1. Neutrino Nucleon Cross Sections: GeV to ZeV Hallsie Reno University of Iowa January 2009

2. The best cross section measurements Particle data group http://pdg.lbl.gov 50350 GeV

3. Plan Review generic neutrino nucleon cross section calculation (with structure functions) Comment on issues at lower energies (say, E=10 GeV) Discuss extrapolations at high energies

4. Cross section Dimensional analysis, low Q:

5. Structure function approach Neglecting lepton mass corrections. See Kretzer&Reno, 2002

6. Parton model approach Charged current structure functions, in terms of parton distribution functions (PDFs), to leading order: Extensive program of extraction of PDFs, eg. Watt, Martin, Stirling, Thorne, arXiv 0806.4890 [hep-ph] Gluck, Jimenez-Delgado, Reya, Eur. Phys. J C53 (2008) Nadolsky et al (CTEQ), Phys. Rev. D78 (2008)

7. Low energy cross section issues Target mass corrections are potentially important Low Q structure functions important, where perturbative QCD is not valid Need more experimental measurements Theory: Experiment: Take a look at this first.

8. “Low energy” cross section Lipari, Lusignoli and Sartogo, PRL 74 (1995) DIS=“deep” inelastic scattering (with W cutoff to avoid double counting), qel=quasi-elastic, one pion exclusive contribution

9. Aside, no double counting Count up exclusive contributions (say 1 pion) up to some total invariant mass W0, then do the inelastic contributions for W larger than this cutoff. for DIS

10. More cross section compilations, circa 2003 G. Zeller, hep-ex 0312061

11. Recent low energy cross section measurements, e.g. MiniBooNE Here, coherent pi0 production, compared with Rein-Seghal based MC. MiniBooNE, Phys. Lett. B664 (2008) Quasi-elastic MiniBooNE measurements: Refinement of nuclear model parameters. MiniBooNE, PRL 100 (2008)

12. Target mass corrections Classic papers: Three corrections: Nachtmann variable, parton vs hadron structure function, pT Georgi & Politzer, PRD 14 (1976) & with deRujula, Ann. Phys. 103 (1977) Barbieri et al, Nucl. Phys. B 117 (1976), Phys. Lett. B 64 (1976) Ellis, Furmanski and Petronzio, Nucl. Phys. B 212 (1983)

13. Nachtmann variable Target mass corrections: kinematic higher twist

14. Hadron-parton “mismatch” Leads to corrections See Aivazis, Olness and Tung, PRD 50 (1994)

15. Another correction: pT Parton model picture Parton is on-shell but has some intrinsic transverse momentum. Transverse momentum up to a scale of M is approximately “collinear” and integrated separately from the hard scattering part. Ellis, Furmanski and Petronzio showed this can give the same results as what I will show next, the (see Georgi, Georgi et al) OPERATOR PRODUCT EXPANSION (OPE)

16. Complicated formulas: electromagnetic case leading plus convolution terms

17. More complicated formulas

18. Target mass corrections-F2 electromagnetic Schienbein … MHR… et al, J Phys G 35 (2008) Most important for large x, low Q. I am interested here in the neutrino- nucleon cross section.

19. Target mass corrections Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005) No extrapolation to low Q- take F2 constant below 1.14 GeV=Q Antineutrino scattering has smaller y, so smaller Q.

20. Target mass corrections, importance of low Q Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005) Big contribution from low Q: these cross sections must have some large uncertainties… Challenge: to find a suitable low Q form for the structure functions.

21. An extrapolation to low Q that works: Capella, Kaidalov, Merino and Tranh Van CKMT, Phys. Lett. B 337, 358 (1994), Moriond 1994, 7 parameters in for electromagnetic scattering. See, Reno, Phys. Rev. D 74 (2006) sea, small x valence, large x

22. Valence component

23. Sea component

24. Now convert to neutrino scattering See also CKMT Moriond proceedings. The sea distribution changes only in overall normalization to match F2 reasonably well with the NLO+TMC evaluation: fixed at Note that for the sea part, This is what you would estimate using the charged current and electromagnetic structure functions:

25. CKMT for neutrinos Expect that the underlying non-perturbative process is governed by the same power law and form factor for the sea part: For the valence part, recalculate B and f : Valence x and Q dependence shouldn’t change between electromagnetic and charged current scattering. For F1, use a parameterization of R from Whitlow et al, Phys. Lett. 1990

26. CKMT for neutrinos For F3, use The denominator of 1.1 adjusts the integral of the valence quark part to give a Gross-Llewellyn-Smith sum rule results of 3x0.9 (QCD corrected.) Strange quark

27. Calculate cross section Use NLO+TMC above a minimum value of Q, attach a parameterization for lower values of Q. Should be insensitive to where the patch is made. Results shown below are for transition between parton model and CKMT parameterization at Q=2 GeV.

