12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Low Energy Neutrino-Nucleus Interactions Makoto Sakuda (KEK) in collaboration with C.Walter, K.McConnel, E. Paschos et al. 10 June 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

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 1. Neutrino-Nucleus Interactions in the Few-GeV Region 1.Oscillation analysis need cross section and spectrum. Y(E )=(Neutrino flux) ·  （ E ) · (Number of target nucleons). Accurate measurements of CC neutrino cross sections exist for E >20 GeV ， with accuracy ±3%. nuint02  Measurements of neutrino-nucleus cross sections at E = 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  → e oscillations at sin 2 2  13 ~0.01, especially after KamLAND result. Cross section and spectrum at a few % level are needed in the future. 2.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%.

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Sensitivity to M A  (MA)stat. ~.06GeV/c 2.  (MA)sys. ~.15GeV/c 2. d  /dQ 2 (quasi-elastic scattering) BNL Deuterium BC Calculation by Ch.L.Smith et al. M A =1.07±0.05

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 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

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Pauli exclusion effect Quasi-elastic  production W/o Pauli effect W/ Pauli effect 10-15% suppression At low Q2 Total 3% reduction E =1.3 GeV ， k F =220 MeV/c  PpPp PpPp  q W   npnp PpPp q If P <k F, suppressed. Total 8% Nuclear effects are large in the low Q 2 region, where the cross section is large. d  /dQ

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Charged-Current Quasi-elastic Scattering This is the simplest and the most important reaction. Calculation by Ch.L.Smith et al. with M A =1.0.    n     p)     p     n) 1x  1.0 (cm 2 ) Pauli effect ~8%

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Single Pion Production Cross Section Prediction = Rein-Sehgal M A =1.2 GeV/c 2 1x  1.0 (cm 2 ) 0.0

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Strange particle production and CC/NC Coherent Pion Production  n    K +  Comparison with NUANCE ／ Neugen

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Total Charged-Current Cross Section Total cross section increases with energy,  =  E . 1.0  x (cm 2 )    / E     / E

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Neutral Current Interactions 1kton Neutral-Current  0 production (P  0 ) Preliminary) P0P (GeV/c) Very few data are available at low energy.  E734  reports  M A = for  p →  p.

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions M A measurements 1.0 M A (GeV/c 2 )

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions d  /dQ 2 (   production) from BNL μ－ｐπ＋ nsμ－ｐπ＋ ns Q 2 (GeV) Rein-Sehgal (M A =1.2 GeV/c 2 ) Normalized by the entries M A (1  ) (Rein-Sehgal model) SKAT89 M A =1.01+/-0.09+/-0.15 CF 3 Br BEBC89 M A =1.01+/-0.10 D 2

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 3. Recent Progress in Calculation (NuInt01/02) Elastic Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering Single Pion Production

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Nucleon Form Factors de p P q ee

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Quasi-elastic interaction   n     p A = Q 2 /4M 2 [(4 + Q 2 /M 2 )|F A | 2 - (4 - Q 2 /M 2 )|F V 1 | 2 + Q 2 /M 2 (1-Q 2 /4M 2 ) |  F V 2 | 2 + 4Q 2 /M 2  ReF V* 1 F V 2 ] B = -Q 2 /M 2 ReF * A (F V １ +  F V ２ ), C = 1/4(|F A | 2 + |F V 1 | 2 + Q 2 /4M 2 |  F V 2 | 2 ). Vector Form factors G E p =D, G M p =  p D, G M n =  n D, G E n =  n  D, D=1/(1+Q 2 /M V 2 ) 2, M V =0.843 (GeV/c 2 )  p  n  =5.6,  = Q 2 /4M 2 Axial-vector form factor F A F A (Q 2 )= /(1+Q 2 /M A 2 ) 2 d  dQ 2 [A(Q 2 )-B(Q 2 )(s-u)+C(Q 2 )(s-u) 2 ] M 2 G 2 cos 2  c ( 8  E 2 ) = Form Factors F 1 V,F 2 V,and F A and (s-u) =4ME -Q 2 -M  2

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Nucleon Vector Form Factors A simple dipole form D=(1+Q 2 /M V 2 ) -2, M V =0.843 is good to 10-20% level for Vector Form Factors. Fig -- Bosted, PRC51,409,’95 Red=Dipole Curve= (1+a 1 Q+a 2 Q 2 +.+a 5 Q 5 ) -1 G Mn  G Mp,G Ep Cross section shape will change if we use these data. G Mp /  p D G Ep /D GMｎ/ｎDGMｎ/ｎD (G E ｎ /D ) 2 Q2Q2

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict Effect of New Vector Form Factors G Mn,G Mp,G Ep,G E n

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict Effect of New Vector Form Factors G Mn,G Mp,G Ep,G E n

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict Effect of finite G E n  (with)/  (without)

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Model beyond the Fermi-gas model Spectral Function Calculation or Local Density Approximation Spectral Functions P(p,E) for various nuclei, eg. 16 O, 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 P (MeV/c) E (MeV) Fermi momemtum Fermi Gas model p

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Lepton energy in quasi-elastic -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. =25 MeV (Fermi-Gas) LDA =40 MeV

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Test of neutrino models using (e,e’) Data (). The energy transfer (  =Ee-Ee ’ ) at the fixed scattering angle. Oxygen Carbon Oxygen Carbon Oxygen 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 E reconstruction in the future while the present accuracy is about MeV due to the energy calibration and nuclear effects. ， q e Ee’Ee’ np 

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions 3.3) N   transition form factors

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Schreiner-von Hippel(’73)/Adler (‘68) model Form factors C i V,A (i=1,6) for N     Vector form factors C 3 V (Q 2 ) = 2.05/ (1+Q 2 /M v 2 ) 2, M v 2 =0.54 （ GeV) 2 C 4 V (Q 2 )=-M/M  C 3 V (Q 2 ), C 5 V (Q 2 )=0. C 6 V (Q 2 )=0. (CVC) Axial form factors C i A (Q 2 ) = C i A (0) /(1+ Q 2 /M A 2 ) 2, (i=3,4,5) C 6 A (Q 2 )= C 5 A (Q 2 ) M 2 /(m  2 +Q 2 ) [PCAC] C 3 A (0)= 0. C 4 A (0)=-0.3, C 5 A (0)=1.2

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions SLAC/Jlab resonance data (not used in the fit) 3.3) DIS (Bodek-Yang at NuInt01/02) Dashed: GRV94 Red:Bodek-Yang This correction is significant at low Q2 region. NB. Three resonances are evident.

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions Nuclear PDF and its effect on the DIS cross section

12 February 2003 M.Sakuda Neutrino － Nucleus Interactions The accuracy of Neutrino-Nucleus ( -N) interactions at E = GeV is about +-10% or more. We will combine both e-N data and -N data to understand -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 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. 5. Summary