OscillationofatmosphericneutrinosacrosstheEarth:
preliminaryassessmentofsensitivitytomasshierarchyandCPasymmetry
SandroPalestini,CERN17October2018
BasedonworkdoneincollaborationwithAraIoannisyan andGordonLeeMang Hei (CERNsummerstudent2018)
• MattereffectsprovidetheopportunitytoextendthephysicsprogramofDUNEbeyondtheneutrinobeamscenario.• Consideranearly-emptyEarth(density0.04g/cm3),torecognizevacuumoscillations:
OscillationprobabilityP(nue->nue)
Enu logscale,0.15to10GeV
Probabilitycomponent,-0.5to1.5
Withsomeassumptionsonenergy,angleresolutions(fast(slow)oscillationsdumpedbelow3(0.25)GeV)
Markingbarsat0.15,0.43,1.2,3.5,10GeV,5,30,60,90degrees.
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Sameoscillationnowforrho=4g/cm3:
• 1st resonancesataboutE=0.1GeV,• flattenedbehaviorin0.5-1.5GeV• 2nd resonanceataboutE=8GeV
• Vacuumoscillationparametersatusualvalues,deltaCP=270deg usedhere
References,assumptionsmadethroughoutthisstudy:- OscillationsprobabilityismatterfromAra’spaper- Earthdensitytakenhomogenous,orinsomecasesin5shellsmodel(Ara’scomputation)- NeutrinosfluxtakenfromG.Battistoni etal.,Astroparticle Ph.19(2003),269-290,291-294
(withsomesimplifications)- Interaction(CC)crosssectionsasdiscussedbelow- Energyandangularresolution
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Atmosphericneutrinoflux
Theneutrinoflux,withE2.5 factorremoved,rapidlydecreasingwithenergy(factor~2000between0.3-0.9GeVand5-9GeV.
Wetaketheapproximationofequalneutrinovs.antineutrinoflux,andnu_mu fluxtwiceaslargeasnu_e flux.
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Crosssection• Dominatedbyquasi-elasticcrosssectionforEuptoabout1GeV,andDISforEabove2GeV.
CConnucleon,fromBarger-Marfatia-Whisnant book
yQ2max(GeV2)
Q2 (GeV2)
• Theantineutrinocrosssectionissmaller(convenientlywhenaimingatCPVeffects)
• Thedependenceonthetheenergytransferredtothehadron(s)issmallerforneutrinos.
• Theresolutioninmeasuringenergyanddirectiondependsontheenergyandenergytransfer.
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• Thistablehasbeenusguidancefordetectorresponse.
• Itrequirestocombinetheresponsetotheleptonicandhadronicparts
yQ2max(GeV2)Q2 (GeV2)
Thecombinationisdoneaccordingtotheenergytransfer,withalargedependenceoftheenergyresolutionontheenergytransferredtothehadronicsystem.Eventswithsmallenergytransfercouldbeselectedinordertoimprovethedetectorresolution.
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Fortheangularresolution,theleptonic andhadroniccomponentscomponentsarecombinedbyareconstructionofthedirectionofthetotalmoment,afterincludingenergyandangularuncertaintiesinthetwosystems
Enu=0.5GeV Enu=4GeV
Theresultingresolutionisdifferentbetweenthescatteringplaneandtheplane,anddependsverysignificantlyontheenergytransferredtothehadronicsystem
Q2 (GeV2) yQ2max(GeV2)
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• Resolutionafteraveragingoverenergytransfer(forneutrinos)• sig(E)/E=13.5%/E[GeV]0.5 +2.5%• Sig(theta)=2/E[GeV]1.5 +4.4deg (or0.035/E1.5+0.077)rad
• Thephaseofneutrinooscillationdependsonenergyandangleas• phase=2*1.37*Dm2
sol/atmo*L/E,withL=2Rcos(theta)(thetaistheangletothevertical)
• Thereforesig(phase)=phase*[sig(E)/E(+)sig(theta)*tan(theta)](quadraticsumapproximation)sothattheerrorintheangleisnotrelevantneartheverticaldirectionanddominatesnearthehorizon)
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Subject1:masshierarchy
• Forthis,Gordonhasconsideredthesensitivitytothefastoscillations,andappliedaselectiontheenergytransfer:• Selectingonlowyprovidesabetteraveragesigma(E),withthecostofasmallernumberofevents• Theselectionisguidedbytheratioofapparentamplitudeanduncertanty inthenumberofevents:
hereistheeffectiveenergywavelengthoftheoscillation(whichisproportionaltoE2 atlowenergies,toEatlargeenergies)
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Theselectionresultedsharpintheplaneenergy-angle,withalltheeventsretainedbeyondsomeboundary(efficiency:=20/20=100%)andonly10%oftheeventsretainedatlowerenergy/largerangle)
Selection
Thisisbasedon:Prob(nu_e ->nu_e)+2Prob(nu_mu ->nu_e)
+0.5[Prob(anti-nu_e ->anti-nu_e)+2Prob(anti-nu_mu ->anti-nu_e)]
Multipliedbycrosssectionsandaveragedatmosphericfluxes.
