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Neutrino cross sections in few hundred MeV energy region

Neutrino cross sections in few hundred MeV energy region. Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with A. Ankowski and J. Nowak). Plan of the talk: Introduction Quasi-elastic scattering off free target (form-factors, axial mass).

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Neutrino cross sections in few hundred MeV energy region

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  1. Neutrino cross sections in few hundred MeV energy region Jan T. Sobczyk Institute of Theoretical Physics, University of Wrocław (in collaboration with A. Ankowski and J. Nowak)

  2. Plan of the talk: • Introduction • Quasi-elastic scattering off free target (form-factors, axial mass). • 3. Significance of single pion production. • Nuclear effects – general remarks. • Nuclear effects – numerical results (models: Fermi gas, • spectral function, momentum dependent effective potential). • 5. Conclusions. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  3. Total neutrino – nucleon CC cross sections neutrino anti-neutrino • We distinguish: • quasi-elastic • single pion production („RES region”, • e.g. W<=2 GeV) • more inelastic („DIS region”) Focus on few hundred MeV neutrino energies: quasi-elastic region. Plots from Wrocław MC generator Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  4. The aim of analysis „Double ratio”: As intermediate step also „ratios”: Targets: water (argon computations are not yet finished). Basic problem: How sensible the double ratio is to nuclear effects in the energy range of few hundred MeV? Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  5. Quasi-elastic reaction - theory 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, ISS meeting, RAL, April 26, 2006

  6. Quasi-elastic reaction (from Naumov) Huge experimental uncertainty The limiting value depends on the axial mass Under assumption of dipole vector form-factors: (A. Ankowski) Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  7. 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, ISS meeting, RAL, April 26, 2006

  8. Quasi-elastic reaction – first step Free target cross sections: Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  9. Quasi-elastic reaction - uncertainties • Do theoretical/experimental uncertainties: • axial mass • electromagnetic form-factors • have an impact on cross-section ratios? Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  10. Quasi-elastic reaction - uncertainties Axial mass … … no change! Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  11. Quasi-elastic reaction - uncertainties Electromagnetic form-factors … … no change! Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  12. Single pion production - kinematics Threshold for the pion production Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  13. Single pion production 3 CC channels for neutrino and 3 CC channels for anti-neutrino reactions. The characteristic feature is that the dominant contribution comes from resonance excitation (mainly Δ): Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  14. Single pion production What is a significance of spp channels in few hundred MeV energy region? What is their impact on total cross sections ratios? Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  15. Relevance of single pion production Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  16. Relevance of single pion production Target: free nucleons Relevant at <0.35% level for E<500MeV. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  17. Nuclear effects – general remarks • The treatment is energy-dependent: • low energies: shell model • intermediate energies: CRPA • higher energies: impulse approximation (Fermi gas, spectral function) What does it mean: „low”, „intermediate”, „higher”?! Peter Vogel (nucl-th/9901027): For electron neutrino energies starting from ≈ 200 MeV CRPA and FG give rise to very similar total and differential cross-sections. Giampaolo Co’: Impulse approximation methods make sense for momentum transfer > 400 MeV. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  18. Nuclear effects – general remarks The methods well justified in GeV region will be used and … … the results which follow should be treated with caution. Impulse approximation based computations will be presented. The hope is that ratios are not very much sensitive to details of nuclear effects modelling. The methods are reliable for E>250 MeV (?). Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  19. Impulse approximation • neutrino interacts with an individual (bound) • nucleons • „final state interactions” (FSI) follows (does • not change inclusive cross-section) (from Ch. Maieron, XX Max Born Symposium) Step 1: Fermi gas Step 2: Spectral function The simplest realization: Fermi gas model defined by 2 parameters. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  20. Spectral function 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, ISS meeting, RAL, April 26, 2006

  21. Spectral function Spectral function for oxygen 1p (1/2) 1p (3/2) (from O. Benhar) Spectral function approach is parameter free. But FSI/Pauli blocking effects must be added. 1s Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  22. Effective (momentum dependent) potential (from Leitner, Alvarez-Ruso, Mosel, nucl-th/0601103) (from Juszczak, Nowak, Sobczyk, Eur. Phys. J. C39 (2005) 195) Step 1: LDA (Fermi gas + nucleus density profile) Step 2: LDA + effective potential Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  23. ??? ??? ??? ??? Spectral function - results Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  24. Effective potential – results ??? ??? ??? ??? Preliminary Preliminary Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  25. ??? ??? Spectral function - ratios FG – Fermi gas model SF – spectral function with Pauli blocking Binding energy 27 MeV is very important at low energies. The model is obviously not appropriate at low energies. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  26. Effective potential – ratios ??? ??? Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  27. ??? Spectral function - ratios Measure of relevance of nuclear effects: FG – Fermi gas model SF – spectral function with Pauli blocking Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  28. Effective potential – ratios Measure of relevance of nuclear effects: ??? ??? Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  29. Effective potential – ratios Measure of relevance of nuclear effects: Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  30. Spectral function – double ratios ??? Targets: free nucleons and water Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  31. Spectral function – double ratios ??? Targets: free nucleons and water At 250 MeV the reduction of DR is ~5% At 300 MeV the reduction of DR is ~2.5% Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  32. Effective potential – double ratios ??? Targets: free nucleons and water Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  33. Effective potential – double ratios ??? Targets: free nucleons and water Preliminary Preliminary Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  34. Conclusions The energy region 250-500 MeV has been investigated. The caution is necessary: the methods are well justified only at higher energies. „Ratios” R (and automatically also „double ratios” - DR) are not sensitive to uncertainties of free quasi-elastic description. Pion production changes DR by less than ~0.4%. For energies ~250 MeV nuclear effects can reduce DR by 2-6%. The sensitivity of DR to nuclear effects seems to decrease quickly for higher energies. Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  35. The end Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  36. Fermi gas – dependence on Fermi momentum (the same value of binding energy: 27 MeV) Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

  37. Comparison with Amaro-Nieves group (very recent paper: hep-ph/0604042) FG – Fermi gas model SF – spectral function with Pauli blocking LDA – local density approximation Oxygen – effective potential Jan T. Sobczyk, ISS meeting, RAL, April 26, 2006

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