Imposing the Froissart Bound on Hadronic Interactions:

1. Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering & new structure functions for ultra-high energy n-n cross sections Martin BlockNorthwestern University M. Block, Aspen Workshop Cosmic Ray Physics 2007

2. Prior Restraint! the Froissart Bound M. Block, Aspen Workshop Cosmic Ray Physics 2007

3. Outline 1) The Proton Structure Function F2p(x,Q2) : “Small-x Behavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep-Inelastic-Scattering Cross Sections”, M. M. Block, Edmund L. Berger and Chung-I tan, Phys.Rev. Lett. 308 (2006). 2) Global Structure Function Fit and Predictions for Ultra-high Energy Neutrino-nucleon Cross Sections, Work in progress for this meeting ! M. M. B, Edmund L. Berger and Chung-I Tan M. Block, Aspen Workshop Cosmic Ray Physics 2007

4. e e’ g* p g*p scattering Deep inelastic electron scattering M. Block, Aspen Workshop Cosmic Ray Physics 2007

5. M. Block and F. Halzen, Phys Rev D 70, 091901, (2004) gp log2(s/s0) fit, compared to the pp even amplitude fit Now employ same formalism for g*p scattering! M. Block, Aspen Workshop Cosmic Ray Physics 2007

6. Virtuality Bjorken x Proton Structure Function F2(x,Q2), from Deep Inelastic Scattering, Block, Berger & Tan, PRL 99, 88 (2006). M. Block, Aspen Workshop Cosmic Ray Physics 2007

7. Reduced Virtual Photon Total Cross Section M. Block, Aspen Workshop Cosmic Ray Physics 2007

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9. Only ln2(s/s0) term needed! M. Block, Aspen Workshop Cosmic Ray Physics 2007

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12. Froissart bound fit, ln2 W, to reduced cross sections M. Block, Aspen Workshop Cosmic Ray Physics 2007

13. Bjorken x Individual fits of the proton structure F2(x,Q2) vs. x, for 15 different Q2 values, in GeV2 ONE functional form, ln2 s, fits ALL! M. Block, Aspen Workshop Cosmic Ray Physics 2007

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16. Scaling Point Global (Simultaneous) Fit of F2(x,Q2) to x and Q2 M. Block, Aspen Workshop Cosmic Ray Physics 2007

17. Excellent c2/d.f. for 169 degrees of freedom F2(x, Q2): Global Fit Parameters for Q2/x >>m2, x<0.09 0.11 < Q2 < 1200 GeV2 M. Block, Aspen Workshop Cosmic Ray Physics 2007

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19. 1 £Q2£ 100 GeV2 Predictions are made using ZEUS data in global fit Experimental data are from H1 collaboration NO RENORMALIZATION made! M. Block, Aspen Workshop Cosmic Ray Physics 2007

20. Comparing ln2x and CTEQ6.5 fits M. Block, Aspen Workshop Cosmic Ray Physics 2007

21. Factor of 8 ! Standard CTEQ3 snn Froissart Bound snn snn estimates, courtesy F. Halzen M. Block, Aspen Workshop Cosmic Ray Physics 2007

22. SUMMARY M. Block, Aspen Workshop Cosmic Ray Physics 2007

23. To be done: • Include H1 in global fit, simultaneously fitting F2 and • dF2 /d(logQ2), d(logF2) /d(log x) 2. Constrained gluon particle distribution functions (p.d.f.’s) for LHC &ILC 3. Constrained quark p.d.f’s for LHC & ILC 4. Recalculate cosmic ray neutrino cross sections using bounded p.d.f.’s; current values are much too big! Needs x~10-8 and Q2~6400 GeV2 . Enormous extrapolation ! M. Block, Aspen Workshop Cosmic Ray Physics 2007