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orthereac4on:neutrino nucleon!muon osca8eringwecategorizecrosssec onsbythemassofthefinalstatehadronicsystem:WW M 0.938GeV- ‐ elas9c(hydrogen)quasielas9cscaLering(nuclei)1.1 W 1.9Inelas9cscaLeringintheresonanceregionW 1.9GEVInelas9cscaLeringinthecon9nuumW2 (p q)2 M2 2Mν–Q2ν energytransfertotargety ν/E inelas9cityQ2 squareofthefourmomentumtransferx Q2/2Mν frac9onofmomentumcarriedbyquark)A.Bodekx 1forquasielas9cscaLering)2
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Structurefunc ondescrip onRela onbetweenthetwodescrip ons.Transverseandlongitudinaldescrip onSinceRissmallWhatisgenerallyusedisamixeddescrip ek5
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ecannotoccupythesamestateastheothernucleons.(Q2 0.1GeV2) esonExchangeCurrents). ulisuppression(Q2 thesenucleareffects chargeA.Bodek7
vA)andseveralelectronexperiments(SLAC,SLAC- thefollowingtopics1 EMCeffectinnucleartargets2Bodek- onsonnucleartargets,soIwillneedtomen4on3. Bodek- gtheShortRangecorrela4onscomponent(highmomentum)4. al)5 Bodek- ‐Budd- eartargets(mesonexchangecurrents- 4onsrelatedtoanyoftheabovetopics.A.Bodek8
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rosssec9onanditswidth(inenergytransfer).A.Bodek11
etweennucleonscanresultintwo- Leringdataindicatesthatn- ‐ppairsdominate)2p2hprocessρo entumcomponentofthe1981Bodek- ecauseSRCFrac4onhavefinallybeenmeasuredρo 0.17NucleonsNote:Thethree- )andIwillignoreit.A.Bodek12
1p1h 1nucleon 1holeinfinalstate2p2h 2nucleons 2holesinfinalstateP KfP hBodek- gremovalenergy)Kf spectator.Ps 200MeVPs 300MeVPs2/2MA- ‐1* 2MeVForarecoilA- “quasideutrons)processMA- ‐2* MA- ‐1 2BEMA- ‐1* MA- ‐1 BE(onshellexcited)(onshellexcited)MD* MD- ‐2BE(offshell)Pi (offshell)Pi (offshell),Ps excitedMA- ‐1*1excitedMA- andA.Bodekneedstobemodeled.A- *
Moniz1p1honlyThis1969- es.KuzminFermigas1p1hA.Bodek14
mFermimomentum,andisabout200MeV/c.W2 M2 2MνΔW2 2MΔν 2Με ε1p1h 20 K2/2MA- ‐1* 22MeV( ε2p2h 40 K2/2Mp 85MeV(K Kf)2p2hfrac9on 6(2Kf/π)2forCarbon12.7% K 300MeV/cA.Bodek15
- orysystem.Ø Tocalculatea2N(2H)indeuteriumthisiswhatisused§ § 2HWaveFunc9onMeasuredpmin(Q2onset,xBonset) 275 25MeVØ Integraloverdeuteriumwavefunc9oninpi pminregionisa2N(2H)Ø Defini9onofSRC- ‐nucleonswithmomentumP 275MeV/cDeuteriumWaveFunc9onØ JlabmeasuresatQ2 2GeV2.Thisregionispmin(4. (2GeV2),MesonexchangecurrentsarewellathighQ2.§ § § aveasC12andFe.func on.CutssuchasX 1areimposedtoreducebackgrounda2N(2H) 0.040 0.007(Deuterium)a2N(3He) 0.080 0.016A.Bodek16
JlabmeasurementsfornucleiwithA 56(P 0.275GeV)TheBodek- Single particle (%)2N SRC (%)with P 275 MeV/c3N SRC (%)76 0.2 4.723.0 0.2 4.70.79 0.03 0.2512C80 02 4.119.3 0.2 4.10.55 0.03 0.184He86 0.2 3.315.4 0.2 3.30.42 0.02 0.143He92 1.68.0 1.60.182H96 0.74.0 0.7-----Independentnucleons56FeFrac onsNucleus(D)Fe5683.516.4%(P 0.26GeV) 0.061981Bodek- ‐RitchieC1288.012.0%(P 0.22GeV)1981Bodek- ‐RitchieThe1981Bodek- sinnuclearmaFer(12%forCarbon,16.4%forFe)forK K nand3NSRCissmall,0.55%.A.Bodek17
