Prospects for measuring coherent neutrino-nucleus elastic scattering at a stopped-pion neut

stopped-pionneutrinosource

KateScholberg1

1

DepartmentofPhysics,DukeUniversity,Durham,NC27708USA

(Dated:February7,2008)

Ratesofcoherentneutrino-nucleuselasticscatteringatahigh-intensitystopped-pionneutrinosourceinvariousdetectormaterials(relevantfornovellow-thresholddetectors)arecalculated.Sen-sitivityofacoherentneutrino-nucleuselasticscatteringexperimenttonewphysicsisalsoexplored.

PACSnumbers:13.15.+g,13.40.Em,23.40.Bw

I.INTRODUCTION

Coherentelasticneutralcurrent(NC)neutrino-nucleusscattering[1,2]hasneverbeenobserved.Inthisprocess,aneutrinoofanyflavorscattersoffanucleusatlowmomentumtransferQsuchthatthenucleonwavefunctionamplitudesareinphaseandaddcoherently.Thecrosssectionforaspin-zeronu-cleus,neglectingradiativecorrections,isgivenby[3],󰀈dσ

Q2w

2π

k2

󰀃

,(1)

wherekistheincidentneutrinoenergy,Eisthe

nuclearrecoilenergy,Misthenuclearmass,Fisthegroundstateelasticformfactor,Qwistheweaknuclearcharge,andGFistheFermiconstant.The

conditionforcoherencerequiresthatQ<∼

1

xulF0.0350.03νµ (delayed)νe (delayed)0.025νµ (prompt)0.020.0150.010.005001020304050Neutrino energy (MeV)FIG.1:Shapeofneutrinospectrafromastopped-pionsource,forthedifferentproducedflavors.

Hereprospectsformeasuringcoherentelasticneutrino-nucleusscatteringwillbeevaluatedusingparametersrelevantfortheSNS;howevertheresultsshouldbegenerallyapplicabletoexperimentsatanyhigh-intensitystopped-pionνsource.

II.

EXPECTEDEVENTRATES

Theexpectedrateofinteractionsdifferentialinrecoilenergyisgivenby

dN

dE(k),

(2)

whereNtisthenumberoftargetsandφ(k)istheincidentneutrinoflux.Spectraforνµ,ν¯µandνe

fora2stoppedπ+/µ+

source,assuming∼107νs−1cm−perflavorat20mfromthesourceareassumed.Cross40

sectionsandformfactorsfrom[3,26]for20Ne,Ar,76Ge,and132Xeareused.Figs.2through5showtheresults.Theratesarequitepromising:foraton-scaledetectorwithafewto10keVthreshold,104−105signaleventsperyearareexpected.Evenforkilogram-scaledetectors,eventratesmaybeinthetensperyear.

Fig.6plotsintegratedyieldoverthresholdforsev-eralelementsforcomparison.Onecanseethatthehigherthenuclearmass,thehighertheoveralleventrateatlowthreshold(scalingapproximatelyasthesquareofthenumberofneutrons),butthesmallerthetypicalrecoilenergies(Emax=2k2/M).

Intheabsenceofaspecificdetectormodel,per-fectdetectionefficiencyandzerobackgroundareassumed,whichisnotrealistic.Detectioneffi-cienciesformanylow-thresholddetectortypes(seeSec.I)canbereasonablyhigh,butcandependonbackgroundlevels.Backgroundswillincludebeam-relatedneutrons,cosmogenics,radioactivityandin-strumentalbackground,aswellasotherCCandNC

2

3SNS spectrum, Nen×10ot 8reprompt (νp7µ) ry 6rdelayed (νµ+ νe)ep 5hse4rht3 rev2o st1nevE50100150200Threshold (keV)250not60 reνµ (prompt)p 50rνye (delayed) re40νµ (delayed)p Vek30 rep20 stne10vE50100150200Recoil energy (keV)250FIG.2:Bottompanel:DifferentialyieldattheSNSin1tonof20Ne(solid:νµ,dotted:νe,dashed:ν¯µ)peryearperkeV,asafunctionofrecoilenergy.Toppanel:Numberofinteractionsoverrecoilenergythresholdin1tonof20Nefor1yrofrunningattheSNS(solid:νµ,dashed:sumofνeandν¯µ),asafunctionofrecoilenergythreshold.

