April 4-11, 2003 Frascati Photon 2003 Nucleon-nucleon,  p and  scattering  using factorization: the Aspen Model and analytic amplitude analysis Martin Block Northwestern University

April 4-11, 2003 Frascati Photon 2003 Outline Part I: fitting  tot,  values and B, nuclear slopes of accelerator data--p-p and pbar-p-- using a QCD-inspired model (Aspen Model) M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri Part II: global fit using both cosmic ray and accelerator data simultaneously M.M. Block, F. Halzen & T. Stanev Part III: predictions of forward scattering parameters for LHC (14 TeV)---  tot,  elastic, , and B

April 4-11, 2003 Frascati Photon 2003 Part IV-The factorization hypothesis: relating n-n,  p and  collisions M. M. Block and A. B. Kaidalov Part V-Experimental evidence for factorization, quark counting and vector dominance in n-n,  p and  collisions, using the Aspen Model M. M. Block, F. Halzen, A.B. Kaidalov and G. Pancheri Part VI-Experimental evidence for factorization, using real analytical amplitudes, for n-n,  p and  collisions M. M. Block and K. Kang

April 4-11, 2003 Frascati Photon 2003 Part I: fitting  tot,  values and B, nuclear slopes, of accelerator data--p-p and pbar-p-- using a QCD- inspired model (Aspen Model) Eduardo, Martin, Francis 3 of 4 authors working hard! Giulia, #4 author M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri

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April 4-11, 2003 Frascati Photon 2003 We set

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April 4-11, 2003 Frascati Photon 2003 Results of the  2 Fit to  and B data from pp and pbar-p  vs. energy  vs. energy B vs. energy

April 4-11, 2003 Frascati Photon 2003 Part II: 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?)

April 4-11, 2003 Frascati Photon 2003 The published cosmic ray data (the Diamond and Triangles) are the problem Accelerator data give good fit

April 4-11, 2003 Frascati Photon 2003 Fig. 7 X max distribution with exponential trailing edge Monte Carlo Example EXPERIMENTAL PROCEDURE 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.

April 4-11, 2003 Frascati Photon 2003 Extraction of  tot (pp) from Cosmic Ray Extensive Air Showers

April 4-11, 2003 Frascati Photon 2003 Published Fly’s Eye Result:  tot ( p-air ) = 540 ± 50 mb, at 30 TeV See R. Engel et al, Phys. Rev. D58, (1998), for  tot (p-air) curves, using Glauber theory

April 4-11, 2003 Frascati Photon 2003  tot (p-p)  vs.  inel (p-air)  inel (p-air) vs. energy Results of Global Fit, Cosmic Ray and Accelerator Data

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April 4-11, 2003 Frascati Photon 2003  vs. energy Result of Global fit for  tot (pp) and  tot (pbar-p), using both Accelerator and Cosmic Ray Data

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April 4-11, 2003 Frascati Photon 2003 Elastic Scattering at the LHC

April 4-11, 2003 Frascati Photon 2003 A Useful High Energy Parameterization of  inel (p-air) :  inel (p-air) = ln s ln 2 s,  in mb, s in Gev 2  inel (pair), in mb Cms Energy, in GeV

April 4-11, 2003 Frascati Photon 2003  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

April 4-11, 2003 Frascati Photon 2003 Alexei Consequences of the Factorization Hypothesis in nucleon-nucleon,  -p and  Collisions, M. M. Block, Northwestern University A. B. Kaidalov, Moscow University

April 4-11, 2003 Frascati Photon 2003 all s

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April 4-11, 2003 Frascati Photon 2003 B c.m.s. energy

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April 4-11, 2003 Frascati Photon 2003 Forward Compton Scattering, using Real Analytic Amplitudes  + p   +p, with  E  C subtraction =f + (0) = -  /m, Thompson scattering limit, A, , c, s 0 and  are real constants to be fit.  =0.5 corresponds to a descending Regge trajectory Forward high energy (real analytic) scattering amplitude, f +

April 4-11, 2003 Frascati Photon 2003  2 /d.f.=0.98, for 40 d.f., for log 2 (s) fit Using optical theorem,

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April 4-11, 2003 Frascati Photon 2003  fitted with log 2 s  2 /d.f.=0.06, for 9 d.f

April 4-11, 2003 Frascati Photon 2003  , using Real Analytic Amplitudes

April 4-11, 2003 Frascati Photon 2003 Compton Scattering, using Real Analytic Amplitudes  p   p, using real analytic amplitudes  E  (lab), in GeV

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April 4-11, 2003 Frascati Photon 2003 Does factorization depend on using a dipole- dipole form factor? Could we also use a monopole-monopole for , with a monopole-dipole for  -p?