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Projectionofdifferenceincountsperbinbetweennormalandinvertedhierarchy,With5layersmodelofEarth(Ara’scomputation),anddeltaCP=0Theamplitudesissmallcomparedtotheexpectednumberofcounts,butthereiscoherenceovermanybins.
Simplifiedanalysisofsignificanceoftheeffect:• definetheboundariesoftheregionwithpositiveandnegativedifference.• Comparethesumoftheabsolutevalueofthedifferencetothesquarerootofthetotalcounts:that
providestheexpectedsignificanceofthedifference• Repeatwiththesameboundaries,butwithoscillationscomputedwithparametervariation(2sigma
errorsonoscillationparametersinvacuum,Earthdensity+-5%,resolutions+-20%,deltaCP value)
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Resultsformasshierarchy(highEnu):• With40kton Dune,10yearsofdata,usingthenu_e,anti-nu_e channelalone:• With4.0g/cm3 homogeneousEarthmodel.deltaCP=270deg,6.5sigmasignificance
• With5layersmodel,deltaCP=0deg :4.3sigmasignificance[forreference,crosscheck:totalnumberofevents27,000(ineitherhypothesis),“difference”betweenhypotheses:700events]
• Systematiceffectsofparametersvariations,homogeneousEarth,maineffects:• +-1sigmaforsin2(2theta23)uncertainty• -0.7sigmafordeltaCP=90deg
• Conclusions:themasshierarchycanberesolved,butonlywithalongexposureofthefulldetector.
• Thesensitivitymightbeincreasedaddingthemuonfinalstate(somewhatlimitedbymuonfullcontainment)
• Thefive-layer,realisticmodelprovidessmallereffectsthanthehomogeneousEarthmodel.
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Subject2:CPasymmetry
Atlowneutrinosenergies,thefastoscillationcannotbeobservedbecauseoflimiteddetectorresolution,buttheCPdependentterminthenu_mu->nu_e oscillationhasbothfastandslowcomponents.
CPviulating componentofoscillationprobabilityinnu_nu->nu_e (left)andanti-nu_mu->anti-nu_e (right),enhancedbyfactor20. Obtainedassuminganeventselectionthatreducesbyafactor2theexpressionfortheresolutionexpressiongivenabove.Thetruepeak-to-peakamplitudesare0.06(neutrinos)and0.03(antineutrinos).
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Oscillationparametersfor“slow”oscillationsin4g/cm3,forneutrinos,antineutrinos,neutrinoswithinvertedhierarchy.
Thelinearbehaviorofdm221 vsEimpliesthat
thephaseoftheoscillationdoesnotdependontheenergyanymore.
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Ifthemeasurementerrorswouldbereducedbyafactor2,theCPdependentpeakswouldhavelargeramplitudeandbeshiftedtolowerenergy.
InteractionwithEnu <1Gev aredominatedbyquasi-elasticscatteringonnucleons,withsomeDelta(singlepion)events:• Eventswithfinal-stateprotons(ratherthanneutrons)(+pions)willbeeasiertoidentifyand
measure• Andtheywillalsofavortheselectionofneutrinovs.antineutrinoevents,whichwill
contributetoenhancingthevisibilityoftheCPdependentterminthesumofneutrinoandantineutrinoevents.
Despitethisconsiderations,thefollowingplotsarebasedonapproximatecombinations(nu_e ->nu_e)+2(nu_mu ->nu_e)+0.5[(anti-nu_e ->anti-nu_e)+(anti-nu_mu ->anti-nu_e).
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Combinationsofoscillationprobabilities,densityof4g/cm3
curvesat0.025intervals,topofplotsatvalueof1.5
deltaCP=270deg,normal hierarchy
deltaCP=90deg,normal hierarchy
deltaCP=270deg,invertedhierarchy
deltaCP=90deg,invertedhierarchy
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• Thepeak-to-peak,CPdependentamplitudesshownaboveareequaltoabout0.15fornormalhierarchy,and0.11forinvertedhierarchy.
• Thesearelargeeffects,whencomparedtothetopvalueofthedistribution,equalto1.5.
• Also,theCP-dependentdifferencesextendsoverratherlargeintervalinenergyandangle.
• Wehavenotcompleted:a) thecomputationfor5-layersEarth,b) acrosssectionevaluationforfinalstateswithprotonsc) anestimateofthesensitivityforgivenassumptionsondetectorsizeand
exposure.Itisencouragingtheselectionofprotonswillenhancetheneutrinos.Itisalsoencouragingthattheintegratedatmosphericspectrumin0.30-0.94GeVisabout300timeshigherthanin5.3-9.4GeV,andafterincludingthecrosssection,westillexpectorderof20timesmoreeventsinthelowenergyrange.Inconclusion,atafirstlookthestudyofCPviolationfromatmosphericneutrinososcillatingacrosstheEarthappearsaccessibletoDUNEinalimited/ealry detectorconfigurationandexposure.
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