×103SNS spectrum, Arnot r18e16prompt (νpµ) ry 14rdelayed (νµ+ νe)ep12 hs10erh8t re6vo4 stn2evE20406080100Threshold (keV)120140no300t reνp250νµ (prompt) ry re200νe (delayed)µ (delayed)p Ve150k rep100 stne50vE20406080100Recoil energy (keV)120140FIG.3:AsinFig.2for

40

Ar.

neutrinoreactions;thesewillneedtobeevaluatedforaspecificdetector’srejectioncapabilitiesandlo-cation.Backgroundsarenotobviouslyoverwhelm-ing,especiallygiventhatthepulsedstructureofthebeamsuchasthatattheSNSleadstoapowerfulre-jectionfactor(∼4×10−4)againststeady-stateback-grounds.Itisnotreallyclearatthispointwhetherbeam-relatedbackgroundswillbeworseforpromptordelayedneutrinos;itwilldependonshieldingand

n×103SNS spectrum, Geot 35reprompt (νpµ) 30ry rdelayed (νµ+ νe)e25p h20serh15t re10vo s5tnevE102030405060Threshold (keV)70n×103ot1.2 reνp 1rνµ (prompt)ye (delayed) re0.8νµ (delayed)p Vek0.6 rep0.4 stne0.2vE1020304050Recoil energy (keV)6070FIG.4:AsinFig.2for

76

Ge.

×103SNS spectrum, Xeno60t reprompt (νpµ) 50ry rdelayed (νµ+ νe)e40p hse30rht r20evo s10tnevE5101520253035Threshold (keV)4045n×103o4t re3.5νµ (prompt)p rνy3e (delayed) rep2.5νµ (delayed) Ve2k re1.5p st1nev0.5E51015202530Recoil energy (keV)354045FIG.5:AsinFig.2for

132

Xe.

detectorlocation.Thereforethecontributionsfrompromptanddelayedfluxesaregivenseparately.

III.PHYSICSPOTENTIAL

Theneutrino-nucleuscoherentelasticscatteringcrosssectioniscleanlypredictedbytheStandardModel(SM);formfactorscanbeknowntobetterthan5%,andradiativecorrectionsareknownatthepercentlevel[27].Anymeasureddeviationsfrompredictionwouldbeinteresting[28].Inthecon-textoftheSM,theweakmixingangleisrelatedtotheabsolutescatteringrate.Onecanalsoconstrain

3

n×103ot 50reDelayed (νµ+ νe), Nep ry40Delayed (ν µ+ νe), Arrep Delayed (νh30µ+ νe), GeserDelayed (νµ+ νe), Xeht20 revo 10stnevE1102Threshold (keV) 10n×103o22t re20Prompt (νµ), Nep 18ry16Prompt (ν µ), Arrep14 Prompt (ν12µ), Gehser10Prompt (νµ), Xeht 8rev6o 4stn2evE1102Threshold (keV) 10FIG.6:Thenumberofinteractionsovertherecoilenergythresholdforvariousdetectormaterials(bottompanel:promptνµ,toppanel:sumofdelayedνeandν¯µ).

non-standardinteractions(NSI)ofneutrinosandnu-cleons.Also,non-zeroneutrinomagneticmomentwillmodifythecrosssectionatlowenergies.Therearefurtherreasonstomeasurecoherentneutrino-nucleusscattering:neutrino-nucleusscatteringpro-cessesareimportantinsupernovaphysics[1],aswellasbeingusefulthemselvesforsupernovaneutrinodetection[3].Becausetheyareflavorblind,NCprocessesallowmeasurementoftotalneutrinoflux,whichcanbecomparedtoindependentlymeasuredCCinteractions.Thereforeonecanobtainlimitsonneutrinooscillation,andinparticularonoscilla-tionstosterileneutrinos[29].Finally,ithasevenbeenproposedtoexploitthelargecrosssectionsofneutrino-nucleusscatteringforpracticalneutrinode-tectors,e.g.reactormonitoring[5,6].