28. Neutrino charged current cross section LO+TMC Low Q extrapolations, from NLO+TMC, with CKMT (and Bodek et al) extrapolation. NLO + TMC, no special low Q extrapolation. MHR, Phys. Rev. D74 (2006)

29. Anti-neutrino charged current cross section Low Q extrapolations, from NLO+TMC, with BYP and CKMT MHR, Phys. Rev. D74 (2006)

30. Ultra-high energy neutrino nucleon scattering Medium energy, High energy: W boson propagatorQuark (parton) distribution functions Given Refs, eg.: Gandhi et al., PRD 58 (1998), Astropart. Phys. 5 (1996) Mocioiu, Int. J. Mod. Phys. A20 (2005) Gluck, Kretzer, Reya, Astropart. Phys. 11 (1999)

31. Structure functions (to get PDF extractions) From B. Foster’s 2002 Frascati Talk LHC! Takes us up to

32. Theory Issues: how to extrapolate? ln Q ln 1/x non-perturbative BFKL DGLAP transition region DGLAP=Dokshitzer, Gribov, Lipatov, Altarelli & Parisi BFKL=Balitsky, Fadin, Kuraev & Lipatov Deep Inelastic Scattering Devenish & Cooper-Sarkar, Oxford (2004) saturation

33. “Evolution” of PDFs LO analysis improved to NLO analysis, heavy flavor quark and gluon distributions rise at small x for Q>a few GeV. EHLQ: Eichten, Hincliffe, Lane and Quigg, 1984. Double Logarithmic Approx (DLA) or at low x.

34. Some extrapolations: 1984 to 2007 Quigg, Reno, Walker (1986), Gandhi et al. (1996,1998), also McKay et al (1986), Gluck et al (1999) DGLAP evolution: log Q. Shown here are power law and double logarithmic extrapolations at small x. As time goes on, a better treatment of heavy flavor.

35. BFKL/DGLAP vs DGLAP BFKL evolution matched to DGLAP accounting for some subleading ln(1/x), running coupling constant,matched to GRV parton distribution functions Kwiecinski, Martin & Stasto, PRD 59 (1999)093002

36. CC Cross Sections KMS: Kwiecinski, Martin & Stasto, PRD56(1997)3991; KK: Kutak & Kwiecinski, EPJ,C29(2003)521 more realistic screening, incl. QCD evolution Golec-Biernat & Wusthoff model (1999), color dipole interactions for screening.

37. Other results Fiore et al. PRD68 (2003), with a soft non-perturbative model and approx QCD evolution. See also, Machado Phys Rev. D71 (2005) factor ~2

38. More recent results KK Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys. Rev. D 74 (2006) 043008 Henley & Jalilian-Marian 2006 Includes QCD corrections, see also Basu, Choudhury and Majhi, JHEP 0210 (2002)

39. More recent results Cooper-Sarkar & Sarkar, JHEP 0801 (2008), new analysis of HERA data incl. heavy flavor, lower cross section at UHE (closer to CTEQ6 results, which also have a better extraction of heavy flavor.

40. Other recent results Fig. from Armesto, Merino, Parente & Zas, Phys. Rev. D 77 (2008) Anchordoqui, Cooper-Sarkar, Hooper & Sarkar, Phys. Rev. D 74 (2006) HERA: extrapolations with lambda=0.5,0.4,0.38 KOPA: DLA, Kotikov & Parente ASW: saturation effects, Armesto, Salgado & Wiedeman

41. General Conclusions The theory of “low energy” neutrino-nucleon cross section still needs work. More experimental measurements will certainly help this. UHE neutrino cross section relies on extrapolations well beyond experimental measurements, however, many extrapolations end in the same “neighborhood” for the cross section. The cross section affects overall event rates, but also attenuation.

42. Fin