April 4-11, 2003 Frascati Photon 2003 dipole-dipole dipole-monopole monopole-monopole set nn =  Fourier transforms yields energy –independent relation:  /  2

April 4-11, 2003 Frascati Photon 2003 W(b), dipole-dipole, dipole-monopole, monopole-monopole

April 4-11, 2003 Frascati Photon 2003 nn uses dipole-dipole,  p uses monopole-dipole,  uses monopole-monopole Total cross section and the ratio of elastic to total cross section

April 4-11, 2003 Frascati Photon 2003 Kyungsik Kang, In Paris To test factorization, we will utilize real analytical amplitudes Part VI: Experimental evidence for factorization, using real analytical amplitudes, for n-n,  p and  collisions M. M. Block and K. Kang

April 4-11, 2003 Frascati Photon 2003 Real Analytic Amplitudes even: odd:

April 4-11, 2003 Frascati Photon 2003 Real analytic amplitudes for  p and 

April 4-11, 2003 Frascati Photon 2003  , using either PHOJET or PYTHIA--data are from L3 and OPAL M. Acciari et al, Phys. Lett. B519, 33 (2001), G. Abbiendi et al, Eur. Phys. J. C14,199 (2000).

April 4-11, 2003 Frascati Photon 2003 GOOD GLOBAL FIT BAD

April 4-11, 2003 Frascati Photon 2003  pp,  pbar-p vs.  s

April 4-11, 2003 Frascati Photon 2003  pp,  pbar-p vs.  s

April 4-11, 2003 Frascati Photon 2003   -p =(2/3*P had )  nn

April 4-11, 2003 Frascati Photon 2003   =(2/3*P had ) 2  nn, L3 and OPAL data, uncorrected with PYTHIA and PHOJET

April 4-11, 2003 Frascati Photon 2003 curve:   =(2/3*P had ) 2  nn data: L3 and OPAL, renormalized by factor 0.929, using PHOJET

April 4-11, 2003 Frascati Photon 2003 solid line:  nn =   p =   dotted line:  nn from QCD-Inspired Fit (Aspen Model)

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April 4-11, 2003 Frascati Photon 2003 d  /dt, for “Elastic” Scattering  +p  +p  +p  +p  +p  +p

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April 4-11, 2003 Frascati Photon 2003 Form Factors W(b), for same

April 4-11, 2003 Frascati Photon 2003 Total cross sections  tot and  el /  tot, for dipole-dipole (n-n), dipole- monopole (  -p) and monopole-monopole (  ) form factors, for same

April 4-11, 2003 Frascati Photon 2003 Toy eikonal  W, for n-n,  p and  scattering where

April 4-11, 2003 Frascati Photon 2003 Survival Probability of Large Rapidity Gaps in nucleon-nucleon,  p and  Collisions M.M. Block, Northwestern University F. Halzen, Wisconsin University Francis, at the table

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April 4-11, 2003 Frascati Photon 2003 To Prove: Survival is process-independent, i.e., nn =  p = 

April 4-11, 2003 Frascati Photon 2003 Survival is process-independent !  nn =  p = 

April 4-11, 2003 Frascati Photon 2003 Gap Survival Probability for pbar-p and pp Collisions Gap Survival (%) for nucleon-nucleon,  p and  Collisions c.m.s. energy

April 4-11, 2003 Frascati Photon 2003 Alexei Consequences of the Factorization Hypothesis in nucleon- nucleon,  -p and  Collisions, M. M. Block, Northwestern University A. B. Kaidalov, Moscow University Survival Probability of Large Rapidity Gaps in nucleon-nucleon,  p and  Collisions M.M. Block, Northwestern University F. Halzen, Wisconsin University Francis, at the table