April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics 2007 1 Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering.

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Presentation transcript:

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Imposing the Froissart Bound on Hadronic Interactions: Part II, Deep Inelastic Scattering & new structure functions for ultra-high energy -n cross sections Martin Block Northwestern University

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Prior Restraint! the Froissart Bound

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics ) The Proton Structure Function F 2 p (x,Q 2 ) : “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 Outline

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Deep inelastic electron scattering ee’ ** p  *p scattering

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics  p log 2 (s/s 0 ) fit, compared to the  p even amplitude fit M. Block and F. Halzen, Phys Rev D 70, , (2004) Now employ same formalism for  p scattering!

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Proton Structure Function F 2 (x,Q 2 ), from Deep Inelastic Scattering, Block, Berger & Tan, PRL 99, 88 (2006). Bjorken x Virtuality

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Reduced Virtual Photon Total Cross Section

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Only ln 2 (s/s 0 ) term needed!

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Froissart bound fit, ln 2 W, to reduced cross sections

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Individual fits of the proton structure F 2 (x,Q 2 ) vs. x, for 15 different Q 2 values, in GeV 2 Bjorken x ONE functional form, ln 2 s, fits ALL!

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Scaling Point Global (Simultaneous) Fit of F 2 (x,Q 2 ) to x and Q 2

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics F 2 (x, Q 2 ): Global Fit Parameters for Q 2 /x >>m 2, x< < Q 2 < 1200 GeV 2 Excellent  2 /d.f. for 169 degrees of freedom

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics What the “Sieve” algorithm accomplished for F 2 (x,Q 2 ) Before imposing the “Sieve algorithm:  2 /d.f.=1.30 for 177 degrees of freedom; Total  2 = After imposing the “Sieve” algorithm: Renormalized  2 /d.f.=1.09 for 169 degrees of freedom, for  2 i > 6 cut; Total  2 = Probability of fit ~0.2. The 8 rejected points contributed to the total  2, an average  2 i of ~8 per point.

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Predictions are made using ZEUS data in global fit Experimental data are from H1 collaboration NO RENORMALIZATION made! 1  Q 2  GeV 2

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Comparing ln 2 x and CTEQ6.5 fits

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Factor of 8 ! Standard CTEQ3  n Froissart Bound  n  n estimates, courtesy F. Halzen

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics SUMMARY

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics To be done: 1.Include H1 in global fit, simultaneously fitting F 2 and dF 2 /d(logQ2), d(logF 2 ) /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 Q 2 ~6400 GeV 2. Enormous extrapolation !

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics q Curvature =  2 F 2 (x, Q 2 )/  q 2, where q = log 10 (1+ 2Q 2 )

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Scaling point

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Extraction of Gluon Distributions xg(x,Q 2 ) from DIS

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics NLO Gluon Distributions, xg(x,Q 2 ) gluon scaling point ! x=0.09,x g=1.8

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Bootstrap Method of Extracting Gluon Distributions

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics Bootstrap Equation for Gluon Distribution G(x,Q 2 )=xg(x,Q 2 )

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics

April 15-19, 2007M. Block, Aspen Workshop Cosmic Ray Physics