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Imposing the Froissart Bound on Hadronic Interactions:
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Transcript of 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
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Prior Restraint! the Froissart Bound
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Deep inelastic electron scattering
e e’
*
p
*p scattering
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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!
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Proton Structure Function F2(x,Q2), from Deep Inelastic Scattering, Block, Berger & Tan, PRL 99, 88 (2006).
Bjorken xVirtuality
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Reduced Virtual Photon Total Cross Section
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Froissart bound fit, ln2 W, to reduced cross sections
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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!
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Scaling Point
Global (Simultaneous) Fit of F2(x,Q2) to x and Q2
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Comparing ln2x and CTEQ6.5 fits
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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Factor of 8 !
Standard CTEQ3 n
Froissart Bound n
n estimates, courtesy F. Halzen
April 15-19, 2007 M. Block, Aspen Workshop Cosmic Ray Physics 2007
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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 !