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Neutrino Nucleon Cross Sections: GeV to ZeV

Neutrino Nucleon Cross Sections: GeV to ZeV. Hallsie Reno University of Iowa January 2009. The best cross section measurements. 50. 350 GeV. Particle data group http://pdg.lbl.gov. Plan. Review generic neutrino nucleon cross section calculation (with structure functions)

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Neutrino Nucleon Cross Sections: GeV to ZeV

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

  2. The best cross section measurements 50 350 GeV Particle data group http://pdg.lbl.gov

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

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

  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 Quasi-elastic MiniBooNE measurements: Refinement of nuclear model parameters. Here, coherent pi0 production, compared with Rein-Seghal based MC. MiniBooNE, Phys. Lett. B664 (2008) 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. Nachtmannvariable 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: leading plus convolution terms electromagnetic case

  17. More complicated formulas

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

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

  20. Target mass corrections, importance of low Q 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. Kretzer & MHR, Nucl Phys Proc Suppl 139 (2005)

  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 sea, small x valence, large x for electromagnetic scattering. See, Reno, Phys. Rev. D 74 (2006)

  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: Given W boson propagator Quark (parton) distribution functions 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) LHC! Takes us up to From B. Foster’s 2002 Frascati Talk

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

  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 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. Quigg, Reno, Walker (1986), Gandhi et al. (1996,1998), also McKay et al (1986), Gluck et al (1999)

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

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

  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

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