81SRCcomponentinBodek- ‐RitchieModel.A.Bodek18
1 Integrated"Momentum"Distribu9on"0.98 "C12""KF 0.220"GeV"Benhar/Fantoni Bodek/Ritchie (a 2,Pmax 1) 10 0.96 Bodek/Ritchie (a 2.76,Pmax 1) (2013)Bodek/Ritche (a 2,pmax 4) 1 0.94 0.92 (1981)0.9 0.1 0.01 Momentum"Distribu5on"C12""KF 0.220"GeV"0.88 Benhar0Fantoni 0.86 Bodek0Ritchie (a 2,Pmax 1) 0.84 Bodek0Ritchie (2013)(a 2.76,Pmax 1) Bodek0Ritche (a 2,pmax 4) 0.82 0.001 (1981)0.8 0 0.2 0.4 0.6 0.8 1 0 0.2 P"(GeV/c)"Bodek(DataforP 0.275GA.eV)19.3%forC120.4 0.6 0.8 1 P"(GeV/c)"19
WhathavepeopleusedtomodelFermimo9on (1)RFG:Probability wavefunc onsquareoftheini alstatemomentumisMonizFermiGas alledFermiGasFGorrela6vis6cFermigas(RFG)- ‐- ‐UsedbyMiniBooNe,T2K(Neut,Nuance)Only1p1h (2)Bodek- ‐RitchieRFG:Probability wavefunc onsquareoftheini alstatemomentumisFermiGas SRCnucleon- ‐nucleoncorrela d2p2hprocessesandisincluded).UsedinMINERvA (3)Morecomplexwaverfunc ons:Probability wavefunc onsquareoftheini alstatemomentum.E.g.Benhar- ‐Fantoni.Hadronicfinalstate1p1hor2p2hinforma onisnotincluded.UsedinNOMAD (4)SPECTRALFUNCTION:Probability func onoftwovariable:ini unc6on.Hadronicfinalstate1p1hvs2p2hinforma onisnotincludedinspectralfunc on. RESPONSEFUNCTION:Probability func onsefunc processes.Hadronicfinalstate1p1hvs2p2hinforma onisnotincluded AllProbabili esarenormalized1.0.Therefore,acceptancecalcula onsdependontheA.Bodekassump onandmodelingofthehighmomentumtail(contribu onof2p2hprocess).20
dependentNucleonModelonlyworkwellforQ2. trinosca8eringforallvaluesofQ2?A.Bodek21
A.Bodek22
BestknownQEscaLeringmodelPsi’scalingsuper- ‐scalingmodelofSick,Donnelly,Maieron(nucl- withthesamefinalstatehA.adronicenergy)Bodek23
pectralfunc9on)ItisuniversalforA ngfortheQ2 tzero)Q2 0.14GeV2Q2 0.33GeV2NopionProduc9onq q3 3- tweenQEpeakandDelta24
)Responsefunc alintegratethetworesponsefunc9ons)Q2 0.09GeV2Q2 0.14GeV2Q2 �)0.51.225
WhataboutQ2 0.33GeV2 2 0.09GeV2,Q2 0.14GeV2and,Q2 0.33GeV2 lasthereference. Note,forQ2 ementedinallmodels.A.Bodek26
Ouranalysis hasbeenaLributedtomesonexchangecurrentsinnuclei. . INERvAexperiments. dek27
elative Cross pendentnucleonQE FermismearedΔpredic ebytheintegralofthetransversecontribu ontotheQEcrosssec onandobtainRT(Q2)Wealsoextractthepeakposi onandwidthoftheresidualexcessforthefirst kW (GeV )posi oninW 22Eur.Phys.J.C71(2011)1726arXiv:1106.0340[hep- ‐ph]2A.Bodek28
Updatedparameteriza onA 5.19andB 0.376Ra otofreenucleonsFROMNEWFITSINBLUETheoriginalfit(A 6.0andB tribu t).29
ichformquasi- process(c)isreferredtoasIsobarexcita on.e.g.Δ eutron(- ‐1.9).Sothemagne9cformfactoroftheΔ - ‐- ‐ Δ is49mesthatofofP- ‐- ‐ heΔ odelhasnofreeparameters.