Thissectionwilldiscussthevariouswaysofprob-ingnewphysicswithacoherentelasticscatteringex-periment.Atthisstage,theexperimentalsystematicuncertaintyontheabsoluterateisnotknown.Itwilldependonthespecificdetectortypeandconfigura-tion,backgrounds,andsourceuncertainties.How-everatotalsystematicuncertaintyof∼10%(includ-ingnuclear,beamanddetector-relateduncertain-ties),whileperhapsoptimistic,maywellbeachiev-able.Systematicuncertaintieswilllikelydominateatthefewtensofakilogramscaleorgreater.

A.

WeakMixingAngle

TheSMpredictsacoherentelasticscatteringrateproportionaltoQ2w,theweakchargegivenbyQw=N−(1−4sin2

θW)Z,whereZisthenumberofpro-tons,NisthenumberofneutronsandθWistheweakmixingangle.Thereforetheweakmixinganglecanbeextractedfromthemeasuredabsolutecrosssection,atatypicalQvalueof0.04GeV/c2.Ade-viationfromtheSMpredictioncouldindicatenewphysics.

Iftheabsolutecrosssectioncanbemeasuredto10%,therewillbeanuncertaintyonsin2θWof∼5%.Thisisnotcompetitivewiththecurrentbestmeasurementsfromatomicparityviolation[30,31],SLACE158[32]andNuTeV[33],whichhavebetterthanpercent-leveluncertainties.Onewouldneedtosignificantlyimprovethesystematicuncertaintyontheabsoluterate(perhapsbynormalizingwithawell-knownrate)forcoherentelasticνAscatteringinordertomakeausefulmeasurementoftheweakmixingangle.Morepromisingwouldbeasearchfornon-standardinteractionsofneutrinoswithnuclei,asdescribedinthefollowingsubsection.

B.Non-StandardInteractionsofNeutrinos

Existingprecisionmeasurementsoftheweakmix-ingangleatlowQdonotconstrainnewphysics

whichisspecifictoneutrino-nucleoninteractions.Hereamodel-independentparameterizationofnon-standardcontributionstothecrosssectionisused,followingRefs.[34,35].Inthisdescription,oneassumesaneffectiveLagrangianforinteractionofaneutrinowithahadron:

LNSIνH=−GF

2

󰀅

[¯ναγµ(1−γ5)νβ]×(3)

q=u,d

α,β=e,µ,τ

(εqLαβ[¯

qγµ(1−γ5)q]+

εqRαβ[¯

qγµ(1+γ5)q]).

Theεparametersdescribeeither“non-universal”(α=β)orflavor-changing(α=β)interactions.AsinRef.[34],nucleiwithtotalspinzero,andforwhichsumofprotonspinsandsumofneutronspinsisalsozero,areconsidered;inthiscasesensitivitytovectorcouplings,εqVqLqR

wehave

crosssectionforcoherentNCαβ=εelasticαβ+εscatteringαβ.Theofneutrinosofflavorαoffsuchaspin-zeronucleusisgivenby

