfine-grainedfullyactivetar-getsurroundedbyelectromagneticandhadroniccalorimetry,theuncertaintiesonthesecrosssectionscouldbeimprovedbyfactorsof5ormore.Asanexample,theMINERνAexperimentproposestoreducetherelevantcrosssectionuncertaintiesforNOνAtoabout5%forallofthechargedcurrentandneutralcurrentDISprocesses,10%fortheneutralcurrentresonanceprocesses,and20%fortheneutralcurrentcoherentπ0processes8).Butbeforedescribinghowthesemeasurementswouldbemade,itisstrikingtoseehowmuchthesemeasurementswouldreducethesystematicerrorsshowninfigure5.

Iftheuncertaintiesdescribedabovewereachieved,thenthesystematicerrorsduetocrosssectionuncertaintieswouldbewellbelowthestatisticalerrors,asshowninfigure6.Forthebackground-dominatedexperiment(left),thesystematicerrorwouldbeaboutafactoroftenlessthanthestatisticalerror,andforthesignal-dominatedexperiment(right)thesystematicerrorwouldbeafactorofthreebelowthestatisticalerror.

Theremainderofthisarticledescribesstrategiesforisolatingtheresonantandco-herentcrosssectionsintheMINERνAdetector,andtheexpectedstatisticalprecisioninafouryearrun.

3.3.1.ResonanceCrossSections

Resonanceproductioninneutrinoscatteringisextremelyimportantforfuturelongbaselineneutrinooscillationexperiments,butitscrosssectionisonlyknownataboutthe40%levelforthechargedcurrentprocess34)at2GeV,andmuchworsefortheneutralcurrentprocess35).

Resonanceproductioncanbestudiedindetailwithafine-grainedexperimentwithgoodvertexingabilitiesandalowthresholdforseeingpions.Byrequiringanoutgoingmuon,pion,andproton,MINERνAexpectstofullyreconstructalargefractionofthe2×105chargedcurrentresonanceeventsthatwilloccurinthedetector,which

wouldenablenotonlyaprecisecrosssectionmeasurementasafunctionofenergy,butalsoenoughstatisticstomeasuretheW2distributions.Withgoodneutralandchargedpionidentificationtheindividualstatescontainingbothchargedandneutralpionscanbeclearlyseen,whichinturnareimportantforνµdisappearanceandνeappearance,respectively.

Bymeasuringchargedandneutralcurrentresonanceproductionandcombiningthiswiththeenergyinformationfromthechargedcurrentresonanceproduction,modelsthatrelatechargedtoneutralcurrentswillbetested,andprecisepredictionsfortheneutralcurrentprocesseswillbecomeavailable.3.3.2.CoherentCrosssections

Theprocessbywhichaneutrinointeractswithanucleuscoherentlyandproducesonlyaneutralpion(intheneutralcurrentprocess)oramuonandachargedpion(inthechargedcurrentprocess)isperhapstheprocessthemostpoorlymeasuredyetstillseen.Ahandfulofmeasurementsexistatthefewsigmalevelinboththeneutral(37))andcharged(38))currentchannels,asshowninfigure7(left).Althoughthecrosssectionforthisprocessislow,itshighuncertaintyandthehighprobabilitythatcoherenteventspassνeanalysiscutsmeansthatthischannelwillcontributeasignificantuncertaintyintheneutralcurrentbackground.Furthermore,becauseitisaninteractionthatdoesnotbreakupthenucleus,thenucleareffectsonthecrosssectionareimportant.

Coherentchargedcurrenteventscanbeidentifiedbylookingattheenergylossofthetwotracksandrequiringittobeconsistentwiththepresenceofamuonandapion,andnothingelse.Thebackgroundwouldcomefromincoherentprocesseswhereotherparticles(forexampleaproton)werelost.Coherentneutralcurrenteventswouldbeidentifiedbylookingfortwoelectromagneticshowerswhichreconstructtothepioninvariantmass.Backgroundsherewouldcomeagainfromincoherentprocesses,andareexpectedtobelargerbecauseseveralprocessesproduceatleastoneneutralpion.Theneutralcurrentcoherentsamplecanbeseparatedstatisticallybylookingatthedistributionofthereconstructedangleoftheneutralpionwithrespecttotheneutrinodirectionandsubtractingthebackgroundundertheforwardscatteringpeak.

TheMINERνAexperimentrunningintheNuMIbeamlinewouldcollectoverathousandchargedandneutralcurrentcoherenteventsina3-tonfiducialvolumeperyear,resultinginaprecisemeasurementasafunctionofneutrinoenergyforthechargedcurrentprocess.Figure7showsboththeenergy(left)andatomicnumber(right)dependencethatcouldbemeasuredbyMINERνAinthechargedcurrentchannelalongwiththecurrentsetofmeasurements.Byusingtheoryandthehighstatisticsneutralcurrentdataonecouldobtainatleastafactoroffiveimprovementintheprecisionontheneutralcurrentcoherentbackgroundprediction.4.Conclusions

Itisclearfromeventhesepreliminarystudiesthatdedicatedneutrinoscattering

CC Coherent Pion Production Cross Section

σ (10-40 CM2)/12C NUCLEUS500

A-Dependence of 5 GeV CC Coherent Cross-Section2.252

400

1.75σ(10-38 cm2/nucleus)1.5300

1.251

200

0.750.5100

0.25002.557.51012.51517.52000255075100125150175200Eν (GEV)

A of Target Nucleus

Figure7:ExpectedMINERνAstatisticalsensitivityforthechargedcurrentcoherentcrosssectionenergy(left)andA(right)dependencemeasurements,fora4yearparasiticMINOSrun,takingintoaccountdetectoracceptance.

experimentssuchasMINERνAwillplayaveryimportantroleinhelpingthecurrentandfutureprecisionoscillationexperimentsreachtheirultimatesensitivity.Inordertogetthemostprecisevaluesof∆m223(whicheventuallyisusedtoextractmixinganglesandtheCP-violatingphase)thisfieldmustbetterunderstandandquantifytheprocessesthatoccurbetweentheinteractionofanincomingneutrinoandthemeasurementoftheoutgoingparticlesinthedetectors.AlthoughtheissuesaredifferentdependingonwhetherthosedetectorsarewaterCerenkovorcalorimetricdevices,inbothcasesmoreinformationisneeded.Extractingthemixingparameterssuchasθ13andultimatelytheneutrinomasshierarchyandCPviolationrequiresmuchbetterunderstandingofresonantcrosssections.Evensettinglimitsontheseparameterswillrequirebettermeasurementsofneutralcurrentprocesses.Precisemeasurementsofnucleareffectsandexclusivecrosssectionswilllayanimportantfoundationforafieldthatisinthemiddleofmakingorderofmagnitudeleapsinbothstatisticsandsensivitity.5.References

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