Predic9ngneutrinoQEcrosssec9onsonnucleartarget Usefreenucleonvectorformfactors Usefreenucleonaxialformfactor ngecurrents).A.Bodek31
freenucleonsRe- nelectro- a9oofFA(Q2)tothedipolewithMA leformisnotbadwithMA- k32
-38( 10 cm2 )NeutrinoQEcrosssec on n1.61.41.21ExtraCrossSec onfromTEis23%ofQEcrosssec ononaveragep !-MiniBooNE, CNomad, CE 1.2GeVMartini et al.MA 1.30MECmodeltransverseenhancementMA 1.0140.80.6Mar nietalE 1.2GeVMECmodelPRC81:045502(2010)0.40.2010-1MA 1.014MA 1.30Tranv Enhance in GVM, MA 1.014110102E (GeV)A.Bodek33
-38( 10 cm2 )An neutrinoQEcrosssec on1.2E 1.2GeVMECmodel10.80.6 pn ! MiniBooNE, CNomad, CMartini et al.ExtraCrossSec onfromTEis23%ofQEcrosssec ononaverageMA 1.0140.4Mar nietalE 1.2GeVMECmodelPRC81:045502(2010)0.2010-1MA 1.014MA 1.30Trans Enhance in GVM , MA 1.014110102E (GeV)A.Bodek34
1. MeasurementofMuonNeutrinoQuasi- ‐Elas9cScaLeringonaHydrocarbonTargetatEν 3.5GeVMINERvACollabora9on.May9,2013e- ‐Print:arXiv:1305.22432. MeasurementofMuonAn9neutrinoQuasi- ‐Elas9cScaLeringonaHydrocarbonTargetatEν Emodeldashedredline- ‐- ‐- ‐- ‐- ‐- ‐- ‐- ‐A.Bodek35
NeutrinosExtraCrossSec onfromTEis23%ofQEcrosssec ononaverage.(30%atQ2 0.5GeV2)Ra energies fferentfunc9onneedstobeusedforneutrinoenergies 9neutrinos)
houldgetMA nlyfitlowQ2.GetMA velowQ2datafromfit.GetMA 1sincetheydon’tincludeTEA.Bodek37
Inves9ga9onofpeakandwidthofTE ��nalstateW(orequivalentlyenergytransferν). ts.A.Bodek38
Relative Cross sectionComparisonofpeakposi9onofTEandQEQETE45MeV Differenceis45MeV. eonQEpeak.A.Bodek3922W (GeV )
Relative Cross sectionRMSwidthTEindependentofQ2 ν RMS 0.115GeV22W (GeV )MagnitudeRa9o (QE 40
Relative Cross sectionRMSwidthoftheνdistribu QEscaLeringwithFermimo9onk.W2 M2W2 M2 2Mν- ‐2k*q–Q2RMSwidthTE- ‐- ‐à ν Q2/2M k*q/MindependentofQ2 ν RMS 0.115GeV ν RMS k3 q3/MWithq3 {Q2(1 Q2/4M2)}expectRMSincreaseswithq3withaslopeof k 3 /MHerek3istheFermimomentumalongq3whichisthe3- ‐momentumtransfertothenucleon.Now k3 (krms)/ 3SoRMSincreaseslinearlywithq32withaslopeof k rms /( 3M)A.Bodek2W (GeV )41
NeutispureFermiGasFermi*Gas*kF 0.22*GeV**krms enharFantoni0.05"krms 0.246GeV0"Uptok i***krms A.Bodek0.25%0.2%Probability*Bodek- ‐RitchieKf 0.225withUpdatedSRCk rms 0.272GeV(uptok 0.8GeV)BenharFantonikrms 0.246GeVUptok ntum*(k)*GeV*42
isnotrealis4cA.Bodek43
Sowherearewe Fortheinelas9cregion(W 3 0.3GeV2vector axial). ithelectronscaLeringdta. tronscaLeringdata. (e.g.dipoleorBBBAaxialformfactor).A.Bodek44
100%. 60%comesfromFSI–Thedominantsources (bylookingateventswithx 1) sources).A.Bodek45
ExtraslidesA.Bodek46
