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Modelling neutrino cross sections

Modelling neutrino cross sections. Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with A. Ankowski, K. Graczyk, C. Juszczak, J. Nowak). Plan of the talk: Overview, „decomposition” of the total cross section.

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Modelling neutrino cross sections

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  1. Modelling neutrino cross sections Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with A. Ankowski, K. Graczyk, C. Juszczak, J. Nowak)

  2. Plan of the talk: • Overview, „decomposition” of the total cross section. • Quasi-elastic scattering (form-factors, axial mass). • Single pion production (Rein-Sehgal model, Δ excitation models) • More inelastic channels (DIS formalism, structure functions, • higher twists, target mass corrections, low Q2 limit, • quark-hadron duality) • Nuclear effects (Fermi gas, spectral function, • nuclear effects in DIS) • 6. Outlook. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  3. Total neutrino – nucleon cross sections Plots from Wrocław MC generator • We distinguish: • quasi-elastic • single pion production („RES region”, • e.g. W<=2 GeV) • more inelastic („DIS region”) Focus od few GeV neutrino energy region: all 3 dynamics are relevant. Focus on MC implementations Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  4. Kinematics Threshold for the pion production Boundary of RES – DIS regions Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  5. Quasi-elastic reaction CVC – use electromagnetic data PCAC We need the axial form-factor; the standard dipole form gA =1.26 from neutron decay; MA a free parameter (the only one) The value of axial mass is obtained from experimental data. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  6. Quasi-elastic reaction where: Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  7. Quasi-elastic reaction (from J.J. Kelly, Phys. Rev. C 70 (2004) 068202) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  8. Quasi-elastic reaction Dipole electromagnetic form-factors: One can find better fits to the existing data, BBBA2005 (from R. Bradford talk at NuInt05) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  9. Quasi-elastic reaction Must be taken into account in the discussion of small Q2 deficit of events in K2K experiment. Two ways of determining axial mass: the shape of differential cross section and total cross section. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  10. Quasi-elastic reaction (from Naumov) The limiting value depends on the axial mass Under asumption of dipole vector form-factors: (A. Ankowski) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  11. Single pion production 3 CC channels for neutrino reactions: Characteristic feature is that the dominant contribution comes from: Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  12. Single pion production BNL data: Kitagaki et al. PRD54 (1986) 2554: Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  13. Single pion production The overall cross sections for SPP reactions (with the W ≤ 2 GeV cut): Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  14. Single pion production • Theoretical models: • resonance excitation • non-resonant background • Resonance excitation: • in most practical applications: Rein-Sehgal model (18 resonances • up to 2 GeV, interference terms, a fit to data of the non-resonant part) • recent detail study: Lalakulich, Paschos; leptonic mass terms are kept • Sato-Lee model (non-resonant background is included) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  15. Single pion production Predictions of the Rein-Sehgal model (with nonresonant background): ANL beam FNAL beam ~ 30 GeV (antineutrinos) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  16. Single pion production CVC: PCAC: Adler model: (from O. Lalakulich, XX Max Born Symposium) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  17. Single pion production New data on helicity amplitudes and rather then C5V=0 (magnetic multipole dominance) (from L.Tiator et al., EPJA 19 (2004) 55) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  18. Single pion production Results from Lalakulich, Paschos model: Non-zero leptonic mass A comparison with Rein-Sehgal model is missing. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  19. Single pion production Very little is known about NC pion production: (NC π0 production is an important background!) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  20. More inelastic channels Structure functions for inclusive cross section: Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  21. More inelastic channels Dimensionless structure functions: W4, W5 in terms with m2 only Instead of Callan-Gross relation: R is measured experimentally. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  22. More inelastic channels Computation of F2 and F3 In the scaling limit: Q2 dependence. Large Q2, perturbative QCD, twist expansion. Expressed by PDFs; Q2 dependence via Altarelli-Parisi equation. