1. Mary Hall Reno Neutrino-nucleon interactions: what can we learn from electromagnetic interactions and quark-hadron duality? Hallsie Reno Trento, May 2005

2. Mary Hall Reno Advertisement for neutrino physics in context of this workshop (Ultra)-high energy neutrinos: Neutrino induced air showers Neutrino interactions in ice Radio Cherenkov signals, detected in situ or with balloon borne detector Rule of thumb: Unitarity Onset of saturation Log(1/x) corrections

3. Mary Hall Reno (Advertisement) Medium energy neutrinos:100’s GeV – 100’s TeV Neutrino scattering: NuTeV’s measurement of the weak mixing angle differs from the world average challenge to assumptions about Neutrino production: “Prompt” neutrino flux

4. Mary Hall Reno (Advertisement) “Low” energy neutrinos: Atmospheric neutrinos from Neutrino beams like NuMI and CNGS.

5. Mary Hall Reno Talk about “low” energy neutrinos I’m interested in a practical solution to calculate neutrino cross sections that at the same time includes the “best” that we can do. Talk: Specifically what low energies, why are we interested? (Neutrino oscillations) Components of the cross section. Help from local hadron duality? Help from phenomenological approach to PDFs at low Q? Put it together – and look for some independence in parameters?

6. Mary Hall Reno Neutrino Cross Section – Required Figure Lipari, Lusignoli and Sartogo, PRL 74 (1994) Deep inelastic scattering Quasi-elastic scattering Pion production 0.1 GeV100 GeV Neutrino data at these energies is not extensive. Antineutrino data even less. C.f. G.P. Zeller, hep-ex/0323062

7. Mary Hall Reno Neutrino Oscillations Atmospheric neutrinos: L=Earth diameter=12000 km Average E around a few GeV http://neutrino.kek.jp/index-e.html Atmospheric neutrinos, coming from all angles, give a wide range of L/E Muon neutrino deficit, as a function of L/E, shows evidence of neutrino oscillation. muon neutrino disappearance

8. Mary Hall Reno Neutrinos from Fermilab http://www-numi.fnal.gov Multiply evt. totals by 3.4 to get nu_mu events per year (without oscillations). 735 km

9. Mary Hall Reno Neutrino Cross Section-Required Figure Lipari, Lusignoli and Sartogo, PRL 74 (1994) Deep inelastic scattering Quasi-elastic scattering Single pion production NuMI Low energy beam is best for MINOS distance.

10. Mary Hall Reno CERN to Gran Sasso – Tau neutrino appearance http://www.mi.infn.it/~psala/Icarus/cngs.htmlhttp://www.mi.infn.it/~psala/Icarus/cngs.html L=1000 km

11. Mary Hall Reno Tau neutrino appearance Threshold energy for tau production: 3.5 GeV Part of our initial motivation to look at the cross section: tau mass, proton mass, charm mass effects along with NLO QCD. Cf. S. Kretzer & MHR, PRD 66,69

12. Mary Hall Reno Calculation – how is it done? Quasi-elastic Resonance dominated by Delta Deep Inelastic Scattering avoid double counting – use a cut on W Concern about missing nonresonant contributions at lower W….

13. Mary Hall Reno Issues in Quasi-elastic Scattering From J. Monroe/MiniBoone for NuInt04, hep-ex/0408019 Preliminary MiniBoone data appear to disagree with Monte Carlo models at low Q. Nuclear models? Llewellyn Smith formalism with dipole form factors.

14. Mary Hall Reno Resonances Monte Carlos, e.g., NUANCE by D. Casper, implements the Rein and Sehgal, Ann. Phys. 133 (1981) 79 updated to current masses, widths. Uses harmonic oscillator quark wavefunctions in model. Resonance production up to some W value (say 2 GeV for NUANCE, or 1.4 GeV as in “Required figure”). Fermi Gas model of Smith and Moniz. Includes some final state interactions. There have been recent studies, including by E. Paschos and collaborators & Hagiwara, Mawatari and Yokoya & Sobczyk, Nowak and Graczyk and others on resonance contributions.

15. Mary Hall Reno DIS Standard DIS formula, 5 structure functions: (Generalized Callan-Gross relation) Target mass corrected See Kretzer & MHR

16. Mary Hall Reno Neutrino-Nucleon Scattering with TMC Georgi-Politzer, DeRujula OPE approach. Nachtmann variable

17. Mary Hall Reno TMC in parton picture Ellis, Furmanski and Petronzio showed that the TMC result can be obtained with: Parton momentum on shell but not collinear with the proton in parton level cross section. Generalized kT dependent PDF of a general form, but NOT of the form: TMC come from mismatch of P(proton) and p (quark) (one massive and one massless). They also come from kT limited to less than M.

