1. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 数 GeV 領域のニュートリノ原子核反応の測定と 計算の進展 作田 誠 (KEK 、 IPNS) 1 August 2003 @ 東工大 Outline 1. ニュートリノ振動実験 2. ニュートリノ原子核反応の測定データ 3. 最近の計算の進展 (NuInt01/02) Nucleon and  Form Factors Spectral Function = Beyond Fermi Gas Deep Inelastic Scattering と Single Pion Production ４. まとめ → 問題提起

2. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region NuInt01 (KEK, Dec.13-16,2001) Nucl.Phys.B(Proc.Suppl.)112. published. NuInt02 (UC Irvine ， Dec.12-15, 2002)

3. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 概要 １． K2K 実験は、提案の 7 割のビームを消化し、順調にデータを収 集している。ニュートリノ振動を９９％まで再確認。 ２． K2K 実験や将来のニュートリノ実験ではニュートリノ原子核反 応の精度が数％で要求される。現在の精度は 10-30 ％。 ３． 1990 年になって JLAB 、 MAMI 等の偏極ビーム、偏極標的を使っ た電子散乱実験で、 1960 年代に測定された核子構造が漸く 10 ％ 以下の精度で測られている。 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 Galster Paremetrization からのずれ。 ４．ニュートリノ実験もこれからは 10 ％以下を問題にしていかな ければならない。ニュートリノ実験では、 V ー A の Axial Structure を探る。 ５．電子原子核、ニュートリノ原子核反応は、対である。 V-A 解析実務では、束縛エネルギー、フェルミ運動量、パウリ禁止 則、形状因子、終状態相互作用、核内  吸収等の原子核の古典的 な問題との苦闘である。

4. 1 August 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 2 0.5 1.0

5. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions R MC =.017 +/- 0.002 We account for the difference of +/-10% 2) Proton Re-scattering

6. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 束縛エネルギーとフェルミ運動量（ホッフーリーツの教 科書） Test of neutrino models using (e,e’) Data (). The energy transfer (  =Ee-Ee ’ ) at the fixed scattering angle. Oxygen Carbon Oxygen Carbon Oxygen 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 20- 40 MeV due to the energy calibration and nuclear effects. MS @nuint01,Walter ， Wood@nuint02 q e Ee’Ee’ np 

7. 1 August 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%. Naples@ nuint02  Measurements of neutrino-nucleus cross sections at E =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  → 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%. Horowitz@nuint02,Singh@nuint01, Budd@nuint02

8. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions K2KSensitivity 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

9. 1 August 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

10. 1 August 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) 1x10 -38  1.0 (cm 2 ) 0. 0.11.010. 50. 1.0.1 1.0 Pauli effect ~8%

11. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Single Pion Production Cross Section Prediction = Rein-Sehgal M A =1.2 GeV/c 2 1x10 -38  1.0 (cm 2 ) 0.0 MS@nuint01

12. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Strange particle production and CC/NC Coherent Pion Production  n    K +  Comparison with NUANCE ／ Neugen (Zeller@nuint02) 10 -38

13. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Total Charged-Current Cross Section Total cross section increases with energy,  =  E . 1.0  x10 -38 (cm 2 )    / E     / E

14. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Neutral Current Interactions K2K 1kton Neutral- Current  0 production (P  0 ) (Mauger @nuint01, Preliminary) P0P0 0.1.0 0. (GeV/c) Very few data are available at low energy.  E734  reports  M A =1.06+-0.05 for  p →  p.

15. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions M A measurements This has to be reevaluated with new vector FFs. 1.0 Singh@nuint01 M A (GeV/c 2 )

16. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions d  /dQ 2 (   production) from BNL Furuno@nuint02 μ－ｐπ＋ nsμ－ｐπ＋ ns Q 2 (GeV) Rein-Sehgal (M A =1. ０８ 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

17. 1 August 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

18. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Nucleon Form Factors de Jager @PANIC02 p P q ee Electromagnetic current (J a em ) and weak hadronic charged current (J a CC =V a 1+i2 –A a 1+i2 ) is written in terms of form factors:

19. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions

20. 1 August 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 - m 2 /4M 2 (| F V 1 + F V 2 | 2 + | F V 1 +2F p | 2 –4 (1+  ) |F p | 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 )=-1.2617/(1+Q 2 /M A 2 ) 2 Form Factors F 1 V,F 2 V,and F A and (s-u) =4ME -Q 2 -M  2

21. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions How to Measure Nucleon Vector Form Factors In the past, the nucleon electromagnetic form factors have been measured from unpolarized electron beam scattering experiments using the Rosenbluth separation technique. The accuracy at high Q 2 (>1 (GeV/c) 2 ) was limited with this method. Nucleaon form factors were studied using a simple dipole parametrizations. Since 1993, new accurate measurements of the nucleon form factors were made possible with a new method using polarized electron beams and polarized targets. Clear deviation from a simple dipole parametrization is seen for the form factors and the better parametrizations for vector form factors were proposed. Recoil polarization P x  G E N, P x /P z  G E N / G M N The effect of those new form factors on the neutrino quasi-elastic cross sections was shown to be a few %.

