Flavio Cavanna L’Aquila Univ. & INFN Yale - July. 11th, 2006

1. Neutrino cross-sections: current studies and experimental programs Flavio Cavanna L’Aquila Univ. & INFN Yale - July. 11th, 2006 • References: • http://fphy.hep.okayama-u.ac.jp/NuInt05/(in printing on Nucl. Phys. B) • http://NuInt04.lngs.infn.it (Nucl. Phys.B - Proc.Supll. 139, 2005) • http://www.ps.uci.edu/~NuInt02 • http://neutrino/kek.jp/NuInt01(Nucl. Phys.B - Proc.Supll. 112, 2002)

2. The discovery of the neutrino non-standard properties (mass and mixing) • refocused on various aspects, both theoretical and experimental, • of neutrino standard properties (e.g. cross-sections): • The n-Nucleus Cross-Section and related Nuclear Effects represents • (one of) the most important sources of uncertainty in the • “Intermediaten-EnergyRange”: 0.5 - 5 GeV • of interest for the next generation oscillation studies. QUESTIONS about the neutrino cross section: [A] How well do we know (have we measured) it ? [B] How well do we understand it theoretically ? [C] How well do we need to know it for Oscillation Studies ? [D] What new Experimental Programs can be most effective to improve our Knowledge?

3. 45 systematic error terms in SK Atm-n analysis (T. Kajita - NuInt05,Sept.05) (0, Free parameter) Flux, Nu-int, Fit; absolute normalization (1) Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu < 5GeV ) (2) Flux; (nu_mu + anti-nu_mu) / (nu_e + anti-nu_e) ratio ( E_nu > 5GeV ) (3) Flux; anti-nu_e / nu_e ratio ( E_nu < 10GeV ) (4) Flux; anti-nu_e / nu_e ratio ( E_nu > 10GeV ) (5) Flux; anti-nu_mu / nu_mu ratio ( E_nu < 10GeV ) (6) Flux; anti-nu_mu / nu_mu ratio ( E_nu > 10GeV ) (7) Flux; up/down ratio (8) Flux; horizontal/vertical ratio (9) Flux; K/pi ratio (10) Flux; flight length of neutrinos (11) Flux; spectral index of primary cosmic ray above 100GeV (12) Flux; sample-by-sample relative normalization ( FC Multi-GeV ) (13) Flux; sample-by-sample relative normalization ( PC + Up-stop mu ) Flux (13) Detector, reduction and reconstruction (20) (14) MA in QE and single-p (15) QE models (Fermi-gas vs. Oset's) (16) QE cross-section (17) Single-meson cross-section (18) DIS models (GRV vs. Bodek's model) (19) DIS cross-section (20) Coherent-p cross-section (21) NC/CC ratio (22) nuclear effect in 16O (23) pion spectrum (24) CC ntcross-section (25) Reduction for FC (26) Reduction for PC (27) Reduction for upward-going muon (28) FC/PC separation (29) Hadron simulation (contamination of NC in 1-ring m-like) (30) Non-n BG ( flasher for e-like ) (31) Non-n BG ( cosmic ray muon for mu-like ) (32) Upward stopping/through-going mu separation (33) Ring separation (34) Particle identification for 1-ring samples (35) Particle identification for multi-ring samples (36) Energy calibration (37) Energy cut for upward stopping muon (38) Up/down symmetry of energy calibration (39) BG subtraction of up through m (40) BG subtraction of up stop m (41) Non-necontaminationformulti-GeV 1-ringelectron (42) Non-necontaminationformulti-GeV multi-ringelectron (43) Normalizationofmulti-GeV multi-ringelectron (44) PC stop/through separation ninteraction (11)

4. Neutrino Energy of O(1 GeV): a natural choice for LBL (precision measurements) experiments n-Interactions on p-n/ q-q in C, O, Fe, Ar, Pb,.. Nuclei X-Section Natural Decompositions: stot = sQ-El  sRes sDIS = s0 p s1 p s2 p … Well known problem: Experimental Data rather poor and affected by large errors