4

󰀈

dσ

π

F2(2ME)󰀂

1−

ME

−2sin2θW),

gnV=−1

2

−1<εuLee<0.3

CHARMνeN,ν¯eNscattering−0.4<εuRee<0.7−0.3<εdLee<0.3

CHARMνeN,ν¯eNscattering−0.6<εdR

ee<0.5|εuLµµ|<0.003NuTeVνN,ν¯Nscattering−0.008<εuRµµ<0.003

|εdL

µµ|<0.003NuTeVνN,ν¯Nscattering−0.008<εdRµµ<0.015

|εuP

eµ|<7.7×10−4

µ→econversiononnuclei

|εdPeµ|<7.7×10

−4

µ→econversiononnuclei|εuPeτ|<0.5CHARMνeN,ν¯eNscattering|εdPeτ|<0.5CHARMνeN,ν¯eNscattering|εuP

µτ|<0.05NuTeVνN,ν¯Nscattering|εdPµτ|<0.05

NuTeVνN,ν¯Nscattering

Fromthistable,onecanseethatofthesepa-rameters,εeeandεeτarequitepoorlyconstrained:valuesoforderunityareallowed.|εµβ|couplingsare,however,constrainedtobetterthan0.05.Giventhissituation,thefocushereisonεeeandεeτcou-plings[38].Thesewouldbeaccessibleusingtheelec-tronflavorcomponentofthesource.Thatnooscil-lationstakeplace(i.e.thatthestandardthree-flavormodelofneutrinomixingholds,andthatthebase-lineistooshortforsignificantflavortransition)isalsoassumed.

ThesignatureofNSIisadeviationfromtheex-pectedcrosssection.Thefollowingshowafewex-

5

amplesoftwo-dimensionalslicesofregionsinεαβparameterspacethatwouldbeallowedifonemea-suredexactlytheSMexpectation.

Fig.7shows90%C.L.allowedregionsonewould

dV

drawforεuVee,εee,iftheratepredictedbytheSMweremeasuredforthedelayedflux(whichcontainsνe),assumingthattheεµβparametersarenegligible,andforεqVeτ=0,for100kg-yrofrunningofaneondetectorat20mfromthesource.A10keVthresh-oldisassumed.Thiscalculationconsidersonlythetotaldelayed(νe+ν¯µ)fluxrate[39].Theregionscorrespondingtoassumptionsof5%and10%sys-tematicerrorinadditiontostatisticalerror,andforstatisticalerroraloneareshown[40].Asbe-fore,aperfectlyefficient,background-freedetectorisassumed.

NotethatinEq.4,eveninthepresenceofnon-universalNSI,onecanobtainratesidenticaltotheSMpredictioninthecasethat

pdVdVnuVZ(gV+2εuVee+εee)+N(gV+εee+2εee)(5)

pn

=±(ZgV+NgV),

sofor

εuVee=−

(A+N)

(A+Z)

εdVee

−

pn2(ZgV+NgV)

FIG.9:Allowedregionat90%C.L.forεdVeeandεdV

eτ,for

100kg-yrof20

NeattheSNS.Theshadedregionbetweentheouterandinnerellipsescorrespondstoanassumedsystematicuncertaintyof10%inadditiontostatisticaluncertainty;thenextlargestregioncorrespondstoanassumedsystematicuncertaintyof5%,andtheinnerregioncorrespondstostatisticaluncertaintyonly.

FIG.10:Allowedregionswithsameassumptionsas

Fig.9,13210%systematicuncertainty,for20Ne(shadedre-gion),Xe(regionbetweenpalelines)andbothcom-bined(regionbetweenblacklines).

andatmosphericneutrinos[36].

Itisworthnotingthatacoherentneutrino-nucleuselasticscatteringexperimentwillprovidesignifi-cantconstraintsonstill-allowedNSIparametersthatmodifysolarneutrinosurvivalprobabilities[37].Asacaseinpoint,considerspecificNSIparameters

6

FIG.εuV11:ee=εuVAllowedregionat90%C.L.fordV

eτ=0,for100kg-yreachof20εdVeeandNeand132εeτ,XeattheSNSisshowninblack.Theshadedregioncorre-spondstoasliceofallowedNSIforεττ=0,andεeVee=εeV

parametersfromRef.[36]

eτ=0;theparabolicregionsinsidethedarkandlightlinescorrespondtoslicesofal-lowedparameterspaceforsomespecificvaluesofεeVeeandεeVeτ

.thatyieldthe“LMA-0”solutionofRef.[37]:εuVεdV11=−0.065,andεuV12=εdV

11=12=−0.15,whereε11=εee−εττsin2θ23,andε12=−2εeτsinθ23,andθ23istheatmosphericmixingangle,knowntobe∼π/4.Followingtheapproachinthisref-erence,εuVαβ=εdV

αβisassumed.

