The Elusive p-air Cross Section
-
Upload
curran-glass -
Category
Documents
-
view
43 -
download
0
description
Transcript of The Elusive p-air Cross Section
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 1
The Elusive p-air Cross Section
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 2
The Elusive p-air Cross Section
Martin BlockNorthwestern University
The E(xc)lusive p-air (Pierre) Cross Section
for cosmic ray conoscenti, the real title is:
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 3
1) Data selection---“Sifting data in the real world”, M. Block, arXiv:physics/0506010 (2005).
2) Fitting the accelerator data---“New evidence for the Saturation of the Froissart Bound”, M. Block and F. Halzen, arXiv:hep-ph/0506031 (2005); Phys. Rev. D 72, 036006 (2005).
3) The Glauber calculation: Obtaining the p-air cross section from accelerator data, M. Block and R. Engel (unpublished)
OUTLINE
4) Details of Robust Fitting: Time permitting
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 4
Part 1: “Sifting Data in the Real World”,
M. Block, arXiv:physics/0506010 (2005).
“Fishing” for Data
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 5
All cross section data for Ecms > 6 GeV,
pp and pbar p, from Particle Data Group
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 6
All data (Real/Imaginary of forward scattering amplitude), for Ecms > 6 GeV,
pp and pbar p, from Particle Data Group
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 7
All cross section data for Ecms > 6 GeV,
+p and -p, from Particle Data Group
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 8
All data (Real/Imaginary of forward scattering amplitude), for Ecms > 6 GeV,
+p and -p, from Particle Data Group
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 9
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 10
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 11
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 12
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 13
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 14
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 15
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 16
“Sieve’’ Algorithm: SUMMARY
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 17
2renorm = 2
obs/R-1
renorm = r2 obs,
where is the parameter error
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 18
Francis, Francis, personally personally funding ICE funding ICE CUBECUBE
Part 2: Fitting the accelerator data---“New evidence for the Saturation of the Froissart Bound”, M. Block and F. Halzen, arXiv:hep-ph/0506031 (2005).
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 19
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 20
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 21
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 22
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 23
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 24
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 Dual equivalents to
finite energy sum rules (FESR)!
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 25
Cross section fits for Ecms > 6 GeV, anchored at 4 GeV,
pp and pbar p, after applying “Sieve” algorithm
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 26
-value fits for Ecms > 6 GeV, anchored at 4 GeV,
pp and pbar p, after applying “Sieve” algorithm
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 27
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.
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 29
log2(/mp) fit compared to log(/mp) fit: All known n-n data
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 30
Comments on the “Discrepancy” between CDF and E710/E811 cross sections at the Tevatron Collider
If we only use E710/E811 cross sections at the Tevatron and do not include the CDF point, we obtain:
R 2min/probability=0.29
pp(1800 GeV) = 75.1± 0.6 mb pp(14 TeV) = 107.2± 1.2 mb
If we use both E710/E811 and the CDF cross sections at the Tevatron, we obtain:
R 2min/ =184, probability=0.18
pp(1800 GeV) = 75.2± 0.6 mb pp(14 TeV) = 107.3± 1.2 mb, effectively no changes
Conclusion:
The extrapolation to high energies is essentially unaffected!
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 31
Cross section fits for Ecms > 6 GeV, anchored at 2.6 GeV,
+p and -p, after applying “Sieve” algorithm
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 32
-value fits for Ecms > 6 GeV, anchored at 2.6 GeV,
+p and -p, after applying “Sieve” algorithm
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 33
p log2(/m) fit, compared to the p even amplitude fit
M. Block and F. Halzen,
Phys Rev D 70, 091901, (2004)
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 34
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
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 35
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).
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 36
Part 3: The Glauber calculation: Obtaining the p-air cross section from accelerator data, M. Block and R. Engel
Ralph Engel, At Work
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 38
Glauber calculation with inelastic screening, M. Block and R. Engel (unpublished) B (nuclear slope) vs. pp, as a function of p-air
pp from ln2(s) fit and B from
QCD-fit
HiRes Point
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 40
p-air as a function of s, with inelastic screening
p-airinel = 45617(stat)+39(sys)-11(sys) mb
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 41
Measured k = 1.29
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 42
To obtain pp from p-air
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 43
Generalization of the Maximum Likelihood Function
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 44
Hence,minimize i (z), or equivalently, we minimize 2 i 2i
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 45
Problem with Gaussian Fit when there are Outliers
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 46
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 47
Robust Feature:
w(z) 1/i2 for large i
2
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 48
Lorentzian Fit used in “Sieve” Algorithm
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 49
Why choose normalization constant =0.179 in Lorentzian 02?
Computer simulations show that the choice of =0.179 tunes the Lorentzian so that minimizing 0
2, using data that are gaussianly distributed, gives the same central values and approximately the same errors for parameters obtained by minimizing these data using a conventional 2 fit.
If there are no outliers, it gives the same answers as a 2 fit.
Hence, using the tuned Lorentzian 02 , much like using the
Hippocratic oath, does “no harm”.
Sept. 7-13, 2005 M. Block, Prague, c2cr 2005 50
CONCLUSIONS
The Froissart bound for pp collisions is saturated at high energies.
2) At cosmic ray energies,we have accurate estimates of pp and Bpp from collider data.
3) The Glauber calculation of p-air from pp and Bpp is reliable.
4) The HiRes value (almost model independent) of p-air is in reasonable agreement with the collider prediction.
5) We now have a good benchmark, tying together