entnucleonmodelFermiMo onEffectsinDeepInelas tronprotonElas csca8eringNonrela9vis9callye- ‐D.Pi - ‐PsEi M–BE–Ps2/2M- ‐à offshellPf Pi qDeuterontargetElectronDeuteronQuasielas csca8ering:BE 2MeVbindingSpectatornucleonisonshellInterac ansferofqA.Bodek47
.A.BodekandJ.RitchiePhys.Rev.D23(1981)Bodek107048
ConclusionsonTE/MECinQEscaLering ewdatareasonablywell.Updatedparameteriza9onA 5.19andB 2. eVtowardshigherν.TheshivsareindependentofQ2. actormodelareexpected WearecurrentlyextendingtheanalysislowerQ2( 0.3GeV2)tooverlapwithouranalysisofthelowQ2L- ‐TseparatedresultsfromCarlsonetal. )canbetested.A.Bodek49
- resultsina2ndnucleoninthefinalstatewithKE VthespectatornucleonhasKE45- thKE 48- ‐90MeV- ‐à 50
ectatorA- lowenergyspectatornucleon.A.Bodek51
CanwedetermineifextranucleonsareassociatedwithTE? eutrinoscaLeringassumesthatthesethreeprocesses(QE c9onsandQ2distribu9ons.HowevA.Bodek52
A.Bodek53
alA.BodekEffectofFermimo9onisveryQ2dependent54
A. sitagreewiththeSRCmeasurementsin2013?ß 1p1h(FermiGas)ß 2p2h(SRC)quasideuteronbacktobackn- ‐ppairs.4(GeV)]A.Bodek55
ouldbechangedto1.5GeV)ß 1p1hß aFer(12.8%forCarbon,16%forFe)56
energyis25MeVß 1p1h(FermiGas)0.8GeV/cß 2p2h(SRC)0.8GeV/ca 2.76GeV- ‐1forC12a 2.44GeV- ‐1forFe56Spectator:k2 0.3- ‐0.4GeVKE k22/2M 45- ‐80MeV0.8GeV/c]TheBodekRitchieModelIsanapproxima ontotheSpectralFunc emovalenergysincethasaspectatornucleon.57
Bodek58
isnotrealis4cA.Bodek59
Relative Cross sectionRMSwidthoftheνdistribu QEscaLeringwithFermimo9onk.W2 M2W2 M2 2Mν- ‐2k*q–Q2- ‐- ‐à ν Q2/2M k*q/M ν RMS k*q3/M q3 k3 /MRMSwidthTEWithq3 {Q2(1 haslopeof k 3 /M ν RMS - ‐momentumtransfertothenucleon.{ k3 (krms)/ 3}22W (GeV )A.Bodek60
Relative Cross sectionRelative Cross edata.Weshowafewexamples:- ‐Q2 0.3GeV2ε 0.98Residual TEcontribu9on)Q2 0.3GeV2ε 0.88Residual istribu9onW (GeVQ2 0.3GeV2fortwodifferentvirtualp)hotonpolariza on–getsamesameTEA.Bodekσ σL εσT2222W (GeV )61
Q2 0.68GeV2ε 0.98Relative Cross sectionRelative Cross sectionRelative Cross sectionσ σL εσTQ2 0.65GeV2ε 0.96Residual TEcontribu9on)Q2 0.62GeV2ε 0.71Residual TEcontribu9on)Q2 0.62- ‐0.68GeV2:threedifferentvirtualphotonpolariza on–getsimilarTEA.BodekW (GeV )W (GeV ) σ σL εσT22226222W (GeV )
Q2 0.98GeV2Residual TEcontribu9on)Relative Cross sectionRelative Cross sectionRelative Cross sectionσ σL εσTQ2 1.03GeV2Q2 1.1GeV2Residual TEcontribu9on)Residual TEcontribu9on)A.BodekQ2 0.98- –getsimilarTE22W (GeV )22W (GeV )6322W (GeV )
Q2 1.2GeV2ε 0.92Relative Cross sectionRelative Cross sectionσ σL εσTQ2 2.0GeV2ε 0.91Residual TEcontribu9on)Residual TEcontribu9on)AthighQ2,theTE/MECcontribu onW (GeV i) smuchsmaller(andTEpeakissmallerthantheW (GeV )QEcontribu onA.Bodek642222
Neutrino!Cross!sec9ons! ng(the(energy(dependence(of(neutrino