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Low Energy Neutrino-Nucleus Interactions

Low Energy Neutrino-Nucleus Interactions. Makoto Sakuda (KEK) in collaboration with C.Walter, K.McConnel, E. Paschos et al. 10 June 2003 @ NuFact03 Outline 1. Neutrino-Nucleus Interactions 2. Data of low-energy neutrino-nucleus scattering

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Low Energy Neutrino-Nucleus Interactions

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  1. Low Energy Neutrino-Nucleus Interactions Makoto Sakuda (KEK) in collaboration with C.Walter, K.McConnel, E. Paschos et al. 10 June 2003 @ NuFact03 Outline 1. Neutrino-Nucleus Interactions 2. Data of low-energy neutrino-nucleus scattering 3. Recent Progress in Calculation (NuInt01/02) • Elastic Form Factors • Spectral Function = Beyond Fermi Gas • Deep Inelastic Scattering • Single Pion Production 4. Summary M.Sakuda Neutrino－Nucleus Interactions

  2. 1. Neutrino-Nucleus Interactions in the Few-GeV Region • Oscillation analysis need cross section and spectrum. Y(En)=(Neutrino flux) ·s（En) · (Number of target nucleons). • Accurate measurements of CC neutrino cross sections exist for En>20 GeV，with accuracy ±3%.Naples@ nuint02 • Measurements of neutrino-nucleus cross sections at En=0.5-20 GeV are still poor. Accuracy is about ±20% and spectrum even worse. Nuclear effects become significant. • Neutrino oscillation experiments (K2K，MiniBooNE, MINOS，OPERA, ICARUS, JHF-Kamioka) have to work in this complex energy region. • We want to measure nm→ne oscillations atsin22q13~0.01, especially after KamLAND result. Cross section and spectrum at a few % level are needed in the future. • Weak nucleon form factor itself is very interesting. We need to update both vector and axial-vector form factors if we want to predict the spectrum better than 10%. Horowitz@nuint02,Singh@nuint01, Budd@nuint02 M.Sakuda Neutrino－Nucleus Interactions

  3. ds/dQ2 (quasi-elastic scattering) Ishida(K2K)@nuint02 Sensitivity to MA D(MA)stat. ~ .06GeV/c2. D(MA)sys. ~ .15GeV/c2. BNLDeuterium BC Calculation by Ch.L.Smith et al. MA=1.07±0.05 M.Sakuda Neutrino－Nucleus Interactions

  4. 2. Data of low-energy neutrino-nucleus scattering • Overall flux error is about ±10-20% at low energy. • Experiments below 20 GeV were performed with wide-band beams. • Many processes contribute equally, with ±20% errors. • Quasi-elastic scattering • Single pion production • Multi-pion production/DIS • Coherent-pion production • NC • Nuclear effects can be different for different target. • Fermi-motion and Binding energy • Pauli exclusion effects • Nuclear rescattering • Pion absorption M.Sakuda Neutrino－Nucleus Interactions

  5. Pauli exclusion effect Nuclear effects are large in the low Q2 region, where the cross section is large. En=1.3 GeV，kF=220 MeV/c ds/dQ2 n m- Quasi-elastic q W/o Pauli effect n p P p W/ Pauli effect Total 8% 0.5 1.0 ds/dQ2 If P <kF , suppressed. n m- D production 10-15% suppression At low Q2 Total 3% reduction q p D P p P p W M.Sakuda Neutrino－Nucleus Interactions

  6. Charged-Current Quasi-elastic Scattering • This is the simplest and the most important reaction.Calculation by Ch.L.Smith et al. with MA=1.0. _ s(nmpm+n) s(nmnm-p) 1.0 1x10-381.0 (cm2) Pauli effect ~8% 0.1 1.0 10. 50. 0. 0.1 1. 10. M.Sakuda Neutrino－Nucleus Interactions

  7. Single Pion Production Cross Section Prediction = Rein-Sehgal MA=1.2 GeV/c2 MS@nuint01 1x10-381.0 (cm2) 0.0 M.Sakuda Neutrino－Nucleus Interactions

