Imposing the Froissart bound on DIS

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Imposing the Froissart bound on DIS ---gt New
PDF's for the LHC
Martin BlockNorthwestern University
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OUTLINE

• Data selection The Sieve Algorithm---Sifting
  data in the real world,
• M. Block, Nucl. Instr. and Meth. A, 556, 308
  (2006).

3) Fitting the accelerator data---New evidence
for the Saturation of the Froissart Bound, M.
Block and F. Halzen, Phys. Rev. D 72, 036006
(2005).

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4) 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).
5) Global Structure Function Fit and New Gluon
Distributions using the Froissart Bound
Work in progress for this meeting ! M. M. Block,
Edmund L. Berger and Chung-I Tan,
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Part 1 Sifting Data in the Real World, M.
Block, arXivphysics/0506010 (2005) Nucl. Instr.
and Meth. A, 556, 308 (2006).
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Lorentzian Fit used in Sieve Algorithm
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You are now finished! No more outliers. You
have 1) optimized parameters
2)
corrected goodness-of-fit
3) squared error matrix.
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This is FESR(2) derived by Igi and Ishida, which
follows from analyticity, just as dispersion
relations do.
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We can also prove that for odd amplitudes sodd
(n0) sodd (n0).
so that sexpt (n0) s (n0),
dsexpt (n0)/dn ds (n0) /dn, or, its practical
equivalent, sexpt (n0) s
(n0), sexpt (n1) s (n1),
for n1gt n0 for both pp and pbar-p expt cross
sections
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Part 3 Fitting the accelerator data---New
evidence for the Saturation of the Froissart
Bound, M. Block and F. Halzen, Phys. Rev. D 72,
036006 (2005).
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Only 3 Free Parameters
However, only 2, c1 and c2, are needed in cross
section fits !
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Cross section fits for Ecms gt 6 GeV, anchored at
4 GeV, pp and pbar p, after applying Sieve
algorithm
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r-value fits for Ecms gt 6 GeV, anchored at 4
GeV, pp and pbar p, after applying Sieve
algorithm
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What the Sieve algorithm accomplished for the
pp and pbar p data
Before imposing the Sieve algorithm
c2/d.f.5.7 for 209 degrees of freedom Total
c21182.3.
After imposing the Sieve algorithm
Renormalized c2/d.f.1.09 for 184 degrees of
freedom, for Dc2i gt 6 cut Total
c2201.4. Probability of fit 0.2. The 25
rejected points contributed 981 to the total c2
, an average Dc2i of 39 per point.


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Cross section and r-value predictions for
pp and pbar-p
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More LHC predictions, from the Aspen Eikonal Model
Differential Elastic Scattering
Nuclear slope B 19.39 0.13 (GeV/c)-2
selastic 30.79 0.34 mb
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Saturating the Froissart Bound spp and spbar-p
log2(n/m) fits, with worlds supply of data
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Conclusions From hadron-hadron scattering
1) The Froissart bound for gp, pp and pp
collisions is saturated at high energies.
2) At the LHC, stot 107.3 1.2 mb, r
0.1320.001.
3) At cosmic ray energies, we can make accurate
estimates of spp and Bpp from collider data.
4) Using a Glauber calculation of sp-air from
spp and Bpp, we now have a reliable benchmark
tying together colliders to cosmic rays.
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Proton Structure Function F2(x,Q2), from Deep
Inelastic Scattering, Block, Berger Tan,
PRL 99, 88 (2006).
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Reduced Virtual Photon Total Cross Section
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Froissart bound fit, ln2 W, to reduced cross
sections
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Global (Simultaneous) Fit of F2(x,Q2) to x and Q2
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What the Sieve algorithm accomplished for
F2(x,Q2)
Before imposing the Sieve algorithm
c2/d.f.1.30 for 177 degrees of freedom Total
c2229.4.
After imposing the Sieve algorithm
Renormalized c2/d.f.1.09 for 169 degrees of
freedom, for Dc2i gt 6 cut Total
c2184.2. Probability of fit 0.2. The 8 rejected
points contributed 63.45 to the total c2 , an
average Dc2i of 8 per point.


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1 Q2 100 GeV2
Predictions are made using ZEUS data in global
fit Experimental data are from H1
collaboration NO RENORMALIZATION made!
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SUMMARY
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• To be done
• Include H1 in global fit, simultaneously fitting
  F2, dF2 /d(logQ2), d(logF2) /d(log x)

2. More gluon distributions
3. Quark distributions
4. Recalculate cosmic ray neutrino cross
sections current values are much too big!
Needs x10-8 and Q26400 GeV2 ! Enormous
extrapolation.