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The Elusive p-air Cross Section

The Elusive p-air Cross Section. The Elusive p-air Cross Section Martin Block Northwestern University. for cosmic ray conoscenti , the real title is:. The E(xc)lusive p-air (Pierre) Cross Section. OUTLINE.

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The Elusive p-air Cross Section

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  1. The Elusive p-air Cross Section M. Block, Prague, c2cr 2005

  2. The Elusive p-air Cross SectionMartin BlockNorthwestern University for cosmic ray conoscenti, the real title is: The E(xc)lusive p-air (Pierre) Cross Section M. Block, Prague, c2cr 2005

  3. OUTLINE • 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(2005). 3) The Glauber calculation: Obtaining the p-air cross section from accelerator data, M. Block and R. Engel (unpublished) 4) Details of Robust Fitting: Time permitting M. Block, Prague, c2cr 2005

  4. “Fishing” for Data Part 1: “Sifting Data in the Real World”, M. Block, arXiv:physics/0506010 (2005). M. Block, Prague, c2cr 2005

  5. All cross section data for Ecms > 6 GeV, pp and pbar p, from Particle Data Group M. Block, Prague, c2cr 2005

  6. All r data (Real/Imaginary of forward scattering amplitude), for Ecms > 6 GeV, pp and pbar p, from Particle Data Group M. Block, Prague, c2cr 2005

  7. All cross section data for Ecms > 6 GeV, p+p and p-p, from Particle Data Group M. Block, Prague, c2cr 2005

  8. All r data (Real/Imaginary of forward scattering amplitude), for Ecms > 6 GeV, p+p and p-p, from Particle Data Group M. Block, Prague, c2cr 2005

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  16. “Sieve’’ Algorithm: SUMMARY M. Block, Prague, c2cr 2005

  17. c2renorm = c2obs/R-1 Srenorm = rc2 ´ Sobs, where S is the parameter error M. Block, Prague, c2cr 2005

  18. Francis, personally funding ICE CUBE 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). M. Block, Prague, c2cr 2005

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  24. These anchoring conditions, just above the resonance regions, are Dual equivalents to finite energy sum rules (FESR)! Only 3 Free Parameters However, only2, c1andc2, are needed in cross section fits ! 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 M. Block, Prague, c2cr 2005

  26. r-value fits for Ecms > 6 GeV, anchored at 4 GeV, pp and pbar p, after applying “Sieve” algorithm M. Block, Prague, c2cr 2005

  27. 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 c2=1182.3. After imposing the “Sieve” algorithm: Renormalized c2/d.f.=1.09 for 184 degrees of freedom, for Dc2i > 6 cut; Total c2=201.4. Probability of fit ~0.2. The 25 rejected points contributed 981 to the total c2 , an average Dc2i of ~39 per point. M. Block, Prague, c2cr 2005

  28. log2(n/mp) fit compared to log(n/mp) fit: All known n-n data M. Block, Prague, c2cr 2005

  29. 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´ c2min/n=1.055, n=183, probability=0.29 spp(1800 GeV) = 75.1± 0.6 mb spp(14 TeV) = 107.2± 1.2 mb If we use both E710/E811 and the CDF cross sections at the Tevatron, we obtain: R´ c2min/n=1.095, n=184, probability=0.18 spp(1800 GeV) = 75.2± 0.6 mbspp(14 TeV) = 107.3± 1.2 mb, effectively no changes Conclusion: The extrapolation to high energies is essentially unaffected! M. Block, Prague, c2cr 2005

  30. Cross section fits for Ecms > 6 GeV, anchored at 2.6 GeV, p+p and p-p, after applying “Sieve” algorithm M. Block, Prague, c2cr 2005

  31. r-value fits for Ecms > 6 GeV, anchored at 2.6 GeV, p+p and p-p, after applying “Sieve” algorithm M. Block, Prague, c2cr 2005

  32. M. Block and F. Halzen, Phys Rev D 70, 091901, (2004) gp log2(n/m) fit, compared to the pp even amplitude fit M. Block, Prague, c2cr 2005

  33. LHC prediction Cosmic Ray Prediction The errors are due to the statistical uncertainties in the fitted parameters Cross section and r-value predictions for pp and pbar-p M. Block, Prague, c2cr 2005

  34. Cosmic ray points & QCD-fit from Block, Halzen and Stanev: Phys. Rev. D 66, 077501 (2000). Saturating the Froissart Bound: spp andspbar-p log2(n/m) fits, with world’s supply of data M. Block, Prague, c2cr 2005

  35. Ralph Engel, At Work Part 3: The Glauber calculation: Obtaining the p-air cross section from accelerator data, M. Block and R. Engel M. Block, Prague, c2cr 2005

  36. spp from ln2(s) fit and B from QCD-fit HiRes Point Glauber calculation with inelastic screening, M. Block and R. Engel (unpublished) B (nuclear slope) vs. spp, as a function of sp-air M. Block, Prague, c2cr 2005

  37. sp-airinel = 456±17(stat)+39(sys)-11(sys) mb sp-air as a function ofÖs, with inelastic screening M. Block, Prague, c2cr 2005

  38. Measured k = 1.29 M. Block, Prague, c2cr 2005

  39. To obtain spp from sp-air M. Block, Prague, c2cr 2005

  40. Generalization of the Maximum Likelihood Function M. Block, Prague, c2cr 2005

  41. Hence,minimize Sib(z), or equivalently, we minimize c2 º Si Dc2i M. Block, Prague, c2cr 2005

  42. Problem with Gaussian Fit when there are Outliers M. Block, Prague, c2cr 2005

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  44. Robust Feature: w(z) µ1/ÖDci2 for large Dci2 M. Block, Prague, c2cr 2005

  45. Lorentzian Fit used in “Sieve” Algorithm M. Block, Prague, c2cr 2005

  46. Why choose normalization constant g=0.179 in Lorentzian L02? Computer simulations show that the choice of g=0.179 tunes the Lorentzian so that minimizing L02, 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 c2 fit. If there are nooutliers, it gives the same answers as a c2 fit.Hence, using the tuned Lorentzian L02, much like using the Hippocratic oath, does “no harm”. M. Block, Prague, c2cr 2005

  47. 5) We now have a good benchmark, tying together CONCLUSIONS 1) The Froissart bound for pp collisions is saturated at high energies. 2) At cosmic ray energies,we have accurate estimates of spp and Bpp from collider data. 3) The Glauber calculation of sp-air from spp and Bpp is reliable. 4) The HiRes value (almost model independent) of sp-air is in reasonable agreement with the collider prediction. M. Block, Prague, c2cr 2005

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