Venice, 3/9/01"Neutrino Telescopes"1 High Energy Cosmic Ray and Accelerator Cross Sections Reconciled Martin M. Block Northwestern University Evanston.

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Venice, 3/9/01"Neutrino Telescopes"1 High Energy Cosmic Ray and Accelerator Cross Sections Reconciled Martin M. Block Northwestern University Evanston IL Venice Italy

Venice, 3/9/01"Neutrino Telescopes"2 Outline Part I: fitting total cross sections,  values and B, nuclear slopes of accelerator data--p-p and pbar-p--using a QCD-inspired model M.M. Block, E.M. Gregores, F Halzen & G. Pancheri Part II: predicting  -p and  -  cross sections from nucleon-nucleon fit M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri Part III: global fit using both cosmic ray and accelerator data simultaneously M.M. Block, F. Halzen & T. Stanev

Venice, 3/9/01"Neutrino Telescopes"3 Part I: fitting total cross sections,  values and B, nuclear slopes, of accelerator data--p-p and pbar-p-- using a QCD- inspired model Eduardo, Martin, Francis 3 of 4 authors working hard! Giulia, #4 author M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri

Venice, 3/9/01"Neutrino Telescopes"4

Venice, 3/9/01"Neutrino Telescopes"5

Venice, 3/9/01"Neutrino Telescopes"6

Venice, 3/9/01"Neutrino Telescopes"7

Venice, 3/9/01"Neutrino Telescopes"8 Froissart Bound

Venice, 3/9/01"Neutrino Telescopes"9 Low Energy Behavior

Venice, 3/9/01"Neutrino Telescopes"10

Venice, 3/9/01"Neutrino Telescopes"11 Results of the  2 Fit to  and B data from pp and pbar-p  vs. energy  vs. energy B vs. energy

Venice, 3/9/01"Neutrino Telescopes"12 Elastic Scattering d  /dt, at 1800 GeV Predictions from Nucleon-Nucleon Eikonal

Venice, 3/9/01"Neutrino Telescopes"13 Part II: Predicting  -p and  -  cross sections from nucleon-nucleon fit M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri Making predictions isn’t easy work!

Venice, 3/9/01"Neutrino Telescopes"14  

Venice, 3/9/01"Neutrino Telescopes"15

Venice, 3/9/01"Neutrino Telescopes"16  p Predictions  B  Compton amplitude dispersion relation, M. Damashek and F.J. Gilman, Phys. Rev. D 1, 1319 (1970)

Venice, 3/9/01"Neutrino Telescopes"17 “Elastic” Vector Meson Final States  +p  V i +p  V i  +p  V i =   +p   +p  +p   +p

Venice, 3/9/01"Neutrino Telescopes"18 d  /dt, for “Elastic” Scattering  +p  +p  +p  +p  +p  +p

Venice, 3/9/01"Neutrino Telescopes"19 Exact! See M. Block and A. Kaidalov, hep- ph/

Venice, 3/9/01"Neutrino Telescopes"20  tot (  )

Venice, 3/9/01"Neutrino Telescopes"21 Part III: global fit using both cosmic ray and accelerator data simultaneously M.M. Block, F. Halzen & T. Stanev Todor thinking? Francis wearing money tie (for ICE CUBE?)

Venice, 3/9/01"Neutrino Telescopes"22 accelerator data give good fit The published cosmic ray data (the Diamond and Triangles) are the problem

Venice, 3/9/01"Neutrino Telescopes"23 EXPERIMENTAL PROCEDURE Fig. 7 X max distribution with exponential trailing edge Monte Carlo Example Fly’s Eye Shower Profile Fig. 1 An extensive air shower that survives all data cuts. The curve is a Gaisser-Hillas shower- development function: shower parameters E=1.3 EeV and X max =727 ± 33 g cm -2 give the best fit.

Venice, 3/9/01"Neutrino Telescopes"24

Venice, 3/9/01"Neutrino Telescopes"25 Published Fly’s Eye Result:  tot ( p-air ) = 540 ± 50 mb See R. Engel et al, Phys. Rev. D58, (1998), for  tot (p-air) curves, using Glauber theory

Venice, 3/9/01"Neutrino Telescopes"26  tot (p-p)  vs.  inel (p-air)  inel (p-air) vs. energy Results of Global Fit, Cosmic Ray and Accelerator Data

Venice, 3/9/01"Neutrino Telescopes"27

Venice, 3/9/01"Neutrino Telescopes"28  vs. energy Result of Global fit for  tot (pp) and  tot (pbar-p), using both Accelerator and Cosmic Ray Data

Venice, 3/9/01"Neutrino Telescopes"29

Venice, 3/9/01"Neutrino Telescopes"30 A Useful High Energy Parameterization of  inel (p-air) :  inel (p-air) = ln s ln 2 s,  in mb, s in Gev 2  inel (p-air), in mb Cms Energy, in GeV

Venice, 3/9/01"Neutrino Telescopes"31  inel (p-air) =  0 [1+ a 0 ln(E lab /1000)],  0 = mb, a 0 = , E lab in GeV.  inel (p-air), in mb E lab /1000, in GeV A High Energy Parameterization of  inel (p-air), useful for calculating Neutrino Fluxes