imposing the froissart bound on dis ---> new pdf's for the lhc
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Imposing the Froissart bound on DIS ---> New PDF's for the LHC. Martin Block Northwestern University. No time to talk about these. But they are important!. New fitting constraints - --“New analyticity constraints on hadron-hadron cross sections”, M. Block, Eur. Phys. J. C 47, 697 (2006).. - PowerPoint PPT PresentationTRANSCRIPT
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Imposing the Froissart bound on DIS---> New PDF's for the LHC
Martin BlockNorthwestern University
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1) 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
2) New fitting constraints---“New analyticity constraints on hadron-hadron cross sections”, M. Block, Eur. Phys. J. C 47, 697 (2006).
No time to talk about these. But they are important!
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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, arXiv:physics/0506010 (2005); Nucl. Instr. and Meth. A, 556, 308 (2006).
“Fishing” for Data
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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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so that:exp’t ( (0),
dexp’t (dd (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).
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Francis, Francis, personally personally funding ICE funding ICE CUBECUBE
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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ln2(s/s0) fit=0.5, Regge-
descending trajectory
7 parameters needed, including f+(0), a dispersion relation subtraction constant
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Only 3 Free Parameters
However, only 2, c1 and c2, are needed in cross section fits !
These anchoring conditions, just above the resonance regions, are analyticity conditions!
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Cross section fits for Ecms > 6 GeV, anchored at 4 GeV,
pp and pbar p, after applying “Sieve” algorithm
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-value fits for Ecms > 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:
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.
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Cross section and -value predictions for pp and pbar-p
The errors are due to the statistical uncertainties in the fitted parameters
LHC prediction
Cosmic Ray Prediction
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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
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Saturating the Froissart Boundpp and pbar-p log2(/m) fits, with world’s supply of data
Cosmic ray points & QCD-fit from Block, Halzen and Stanev: Phys. Rev. D 66, 077501 (2000).
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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, = 0.1320.001.
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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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Scaling Point
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:
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.
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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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SUMMARY
.
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To be done:
1. 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.