Fixingε11andε12definedinthiswaywillyielddifferentneutrino-nucleusscatteringconstraintsfordifferentassump-tionsofεττ.Fig.12showsthevalueofaχ2de-fineduVasχ2=(NNSI−NSM)2/σ2,asafunctionof

εττ=εdV

ττ;NNSIisthenumberofsignaleventsforthegivenNSIparameters,20andNSMistheSMex-pectation,for100kg-yrofNeat10keVthreshold;σ2includesbothstatisticaluncertaintyandanas-sumed10%systematicuncertainty.Superimposedonthisplotasashadedregionistherestriction

onε(τu,dτ)V

(givenassumptionsabove,andεeVαβ=0)

from󰀄󰀄

beamand󰀄1+εee+εττ−

󰀆atmosphericneutrinooscillations,2χ8765432100.10.20.30.40.5∈(u,d)VττFIG.12:χ2asafunctionofετ(u,dτ

)V

for100kg-yrsof20

Ne,assumingNSIparametersε(u,d)V=−0.065andε(u,d)V

11

=−0.15.Theshadedregionrepresentsallowedε12

ττparametersfromRef.[36],frombeamandatmo-sphericneutrinooscillationconstraints.

TheconclusionoftheseNSIstudiesisthatacoherentelasticneutrino-nucleusscatteringexperi-mentatastopped-pionsourcewouldhavesignificant

sensitivitytocurrently-allowedNSIεqVrameters.

eeandεqV

eτpa-C.NeutrinoMagneticMoment

TheSMpredictsaneutrinomagneticmomentofµν≤10−19µB(mν/1eV),inunitsofBohrmagne-tons.Thisisverysmall,butextensionsoftheSMcommonlypredictlargerones.Themoststringentlimitsareastrophysical:forinstance,basedonlackofobservedenergylossfromelectromagneticcou-plingsinredgiantevolutiononecansetalimitµν≤10−12µB[43].Thebestdirectexperimen-tallimitsresultfromlackofdistortionofneutrino-electronelasticscatteringatlowenergy,andareintherangeofµν(νe)≤1−2×10−10µB[44,45,46].Formuonneutrinoscattering,thebestlimitislessstringent:µν(νµ)≤6.8×10−10µB[47].

Asignatureofnon-zeroneutrinomagneticmo-mentcanbeobservedviadistortionoftherecoilspectrumofcoherentlyscatterednuclei.Themag-neticscatteringcrosssectionisgiveninRef.[48]foraspin-zeronucleus:

󰀈dσ

1−E/k

m2e

󰀈4k2

󰀁

.(6)

7

Fig.13shows20thedifferentialcrosssectionscal-culatedforNe,for30MeVneutrinoenergy,asafunctionofnuclearrecoilenergy.Themagneticscat-teringcrosssectioniscalculatedforneutrinomag-neticmomentjustbelowthecurrentbestexperi-mentallimits(10−10µBforνeand6×10−10µBforνµ).

ν-nucleus scattering at 30 MeV, Ne)210-37mc1 -Ve10-38SMM( noitc10-39es-10-sµν=6 × 10so10-40rC10-41µν=1 × 10-1010-420.0020.0040.0060.0080.010.0120.0140.0160.0180.02MeVFIG.13:Solidline:SMcoherentneutrino-nucleusdiffer-entialcrosssection,asafunctionofnuclearrecoilenergy

E,forneutrinoenergyk=30MeVandfora20Netar-get.Dashedline:differentialcrosssectionforneutrino-nucleusscatteringduetoaneutrinomagneticmomentofµν=10−10µB.Dottedline:differentialcrosssectionforneutrino-nucleusscatteringduetoaneutrinomagneticmomentofµν=6×10−10µB.

