Imposing the Froissart Bound on Hadronic Interactions:

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

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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


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Prior Restraint! the Froissart Bound


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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

Outline


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Deep inelastic electron scattering

e e’

*

p

*p scattering


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p log2(s/s0) fit, compared to the p even amplitude fit

M. Block and F. Halzen,

Phys Rev D 70, 091901, (2004)

Now employ same formalism for p scattering!


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Proton Structure Function F2(x,Q2), from Deep Inelastic Scattering, Block, Berger & Tan, PRL 99, 88 (2006).

Bjorken xVirtuality


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Reduced Virtual Photon Total Cross Section


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Only ln2(s/s0) term needed!


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Froissart bound fit, ln2 W, to reduced cross sections


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Individual fits of the proton structure F2(x,Q2) vs. x, for 15 different Q2 values, in GeV2

Bjorken x

ONE functional form, ln2 s, fits ALL!


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Scaling Point

Global (Simultaneous) Fit of F2(x,Q2) to x and Q2


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F2(x, Q2): Global Fit Parameters for Q2/x >>m2, x<0.09

0.11 < Q2 < 1200 GeV2

Excellent 2/d.f. for 169 degrees of freedom


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Predictions are made using ZEUS data in

global fit

Experimental data are from H1 collaboration

NO RENORMALIZATION

made!

1 Q2 GeV2


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Comparing ln2x and CTEQ6.5 fits


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Factor of 8 !

Standard CTEQ3 n

Froissart Bound n

n estimates, courtesy F. Halzen


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SUMMARY


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To be done:

1. 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 !

Imposing the Froissart Bound on Hadronic Interactions:

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