Neutrino Cross Sections at HERA and Beyond

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

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

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

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

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

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

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

8. Average Q Mary Hall Reno

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

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

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

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

13. 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. Mary Hall Reno

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

15. “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…. Mary Hall Reno

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

17. 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) Mary Hall Reno

18. Theory Issues 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 Mary Hall Reno

19. 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) Mary Hall Reno

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

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

22. 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. Mary Hall Reno

23. 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 Mary Hall Reno

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

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

26. 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. Mary Hall Reno

27. 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. factor ~2 Machado, hep-ph/0311281, color dipole with BFKL/DGLAP. Mary Hall Reno

28. Upward- vs. Downward-going UHE neutrinos 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 Kusenko & Weiler, PRL 88(2002) Mary Hall Reno

29. Small x for lower energies? 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. • 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.) Mary Hall Reno