Fig.14showstheyieldineventsperkeVofrecoil

energy,pertonperyearinaneondetectorat20mfromtheSNStarget,withandwithoutneutrinomagneticmomentcontribution,forpromptandde-layedfluxes.Thedashedlineassumesνµ=10−10µBforbothνeandν¯µ.Thedottedlineassumesνµ=10−10

µBforνeandνµ=6×10−10µBforν¯µ.Thedifferenceincoherentneutrino-nucleusscat-teringyieldduetopresenceofaneutrinomagneticmomentnearthecurrentµνlimitforνeisverysmall,exceptforrecoilenergiesbelowafewkeV.Thissig-nalisthereforelikelyoutofreachforaCLEAN-typeexperimentattheSNS.However,forµνnearthecur-rentlimitforνµ,theremightbeameasurablesignalfora10keVthreshold,anditisconceivablethatonecouldimprovethelimitwithahigh-statisticsmeasurement.Nucleiwithspin,althoughnotcon-sideredhere,haveadditionalµν-dependenttermsintheircoherentneutrino-nucleusscatteringcrosssec-tions[48]andmaybepotentialtargetsforaneutrinomagneticmomentsearch[49]

8

Events per keV per yr per ton2001801601401201008060402010-410-3Prompt fluxSM-10µν=1 × 10-10µν=6 × 10µ10-210-1MeVEvents per keV per yr per ton2001801601401201008060402010-410-3Delayed fluxverypromising.Evenfewkilogram-scaleexperi-mentsmayhavemeasurablerates.Theseestimateshavebeenmadeforanexperimentwithnoback-groundandnoinefficiency;bothwillcertainlybeimportantforarealexperiment.Sensitivitieswillneedtobereevaluatedforaspecificdetectorconfig-urationforwhichbackgroundsandefficienciescanbeestimated.

Unambiguousdetectionoftheprocessisafirststep;highstatisticsmeasurementswillthenfollow.Suchanexperimenthassignificantpotentialforcon-strainingNSIparameters;magneticmomentandprecisionweakmixinganglemeasurementsarealsoconceivable,althoughposeagreaterexperimentalchallenge.

10-210-1MeVFIG.14:DifferentialyieldattheSNSinneonasafunc-tionofnuclearrecoilenergy.Thetopplotisforthepromptflux(νµonly)andthebottomplotisforthedelayedflux(sumofνeandν¯µ).Solidlines:SMexpec-tation.Dashedlines:yieldincludingmagneticmomentcontributionforµν=10−10µBforbothνeandν¯µ.Dot-tedlines:yieldincludingmagneticmomentcontributionforµν=10−10µBforνeandµν=6×10−10µBforν¯µ,νµ.

Acknowledgments

IV.CONCLUSION

Straightforwardcalculationsindicatethatoneex-pectsthousandsofcoherentneutrino-nucleusinter-actionswithrecoilenergies>10keVpertonofmaterialperyearofrunningattheSNS,whichis

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Notethataneutrino-electronmagneticscatteringsearchcaninprinciplebedoneattheSNSwithlowthresholddetectors.Theνemagnetic2scatteringcross-sectionissmallerbyafactorofZthanforneutrino-nucleus,butthereareafactorofZmoreelectrontargets,sothesignalisoverallafactorof10smallerthanforνA.Thisamountsto∼10νemagneticscatteringeventspertonperyearattheSNSabove10keV,forµνatthecurrentνµlimit.TheνemagneticsignalhasnegligibleSMback-ground;howeverabsoluteratesarelowforrealistictargetmassesandlikelytobesubjecttoexperimen-talbackgrounds.