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. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20062 Plan of the talk: 1.Introduction 2.Quasi-elastic scattering off free target (form-factors, axial mass). 3. Significance of single pion production. 3.Nuclear effects – general remarks. 4.Nuclear effects – numerical results (models: Fermi gas, spectral function, momentum dependent effective potential). 5. Conclusions.

3. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20063 Total neutrino – nucleon CC cross sections 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 neutrino anti-neutrino

4. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20064 The aim of analysis „Double ratio”: 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? As intermediate step also „ratios”:

5. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20065 Quasi-elastic reaction - theory CVC – use electromagnetic data PCAC We need the axial form-factor; the standard dipole form g A =1.26 from neutron decay; M A a free parameter (the only one) The value of axial mass is obtained from experimental data.

6. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20066 Quasi-elastic reaction The limiting value depends on the axial mass Under assumption of dipole vector form-factors: (from Naumov) (A. Ankowski) Huge experimental uncertainty

7. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20067 Quasi-elastic reaction One can find better fits to the existing data, BBBA2005 Dipole electromagnetic form-factors : (from R. Bradford talk at NuInt05)

8. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20068 Quasi-elastic reaction – first step Free target cross sections:

9. Jan T. Sobczyk, ISS meeting, RAL, April 26, 20069 Quasi-elastic reaction - uncertainties Do theoretical/experimental uncertainties: axial mass electromagnetic form-factors have an impact on cross-section ratios?

10. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200610 Axial mass … … no change! Quasi-elastic reaction - uncertainties

11. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200611 … no change! Electromagnetic form-factors … Quasi-elastic reaction - uncertainties

12. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200612 Single pion production - kinematics Threshold for the pion production

13. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200613 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):

14. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200614 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?

15. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200615 Relevance of single pion production

16. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200616 Relevance of single pion production Target: free nucleons Relevant at < 0.35% level for E < 500MeV.

17. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200617 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.

18. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200618 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 (?).

19. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200619 Impulse approximation (from Ch. Maieron, XX Max Born Symposium) neutrino interacts with an individual (bound) nucleons „final state interactions” (FSI) follows (does not change inclusive cross-section) The simplest realization: Fermi gas model defined by 2 parameters. Step 1: Fermi gas Step 2: Spectral function

20. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200620 (from O. Benhar et al. hep-ph/0516116) Spectral function Realistic distribution of momenta (from A. Ankowski) Short range correlations (SRC): correlated pairs of nucleons

21. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200621 Spectral function Spectral function for oxygen 1s 1p (1/2) 1p (3/2) (from O. Benhar) Spectral function approach is parameter free. But FSI/Pauli blocking effects must be added.

22. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200622 Effective (momentum dependent) potential (from Juszczak, Nowak, Sobczyk, Eur. Phys. J. C39 (2005) 195) (from Leitner, Alvarez-Ruso, Mosel, nucl-th/0601103) Step 1: LDA (Fermi gas + nucleus density profile) Step 2: LDA + effective potential

23. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200623 Spectral function - results ???

24. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200624 Effective potential – results ??? Preliminary

25. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200625 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. ???

26. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200626 Effective potential – ratios ??? Preliminary

27. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200627 Spectral function - ratios FG – Fermi gas model SF – spectral function with Pauli blocking Measure of relevance of nuclear effects: ???

28. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200628 Effective potential – ratios ??? Measure of relevance of nuclear effects: Preliminary

29. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200629 Effective potential – ratios Measure of relevance of nuclear effects: Preliminary

30. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200630 Spectral function – double ratios Targets: free nucleons and water ???

31. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200631 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% ???

32. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200632 Effective potential – double ratios ??? Targets: free nucleons and water Preliminary

33. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200633 Effective potential – double ratios Targets: free nucleons and water ??? Preliminary

34. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200634 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.

35. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200635 The end

36. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200636 Fermi gas – dependence on Fermi momentum (the same value of binding energy: 27 MeV)

37. Jan T. Sobczyk, ISS meeting, RAL, April 26, 200637 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