5. [sQ-El] Quasi-Elastic Scattering on free N (low Q2, x=1, W=Mp): nl + n  l- + p J lepta G J hada Dynamics described by Current-Current Lagrangian J had = V - A defined through Nucleon Weak Form Factors: Vector F.F. [FV1(Q2), FV2(Q2)], related to El.M. F.F. (Hp. CVC), Axial F.F. [FA(Q2)] and PseudoScalar F.F. [FPS(Q2)] Note: Vector F.F. can be (are) determined from e-scattering exp. Axial F.F. (assumed dipolar form) withMA free parameter PseudoScalar F.F. term in Xsect is proportional to (ml/Mp)2 i.e.relevant only for nl = nt Q-el scattering on Nboundin A: the rise of Nuclear Effects (i.e. non-perturbative effects of strong interactions inside the target)  Absence of a well defined model

6. [sRes] Resonance Excitation (low Q2, large x, W): nl + N  l- + D l- + np + N’ En N 1/2 D 3/2 Mp mass of hadronic final state From theoretical point of view: the Most complicated channel. E.g.: (FKR) N = 3q system bound by harmonic potential in ground state D, N* corresponds to excited states, decaying with p production Each decay channel results from superposition and interference between allowed resonance amplitude [Rein & Seghal, …. ]. If Nboundin A Nuclear Effects, final state (re)interactions are even more severe. From experimental point of view: the least precisely measured channel

7. [sDIS](Deep) Inelastic Interactions [x  (0,1), large Q2]nl + N  l- + X Dynamics described by SM (massive W±) J had defined through Nucleon Structure Functions: Precise high-Q2 DIS data available (from e-N and v-N experiments) Limited Impact of Nuclear Effects but.. How to connect RES and low-Q2 DIS regimes still unclear (“twilight zone”) Note: F4 and F5in Xsect proportional to (ml2/MN)i.e.relevant only for nl = nt

8. A new challenge - in the Intermediate-energy region - • Nuclear Models and Nuclear Effects: • Random Phase Approximation • Nuclear Many Body Theory • Relativistic Shell-Model • Nucleon Form Factors: • new parameterizations [BBA2003 => BBBA2005] • Strange F.F. • Q-El : new Xsect calculations • mass terms correction (mn-mp, ml, rad.corr., ..) • tau polarization • RES: • Nucleon and Pion re-scattering in Nuclear Matter • tau production • DIS: PDF - from high-Q2 DIS data to low-Q2 to describe low-energy n-data: • RES-to-DIS transition (quark-hadron duality) • X-sect at NLO perturb. QCD • PDF modification Current sparkling activity in the theoretical field of the n-A interaction: … and the list is NOT complete … Overall goals: describe all three processes (Q-El, RES, DIS) for both eandn at all energies  progress in modeling Nuclear Effects beyond RF-gas model

9. NMBT : Nuclear Spectral Function SF(k,E) e-A scattering =  s(e-N) SF [Benhar et al.] where s(e-N) is the e-free N Xsect (IA -Impulse Approx.) and SF=P (k ,E) is the nuclear Spectral Fcn. from Nuclear Many Body Th. Probability of removing a nucleon of momentum k leaving the residual system with excitation energy E NMBT calculation: N-N and 3 N correlations are included in both Initial and Final State SF’s from NMBT (for light Nuclei) successfully used in the analysis of A(e,e’) data and extended to 16O(n,l); n=ne, nm [Q-El] “Spectral function for Argon” now available !! (A. Ankowski)

10. Results: RFG RFG SF IA+SF nm+ 16O m+X IA+SF+FSI SF+FSI En = 1 GeV H. Nakamura,Sakuda, Seki Benhar & Coll. • w.r.t. RFG (standard n-MC): • Xsect suppression at low-Q2 in agreement with recent n-data !! (see next slides) • Quenching in final lepton Energy distribution, fundamental for future n-experiments • aiming at 1% or better precision !! • Fin. State Interaction is 10% effect: need of quantitative validation from new exp. n-data

11. New n-Data Active beams (intermediate n-Energy): KEK (Japan), FNAL-MiniBooNE (US) • MiniBooNE: • Beam - Mean n-Energy: 700 MeV; 0.5% ne contamination • Detector - 800 t Mineral Oil, Cherenkov + dlyd Scint. Light • 60,000 CC Q-El evts collected CC Q-El:Q2 distr. En distr.