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  23. More inelastic channels All above (twist expansion) in the massless limit. Target mass corrections (TMC) are necessary. For small x2 M2 /Q2 TMC modify LT is Nachtmann variable Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  24. More inelastic channels (from Wrocław MC) E=1 GeV E=3 GeV E=10 GeV E=5 GeV Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  25. More inelastic channels E=10 GeV E=3 GeV It is clear that low Q2 (Q 2≤ 1GeV2) are important Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  26. More inelastic channels Low Q2 behavior. In electron scattering gauge invariance implies: In neutrino scattering from PCAC: PCAC There is a lot of theoretical activity! and similarly for FL Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  27. More inelastic channels In the few GeV region an important idea from both theoretical and practical (MC) point of view is quark-hadron duality MC: how to combine smoothly RES and DIS regions? Recent JLab electron data (from I. Niculescu et al. PRL 85 (2000) 1184, 1187) In neutrino physics a lot of activity – see the next slide! Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  28. More inelastic channels Quark-hadron duality in neutrino scattering: (from K. Matsui, T. Sato,and T.-S. H. Lee, PRC 72 (2005) 25204) (from O.Lalakulich) (from K.Graczyk, C.Juszczak, JS) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  29. Nuclear effects Red line – Relativistic Shell Model Blue and pink lines – Fermi Gas Model • At E=1 GeV a general picture: • neutrino interacts with an individual (bound) • nucleons • „final state interactions” (FSI) follow Impulse approximation: In MC codes FSI is usually taken into account numerically in nuclear cascade. (from Ch. Maieron, XX Max Born Symposium) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  30. Nuclear effects Fermi gas model – quasi-elastic reaction Fermi momentum average binding energy off shell matrix element PWIA – „plane wave impulse approximation”: outgoing nucleon – plane wave Dirac spinor Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  31. Nuclear effects Fermi gas model – quasi-elastic reaction E= 1GeV Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  32. Nuclear effects Realistic distribution of momenta Short range correlations (SRC): correlated pairs of nucleons (from A. Ankowski) (from O. Benhar et al. hep-ph/0516116) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  33. Nuclear effects Spectral function: In the PWIA we obtain: Precise computations for A≤16. Computations combine mean field part and SRC part. Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  34. Nuclear effects Spectral function for oxygen 1p (1/2) 1p (3/2) (from O. Benhar) 1s Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  35. Nuclear effects Spectral function „cuts” the quasi-elastic peak. In the second figure FSI is reduced to the Pauli blocking Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  36. Nuclear effects - FSI Distorted wave IA: outgoing nucleon is a solution of equation: Scalar and vector complex optical potentials: rescattering and absorption into other channels. RSM – relativistic shell model RFG – reletivistic Fermi gas RMF – relativistic mean field Real ROP – no absorption ROP – full optical potential (from Ch. Maieron, XX Max Born Symposium) FSI effects are important! Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  37. Nuclear effects Kulagin, Petti approach to deal with DIS nuclear effects Scales: x>0.2 → incoherent sum of contributions from bound nucleons (spectral function) x<0.3 → correction from scattering on pions x<<0.2 → coherent effects (shadowing, multiple scattering on nucleons) FMB – Fermi motion, nuclear binding OS – off-shell corections PI – nuclear pion excess NS – nuclear coherent processes Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  38. Nuclear effects Kulagin, Petti approach to deal with DIS nuclear effects The model contains 3 free parameters fitted to the data Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  39. Conclusions: A lot of theoretical activity. Precise data for few GeV neutrino interactions is missing Future experiment: MINERνA Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  40. MINERνA MINERvA is a neutrino detector to study neutrino-nucleus interactions. It will be placed in the NuMI beam line. 3 energy beams Commissioning Fall 2008 Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  41. MINERνA Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  42. MINERνA Now… .. after MINERνA measurements (from V.Naumov, XX Max Born Symposium) Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  43. MINERνA Now… (from V. Naumov) BNL data .. after MINERνA measurements Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

  44. In 6 years a talk on modelling neutrino cross-sections will be very different! THE END Jan T. Sobczyk, Epiphany Conference, Kraków, Jan. 6, 2006

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