1. Mary Hall Reno Neutrino Cross Sections at HERA and Beyond ISVHECRI September 10, 2004

2. Mary Hall Reno Neutrino Energy Ranges TeVPeVEeV Water Cherenkov Radio EAShowers Air Fluorescence AGN, GRB TD, GZK neutrinos Acoustic

3. Mary Hall Reno Outline Review the neutrino cross section and important features. Pre-HERA, what did we know? Implications of HERA measurements of the structure functions. Beyond….

4. Mary Hall Reno Neutrino cross sections Neutrino cross section depends on the usual variables: kk’

5. Mary Hall Reno Charged Current Scattering W-boson propagator parton distribution functions At high energies, Q dependence is important in pdf and propagator cross section grows like E at low energies

6. Mary Hall Reno Q Dependence QCD evolution of PDFs: importance in neutrino cross sections first pointed out by Andreev, Berezinsky and Smirnov, Phys. Lett. 84B (1979). Using old PDFs: CTEQ3 (post-HERA) and EHLQ (pre-HERA). Fig: Gandhi et al. 1995 (GQRS95) no QCD evolution sea quark dominated “Earth is opaque”

7. Mary Hall Reno x dependence Fig: GQRS 95 half the cross section

8. Mary Hall Reno Average Q

9. Mary Hall Reno Measurements Energy of incident particle: neutrino energies up to 350 GeV. (x,Q) for ultrahigh-energy neutrino scattering are not measured. HERA ep scattering, equivalent energy of ~54 TeV.

10. Mary Hall Reno Muon neutrino and antineutrino CC cross section [0 30 || 50 GeV 350] PDG, Hagiwara et al, Phys Rev D66 (2002)

11. Mary Hall Reno Kinematic Reach Plot from Zeus public plots database. HERA Fixed Target

12. Mary Hall Reno PDFs pre-HERA Eichten et al. Rev. Mod. Phys.1984, focus on SSC. Also Duke and Owens.

13. Mary Hall Reno Pre-HERA Parametrizations e.g.,Duke and Owens (1984), Eichten, Lane, Hinchliffe and Quigg (1984) xg and xq are initially constant in x at low x.

14. Mary Hall Reno “Evolution” of PDFs LO analysis improved to NLO analysis quark and gluon distributions rise at small x for Q>a few GeV.

15. Mary Hall Reno “Evolution” of PDFs CTEQ6 – Pumplin et al., JHEP (2002) is part of a series of CTEQ analyses. Martin et al.: series of analyses MRST, HMRS, KMRS, MRS. Gluck, Reya and Vogt: dynamical parton distribution functions. not actually measuring the pdfs at this value – DGLAP evolution….

16. Mary Hall Reno HERA CC and NC Measurements Zeus Collab, Eur. Phys. J. C 32, 1 (2003)H1 Collab, Eur. Phys. J. C 30, 1 (2003)

17. Mary Hall Reno CC Cross Sections-UHE Extrapolations DGLAP extrapolations: power law and double leading log approx. Numerous calculations: Quigg, Reno & Walker (1986), McKay & Ralston (1986), Frichter, McKay & Ralston (1995), Gandhi et al. (1996,1998), Gluck, Kretzer & Reya (1999)

18. Mary Hall Reno Theory Issues 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

19. Mary Hall Reno Small-x extrapolations DGLAP evolution of parton distribution functions: small-x evolution dominated by gluon Sea quarks dominate the cross section. e.g.,Ellis, Kunszt & Levin (1994)

20. Mary Hall Reno Extrapolations-DGLAP This is the extrapolation for EHLQ. Requires double leading log approximation: for Gribov, Levin & Ryskin, Phys. Rep. 100 (1983)

21. Mary Hall Reno CC Cross Sections Revisited DGLAP extrapolations: power law and double leading log approx. Numerous calculations: Quigg, Reno & Walker (1986), McKay & Ralston (1986), Frichter, McKay & Ralston (1995), Gandhi et al. (1996,1998), Gluck, Kretzer & Reya (1999) all power law extrapolations DLA vs. power law

22. Mary Hall Reno More small-x extrapolations LO BFKL, sum leading ln(1/x) (LL(1/x)) Multiple gluon emissions at small-x predict LL(1/x): OK (0.5), NLL(1/x): wrong sign, for fixed Fadin & Lipatov, Camici & Ciafaloni Recent work by Altarelli, Ball & Forte; Ciafaloni, Colferai, Salam & Stasto on ln(1/x) resummation with running coupling, Kutak and Stasto including saturation effects.

23. Mary Hall Reno 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

24. Mary Hall Reno Saturation effects Saturation due to high gluon density at small x (recombination effects) size of proton disk Estimate of scale: for g-g cross section gluons/unit rapidity

25. Mary Hall Reno First Guess Contours of constant cross section for MHR, Sarcevic, Sterman, Stratmann & Vogelsang, hep-ph/0110235 saturation region

26. Mary Hall Reno 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.

27. Mary Hall Reno Other results Fiore et al. PRD68 (2003), with a soft non-perturbative model and approx QCD evolution. Note: J. Jalilan-Marian, PRD68 (2003) suggests that there are enhancements to the cross section due to high gluon density effects; enhancements also in Gazizov et al. astro- ph/0112244. Machado, hep-ph/0311281, color dipole with BFKL/DGLAP. factor ~2

28. Mary Hall Reno Upward- vs. Downward-going UHE neutrinos Kusenko & Weiler, PRL 88(2002) air shower probability per incident tau neutrino: Upward Air Showers (UAS) with different energy thresholds, and Horizontal Air Showers (HAS) KMS and KK cross sections

29. Mary Hall Reno Small x for lower energies? Perturbative cross sections – e.g. for charm-anticharm and bottom-antibottom. This has implications for prompt neutrino fluxes from the semileptonic decays of charmed quarks. (See Stasto et al.) Small x at high energies? LHC will give the opportunity to measure small x values at Q equal to the W boson mass, but still not as low as we need to go. Look at the continuing story of pdfs, small x and theory meets experiment.