22. 1 August 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. RED G Mn  G Mp  G Ep Curve – Bosted, PRC51,409,’95 Curve=(1+a 1 Q+a 2 Q 2 +.+a 5 Q 5 ) -1 E.J.Brash et al.,, Phys.Rev.C65,051001(2002). Similar Neutrino cross section shape will change if we use these data. Q2Q2 de Jager@PANIC02

23. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions GEp  GMnGEp  GMn Polarized electron beam experiments Q2Q2 All dataPolarization

24. 1 August 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

25. 1 August 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

26. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict Effect of finite G E n  (with)/  (without)

27. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions ratio_JhaKJhaJ_D0DD.pict Effect of finite G E n Budd @nuint02  (without)/  (with)

28. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Model beyond the Fermi-gas model Spectral Function Calculation or Local Density Approximation (Pandharipande@nuint01,Benhar,Nakamura,Gallagher@nuint02) 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. 0. 100. 200. P (MeV/c) 20. 40. E (MeV) Fermi momemtum Fermi Gas model p

29. 1 August 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 Benhar,Gallagher,Nakamura@nuint02

30. 1 August 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 20-40 MeV due to the energy calibration and nuclear effects. MS @nuint01,Walter ， Wood@nuint02 q e Ee’Ee’ np 

31. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 3.3) N   transition form factors

32. 1 August 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 )= ０ [PCAC] C 3 A (0)= 0. C 4 A (0)=-0.3, C 5 A (0)=1.2

33. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions N  FF falls more rapidly than Nucleon FF (M V ) Size of  is larger = Q 2 distribution small New 1975

34. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 3.4) For better single pion production model Rein-Sehgal model need nuclear correction. Much simpler model like Schreiner-von Hippel may work. Paschos,Singh,MS Below for W<1.6 GeV/c 2,  model with Schreiner parameters and three resonances may be used. Ci A,V = Ci A,V (0) G(W,Q 2,k F ) 1/2 / (1+Q 2 /M V,A 2 ) 2 /(1+Q 2 /3M N 2 ) G(W,Q 2,k F ) Pauli effect. Non-resonant contribution,<20%, may be added. For W>1.6, Bodek ’ s DIS may be used. Paschos-Pasquali-Yu, NPB588( ‘ 00)263, already show that this scheme may work. Paschos,Yu, & Sakuda, DOTH0301, to be published.

35. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions d  /dQ 2 (   production) from BNL Furuno,Suzuki,Kitagaki,MS,etal, to be published. μ－ｐπ＋ nsμ－ｐπ＋ ns Q 2 (GeV) Rein-Sehgal (M A =1. ０８ 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

36. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Flux independent ratio σ(single π)/σ(QE) : BNL reanalysis Furuno@nuint02 -pπ+-pπ+ -nπ+-nπ+ -pπ0-pπ0 E ν （ GeV)

37. 1 August 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.

38. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Nuclear PDF and its effect on the DIS cross section

39. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions The accuracy of Neutrino-Nucleus ( -N) interactions at E =0.1-10 GeV is still poor, about 10-20% in cross section measurements and distributions. We will combine both e-N data and -N data to understand -N interactions better. Re-analysis of old data (BNL,ANL) using current formalism is still valuable. Old nucleon form factors are now being updated. It has +-5% effect on Q 2 distribution and 2-3% on the cross section. N  FF too. The calculation of resonance production is also being updated. Spectral function calculation which improves the old Fermi-gas model calculation is extensively studied. Transition between DIS and resonance region is complex. Bodek ’ s calculation is the first trial. 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 operation in 2006. All these studies will become a step toward the precision neutrino experiments. 5. Summary

40. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Fig.1 Nuance quasi-elastic (hist) and (e,e ’ ) Data ( ). The energy transfer (  =Ee-Ee ’ ) at the fixed scattering angle. Nuance uses Vb=-27MeV and kF=225 MeV/c. Ee ’ =Ee-  Carbon Oxygen

41. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions A Phased (Installation) High-resolution Detector: Basic Conceptual Design 2m x 2 cm x 2cm scintillator (CH) strips with fiber readout. ( int = 80 cm, X 0 = 44 cm) Fiducial volume: (r =.8m L = 1.5 m): 3.1 tons R = 1.5 m - p:  =.45 GeV,  = 51, K =.86, P = 1.2 R =.75 m - p:  =.29 GeV,  = 32, K =.62, P =.93 Also 2 cm thick planes of C, Fe and Pb. 11 planes C = 1.0 ton (+Scintillator) 3 planes Fe = 1.0 ton (+MINOS) 2 planes Pb = 1.0 ton Readout: Current concept is VLPC. (How about PMT or CCD + Image Intensifier?) Use MINOS near detector as forward  identifier / spectrometer. Considering the use of side  -ID detectors for low-energy  identification.

42. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions Effect of Neutrino Interactions on Oscillation Analysis K2K (Ahn et al., PRL90,041801,2003 and Itow@nuint02 ) shows that the oscillation analysis is not affected by the uncertainties in neutrino interactions at present. Analysis compares the spectrum at near and far detectors and the quasi-elastic and inelastic spectrum are similar in shape. Precise knowledge of neutrino interactions will be important in the future precision experiments where the measurement of  m 2 at 1% level are proposed. Itow@nuint01,Walter,Harris@nuint02

43. 1 August 2003 M.Sakuda Neutrino － Nucleus Interactions 3.1) Nucleon Form Factors de Jager @PANIC02 p P q ee

44. 1 August 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 Jager ＠ PANIC02