  8. Strange particle production and CC/NC Coherent Pion Production • nmnm-K+L Comparison with NUANCE／Neugen (Zeller@nuint02) 10-38 M.Sakuda Neutrino－Nucleus Interactions

  9. Total Charged-Current Cross Section • Total cross section increases with energy, s=a En . _ s(nm) / En s(nm) / En 1.0 x10-38 (cm2) M.Sakuda Neutrino－Nucleus Interactions

  10. Neutral Current Interactions • Very few data are available at low energy. • E734reports • MA=1.06+-0.05 for nmp→ nmp. • 1kton Neutral-Current p0 • production (Pp0) (Mauger @nuint01, Preliminary) Pp0 0. 1.0 0. 1.0 (GeV/c) M.Sakuda Neutrino－Nucleus Interactions

  11. MAmeasurements Singh@nuint01 MA (GeV/c2) 1.0 M.Sakuda Neutrino－Nucleus Interactions

  12. ds/dQ2 (D++ production) from BNL Furuno@nuint02 μ－ｐπ＋ ns Rein-Sehgal (MA=1.2 GeV/c2 ) Normalized by the entries MA(1p)(Rein-Sehgal model) SKAT89MA=1.01+/-0.09+/-0.15 CF3Br BEBC89MA=1.01+/-0.10 D2 Q2(GeV) M.Sakuda Neutrino－Nucleus Interactions

  13. 3. Recent Progress in Calculation (NuInt01/02) • Elastic Form Factors • Spectral Function = Beyond Fermi Gas • Deep Inelastic Scattering • Single Pion Production M.Sakuda Neutrino－Nucleus Interactions

  14. 3.1) Nucleon Form Factorsde Jager @PANIC02 e e q p P M.Sakuda Neutrino－Nucleus Interactions

  15. M.Sakuda Neutrino－Nucleus Interactions

  16. 3.1) Quasi-elastic interactionnmnm-p ds dQ2 M2G2cos2qc (8pEn2) [A(Q2)-B(Q2)(s-u)+C(Q2)(s-u)2] = Form Factors F1V,F2V,and FAand (s-u)=4MEn-Q2-Mm2 • A = Q2/4M2[(4 + Q2/M2)|FA|2 - (4 - Q2/M2)|FV1|2 • + Q2/M2(1-Q2/4M2)|xFV2|2+ 4Q2/M2xReFV*1FV2] • B = -Q2/M2ReF*A(FV１+ xFV２), • C = 1/4(|FA|2 + |FV1|2 + Q2/4M2|xFV2|2). • Vector Form factors GEp=D, GMp=mpD, GMn=mnD, GEn=-mnt/(1+lt)D, • D=1/(1+Q2/MV2)2, MV=0.843 (GeV/c2) • mp=2.792847, mn=-1.913043, l=5.6, t= Q2/4M2 • Axial-vector form factorFA • FA(Q2)=-1.2617/(1+Q2/MA2)2 M.Sakuda Neutrino－Nucleus Interactions

  17. Nucleon Vector Form Factors • A simple dipole form D=(1+Q2/MV2)-2, MV=0.843 is good to 10-20% level for Vector Form Factors. Fig -- Bosted, PRC51,409,’95 Red=Dipole Curve= (1+a1Q+a2Q2+.+a5Q5)-1 • GMnGMp,GEp • Cross section shape will change if we use these data. GMp/mpD GEp/D GMｎ/mｎD (GEｎ/D)2 Q2 M.Sakuda Neutrino－Nucleus Interactions

  18. Effect of New Vector Form Factors GMn,GMp,GEp ,GEn M.Sakuda Neutrino－Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict

  19. Effect of New Vector Form Factors GMn,GMp,GEp ,GEn M.Sakuda Neutrino－Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict

  20. Effect of finite GEn s(with)/s(without) M.Sakuda Neutrino－Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict

  21. 3.1) Model beyond the Fermi-gas modelSpectral FunctionCalculation or Local Density Approximation(Pandharipande@nuint01,Benhar,Nakamura,Gallagher@nuint02) • Spectral Functions P(p,E) for various nuclei, eg.16O, are estimated by Benhar et al. using e-N data. P(p,E) : Probability of removing a nucleon of momentum p from ground state leaving the residual nucleus with excitation energy E. E (MeV) Fermi momemtum 40. 20. Fermi Gas model 0. 100. 200. P (MeV/c) p M.Sakuda Neutrino－Nucleus Interactions