12. Future Measurements:a new dedicated challenge in the Intermediate energy region:

14. Detector Requirements:

17. … nothing else to do??? The fundamental properties of n-interactions have been probed bybubble-chamber experiments LAr technology is the modern version of (electronic) bubble-chamber concept … BEBC - Bubble Chamber - 30 t - CERN 1976 ICARUS - T600 Electronic Bubble Chamber - PAVIA 2001

18. high resolution calorimetry and (virtually) unlimited active mass … with additional • Reconstruction ofg-showers and • p0identification T600 158 MeV  = 141o Minv = 650 MeV 752 MeV  = 25o 140 MeV Minv =140 MeV p0 candidate (error evaluation in progress) Run 975, Event 151 Collection view

19. interaction (with p-recoil reconstruction down to TP > 40 MeV) Muon and hadron Identification D e+ K+ B C A µ+ TP > 40 MeV (range > 2 cm) n Run 939 Event 46 p T600 m K+ d µ+ d 50 lt-prototype

20. Precise measurement of Event kinematics full 3D Reconstruction 50 lt-prototype nm DIS EVENT 50 lt-prototype nm Quasi-elastic EVENT

21. Precise n-Ar Cross Sections (and associated A=40 nuclear effects) is a necessary preliminary step toward future application of LAr-technology in precise n-oscillation experiments So far, n-Ar interactions have (only) been studied with the ICARUS 50-lt prototype exposed to the WANF (high energy) n-beam. A dedicated paper (from recent re-analysis of data collected in ‘97) is ready for publication (based on 86 selected quasi-elastic “golden events”). Dedicated high statistics measurements in the intermediate energy range would be highly envisaged. An intense off-axis n-beam, such as at a near location on the NuMI beamline, would be ideal for this task. The ICARUS LAr-TPC technology fulfills all possible experimental requirements for precise Cross Section Measurements Possibility of using a O(100 t)-LAr detector at a near location on the NuMI beamline will be discussed later at this Workshop

22. Back-up slides

23. Nuclear Models: • At low n Energy, comparable to nuclear excitations, n-A reactions are very sensitive to the actual modeling of nuclear response (e.g. NN correlations);Nuclear Shell Model is effective in this energy range (up to A ≈60). • when n Energy increases (reactions sensitive to Giant-Res. Strength), Random Phase Approximation methods (RPA and CRPA) have been developed to describe the collective excitations of the Nucleus (1p-1h excitations of the correlated ground-state) • At intermediate n Energy individual (quasi-free) Nucleons are off scattered and the remaining (A-1) nucleons can be treated as “spectators”. • Form Factorshave to be suitably determined and parameterized(from e-N and n-N experiments). • Fermi Gas model is effective (depending on parameters - Fermi Momentum and • Binding Energy - to be determined from e-scattering exp.s) • … but other more sophisticated models (NMB Th.) can be adopted.

24. RES Cross Section:

25. The twilight zone • The challenge: • Understanding of RES scattering in terms of quark-parton Model, • i.e. understanding high xPDF’s at very low-Q2 • Different methods under study, e.g.: • 1) Effective LO approach[Bodek, Yang]: • Use “effective L.O. PDFs” with a new scaling variable (xBj xw) to absorb target mass, higher twist, missing higher orders • Good results for DIS p,d(e,e’) F2 SF. • Axial Low-Q2 PDF’s also available, but need to compare to Low-energy n-data to get exact parameter

26. Conclusion/Perspectives in n-physics: • unprecedented richness with a wide spectrum of n- beams • available or approved for the next decade of experiments. • n cross-sections measurement/theory/MC of second generation is • NOW • recognized as a well established, necessary step toward a • second generation oscillation experiments. • n-beams in the FeW-GeV energy range are (and other soon will be) available in Japan and US. • First important results from running experiments start to come out • Proposals for dedicatedexperiments are submitted/approved. The NuIntcommunity, with the important contribution from (e,e’) people, has favored all this and will certainly continue to play a significant role in the field.