# Presentation: 475200

##      Imposing the Froissart bound on DIS

- ---> New PDF's for the LHC

- Martin BlockNorthwestern University

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

##                           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).

-                           OUTLINE

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## 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,

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Part 1: “Sifting Data in the Real World”, 

- M. Block, arXiv:physics/0506010 (2005); Nucl. Instr. and Meth. A,** 556**, 308 (2006).

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Lorentzian Fit used in “Sieve” Algorithm

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 6

- M. Block, Aspen Winter Physics Conference

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## Slide 7

- M. Block, Aspen Winter Physics Conference

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## Slide 8

- M. Block, Aspen Winter Physics Conference

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## Slide 9

- M. Block, Aspen Winter Physics Conference

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## Slide 10

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## You are now finished!  No more outliers. You have:          1) optimized parameters                                                       2) corrected goodness-of-fit                                                   3) squared error matrix.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## This is FESR(2) derived by Igi and Ishida, which follows from analyticity, just as dispersion relations do.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## so that:exp’t ( (0),

-             d*exp’t *(dd (0) d,
- or, its practical equivalent,
- *exp’t *( (0),
- *exp’t *( (1),  for 
- for *both* pp and pbar-p exp’t cross sections

- We can also prove that for odd amplitudes:
- *odd** *(0) = *odd* (0).

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Part 3: Fitting the accelerator data---“New evidence for the Saturation of the Froissart Bound”, 

- 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).

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 15

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Only 3 Free Parameters

***However, only***** *****2*****, *****c******1***** ****and**** *****c******2*****, *****are needed in cross section fits !***

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Cross section fits for Ecms > 6 GeV, anchored at 4 GeV,

- Cross section fits for Ecms > 6 GeV, anchored at 4 GeV,
- pp and pbar p, after applying “Sieve” algorithm

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## -value fits for Ecms > 6 GeV, anchored at 4 GeV,

- -value fits for Ecms > 6 GeV, anchored at 4 GeV,
- pp and pbar p, after applying “Sieve” algorithm

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## What the “Sieve” algorithm accomplished for the pp and pbar p data

- Before imposing the “Sieve algorithm:
- 2/d.f.=5.7 for 209 degrees of freedom;
- Total 2=1182.3.

- After imposing the “Sieve” algorithm:
- Renormalized 2/d.f.=1.09 for 184 degrees of freedom, for 2i > 6 cut;
- Total 2=201.4.
- Probability of fit ~0.2.
- The 25 rejected points contributed 981 to the total  2 , an average 2i             of ~39 per point.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Cross section and -value predictions for       pp and pbar-p

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## More LHC predictions, from the Aspen Eikonal Model

- Nuclear slope B = 19.39 ± 0.13 (GeV/c)-2
- elastic  = 30.79 ± 0.34 mb

- Differential Elastic Scattering

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

**Notes:**
Sig(elastic) = SigLHC(tot)*[sig(el)/sig(tot)]QCD=107.3*(30.4/106..19)

## Saturating the Froissart Boundpp and pbar-p log2(/m) fits, with world’s supply of data

- Saturating the Froissart Boundpp and pbar-p log2(/m) fits, with world’s supply of data

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Conclusions From hadron-hadron scattering

- The Froissart bound  for p, p and pp collisions is saturated at high energies.

- 3) At cosmic ray  energies,we can make accurate estimates of pp and Bpp from collider data.

- 4) Using a  Glauber calculation of p-air from pp and Bpp, we now have a reliable benchmark tying  together colliders to cosmic rays.

- 2) At the LHC,
- tot = 107.3 1.2 mb,  = 0.1320.001.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

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

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

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Reduced Virtual Photon Total Cross Section

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 26

- M. Block, Aspen Winter Physics Conference

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## Slide 27

- M. Block, Aspen Winter Physics Conference

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## Slide 28

- M. Block, Aspen Winter Physics Conference

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## Slide 29

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Froissart bound fit, ln2 W, to reduced cross sections

- Froissart bound fit, ln2 W, to reduced cross sections

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 31

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 32

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

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

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

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## What the “Sieve” algorithm accomplished for F2(x,Q2)

- Before imposing the “Sieve algorithm:
- 2/d.f.=1.30 for 177 degrees of freedom;
- Total 2=229.4.

- After imposing the “Sieve” algorithm:
- Renormalized 2/d.f.=1.09 for 169 degrees of freedom, for 2i > 6 cut;
- Total 2=184.2.
- Probability of fit ~0.2.
- The 8 rejected points contributed 63.45 to the total  2 , an average 2i             of ~8 per point.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Slide 35

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Predictions are made using ZEUS data in global fit

- Experimental data are from H1 collaboration
- NO RENORMALIZATION made!

- 1  Q2 GeV2

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## SUMMARY

- .

- M. Block, Aspen Winter Physics Conference

- Jan, 2007

## Needs x~10-8 and Q2~6400 GeV2 ! Enormous extrapolation.

- 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 x~10-8 and Q2~6400 GeV2 ! Enormous extrapolation.

- M. Block, Aspen Winter Physics Conference

- Jan, 2007