  22. Lepton energy in quasi-elastic n-N interaction -Comparison of Fermi Gas model and Spectral Function Calculation- • Large E and Large p tail exist in data. • Shift at a level of 10 MeV may exist. <eB>=25 MeV (Fermi-Gas) <E>LDA=40 MeV Benhar,Gallagher,Nakamura@nuint02 M.Sakuda Neutrino－Nucleus Interactions

  23. Test of neutrino modelsusing (e,e’) Data (•).The energy transfer (w=Ee-Ee’) at the fixed scattering angle . Ee’ ne q q Spectral function calculation agrees with data. Thus, the lepton energy kinematics can be checked within a few MeV. For example, accuracy of <10 MeV is needed in En reconstruction in the future while the present accuracy is about 20-40 MeV due to the energy calibration and nuclear effects. MS @nuint01,Walter，Wood@nuint02 n p Carbon Oxygen Carbon Oxygen Oxygen Oxygen M.Sakuda Neutrino－Nucleus Interactions

  24. 3.3) ND transition form factors M.Sakuda Neutrino－Nucleus Interactions

  25. Schreiner-von Hippel(’73)/Adler (‘68) model Form factors CiV,A (i=1,6) for nNm-D • Vector form factors C3V (Q2) = 2.05/ (1+Q2/Mv 2)2 ,Mv 2 =0.54　（GeV) 2 C4V (Q2)=-M/MD C3V (Q2), C5V (Q2)=0. C6V (Q2)=0. (CVC) • Axial form factors Ci A (Q2) = Ci A (0)/(1+ Q2/MA2)2, (i=3,4,5) C6A (Q2)= C5A (Q2) M2/(mp2+Q2) [PCAC] C3A (0)= 0. C4A (0)=-0.3, C5A (0)=1.2 M.Sakuda Neutrino－Nucleus Interactions

  26. 3.3) DIS(Bodek-Yang at NuInt01/02) SLAC/Jlab resonance data (not used in the fit) Dashed: GRV94 Red:Bodek-Yang This correction is significant at low Q2 region. NB. Three resonances are evident. M.Sakuda Neutrino－Nucleus Interactions

  27. 1.2 EMC J NMC J 1.1 E139 H J E665 J F J J H F H 1 J J J J J J H F J J J F J H J J H 0.9 H F H J J J J F J 0.8 2 2 Q = 5 GeV 0.7 0.001 0.01 0.1 1 1.2 BCDMS H B H E87 H 1.1 E139 H H B H B B B H E140 B B B B B H H H 1 B B H B H B H H B H H B H H H H H B H H H B H B B H B H H 0.9 H H H H H H H H H H H B 0.8 0.7 0.001 0.01 0.1 1 x Nuclear PDF and its effect on the DIS cross section M.Sakuda Neutrino－Nucleus Interactions

  28. 5. Summary • The accuracy of Neutrino-Nucleus (n-N) interactions at En=0.1-10 GeV is about +-10% or more. We will combine both e-N data and n-N data to understand n-N interactions better. It is very important for the running and the future neutrino oscillation experiments. • A strong community of nuclear and high-energy physicists has been formed at NuInt01/02 Workshop. Some JLAB people not only collaborate on the analysis of form factors and nuclear effects, but also ask proposals for measurements at JLAB usuful for neutrino physics. • K2K near detectors (1kton/SciFi) : producing new data. BooNE : soon. K2K upgraded detector (SciBar) will be complete this summer. MINOS near detector and ICARUS will come in 2006. • Joint nuclear/high-energy physics proposals at NuMI for dedicated measurement of neutrino-nucleus interactions are being discussed. Measurement of strange spin by NC/CC is proposed. • Re-analysis of old data (BNL,ANL) using current formalism is still valuable. • Open Neutrino Generators are available: Nuance and Fluka. M.Sakuda Neutrino－Nucleus Interactions

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