18. Mary Hall Reno Electromagnetic Scattering : Related Processes Extensive study of ep scattering, in the resonance region and beyond, by Jefferson Lab groups, SLAC exps. Local quark-hadron duality shown for a range of W. Local duality means restricted range of x integration of the structure function and data give same result Unpolarized case: at fixed Q, for a range of W (restricted x range) including resonances, above the Delta resonance, integral of F2 agrees well between data and NLOTMC, even better if large x resummation is done. Shown by Fantoni, Bianchi and Liuti. “Quark hadron duality in electron scattering, Melnitchouk, Ent & Keppel, hep-ph/0501217 (Phys. Rept.)

19. Mary Hall Reno Use local duality for neutrino scattering Local duality not explicitly demonstrated in neutrino scattering – one motivation for the MINERvA experiment. Nevertheless use it in neutrino scattering in the region where local duality holds for ep scattering. (Add large x resummation as per Fantoni et al.) Should be in the regime where W is larger than 1.4 GeV to use this.

20. Mary Hall Reno A phenomenological approach: Bodek Park & Yang Fit ep scattering data Use GRV98 PDFs Redefine scaling variable

21. Mary Hall Reno Bodek-Park-Yang hep-ph/0411202 Rescale valence and sea distributions Overall normalization Structure function:

22. Mary Hall Reno Bodek-Park-Yang meets JLAB E. Christy provided me with parameterization of ep data, “Christy param.”

23. Mary Hall Reno Comparisons in the ep case dot-dash: LO and LO-TMC dotted: NLO and NLO-TMC Can see the need for large x resummation here...

24. Mary Hall Reno More comparisons in ep case Range of Q^2 with steps of 0.2 GeV^2.

25. Mary Hall Reno Prescription of BPY-completely phenomenological Use the modified PDFs fit to DIS electromagnetic scattering for neutrino scattering for W greater than 1.35 GeV. Use explicit calculations for resonance region and quasi-elastic. Note: there are not simple Clebsch-Gordon factors in converting to neutrino scattering. (Work on fits to axial vector modifications at low energy.)

26. Mary Hall Reno BTW: PDF uncertainties: using 40 CTEQ6 PDFs more uncertainty in u, d distributions

27. Mary Hall Reno How do NLOTMC corrected neutrino structure functions compare with electromagnetic structure functions of BYP?

28. Mary Hall Reno ep and neutrino-nucleon scattering

29. Mary Hall Reno Comparison in neutrino nucleon structure function assume axial vector contribution is same as vector contribution, and take new combinations to get neutrino structure functions:

30. Mary Hall Reno How do NLOTMC corrected neutrino structure functions compare with electromagnetic structure functions of BYP? Not so well at low Q

31. Mary Hall Reno Neutrino cross section Half the cross section is from Q less than 1 GeV for this energy…. The same figure for LO or NLOTMC with a minimum Q2=0.8 GeV2. NLOTMC structure functions don’t match BPY parameterization well at Q=1 GeV.

32. Mary Hall Reno Neutrino DIS cross section Circumstance of large M/Q and strong coupling. The “K factor” for DIS for this energy is only 1.08-1.11 for Qmin less than 1.3 GeV and W greater than 1.4 GeV. Need phenomenological assistance for low Q, especially low x…

33. Mary Hall Reno Neutrino cross section – dependence on matching scale? Delta cross section for W up to 1.4 GeV. Need Delta contribution up to other values of W. One hopes not!

34. Mary Hall Reno An option Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering. Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV. Use a resonance model below W=1.4-2.0 GeV. Include quasi-elastic scattering. Vary (x,Q,W) boundaries to see that the total cross section remains unchanged.

35. Mary Hall Reno An option Use NLOTMC plus large x resummation to calculate the DIS in the region demonstrated to exhibit local duality in ep scattering. Pick an (x,Q) boundary, below which to use a phenomenological parameterization like Bodek-Park-Yang. Stay above W=1.4-2.0 GeV. Use a resonance model below W=1.4-2.0 GeV. Include quasi-elastic scattering. Vary (x,Q,W) boundaries to see that the total cross section remains unchanged. Tau neutrino scattering cross section is under better control theoretically. Ultimately, the muon neutrino cross section will be measured by MINERvA. Is this step necessary? NNLO – could this solve the x=0.1 discrepancy?