From Aspen with love June 28 July 2

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From Aspen, with love, June 28 -July 2, 2010 Live, to Fermi. Lab! M.

From Aspen, with love, June 28 -July 2, 2010 Live, to Fermi. Lab! M. M. Block, ISVHECRI 2010 1

Hadronic cross sections: cyclotrons to colliders to cosmic rays Martin Block Northwestern University Sorry

Hadronic cross sections: cyclotrons to colliders to cosmic rays Martin Block Northwestern University Sorry I’m not here! June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 Auger 2

Prior Restraint! the Froissart Bound June 28 -July 2, 2010 M. M. Block, ISVHECRI

Prior Restraint! the Froissart Bound June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 3

OUTLINE 1) Data selection: The “Sieve” Algorithm---“Sifting data in the real world”, 2) M.

OUTLINE 1) Data selection: The “Sieve” Algorithm---“Sifting data in the real world”, 2) M. Block, Nucl. Instr. and Meth. A, 556, 308 (2006). 2) New fitting constraints---“New analyticity constraints on hadron-hadron cross sections”, M. Block, Eur. Phys. J. C 47, 697 (2006). Touched on briefly , but these are important constraints! 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). 4) Measuring p-air cross sections from cosmic ray extensive air showers---review of method. 5) Ultra-high energy p-p cross sections, using cosmic ray p-air cross sections and Glauber calculations. June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 4

Conclusions From hadron-hadron scattering BEFORE I present the results and risk losing my audience!

Conclusions From hadron-hadron scattering BEFORE I present the results and risk losing my audience! 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. 132± 0. 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. June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 5

Part 1: “Sifting Data in the Real World”, Getting rid of outliers! M. Block,

Part 1: “Sifting Data in the Real World”, Getting rid of outliers! M. Block, ar. Xiv: physics/0506010 (2005); Nucl. Instr. and Meth. A, 556, 308 (2006). “Fishing” for Data June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 6

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 7

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 7

Lorentzian Fit used in “Sieve” Algorithm For those old enough to remember, we’re putting

Lorentzian Fit used in “Sieve” Algorithm For those old enough to remember, we’re putting the mathematical equivalent of a “French Curve” through the points ! June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 8

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June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 9

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 10

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 10

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 11

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 11

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 12

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 12

You are now finished! No more outliers. You have: 1) optimized parameters 2) corrected

You are now finished! No more outliers. You have: 1) optimized parameters 2) corrected goodness-of-fit 3) squared error matrix. June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 13

Part 2: “New analyticity constraints on hadron-hadron cross sections”, M. Block, Eur. Phys. J.

Part 2: “New analyticity constraints on hadron-hadron cross sections”, M. Block, Eur. Phys. J. C 47 (2006). K. Igi and M. Ishida, Phys. Lett. B 622, 286 (2005). June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 14

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 15

June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 15

Derivation of new analyticity constraints Finite energy cutoff! Experimental low energy cross section June

Derivation of new analyticity constraints Finite energy cutoff! Experimental low energy cross section June 28 -July 2, 2010 Theoretical high energy cross section parametrization M. M. Block, ISVHECRI 2010 16

We can also prove that for odd amplitudes: sodd, exp’t (n 0) = sodd

We can also prove that for odd amplitudes: sodd, exp’t (n 0) = sodd (n 0). so that: sexp’t (n 0) = s (n 0), dsexp’t (n 0)/dn = ds (n 0) /dn, or, its practical equivalent, sexp’t (n 0) = s (n 0), sexp’t (n 1) = s (n 1), for n 1> n 0 for both pp and pbar-p exp’t cross sections June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 17

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). Francis, personally funding ICE CUBE June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 18

m=0. 5, Reggedescending trajectory ln 2(s/s 0) fit 7 parameters needed, including f+(0), a

m=0. 5, Reggedescending trajectory ln 2(s/s 0) fit 7 parameters needed, including f+(0), a dispersion relation subtraction constant June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 19

Only 3 Free Parameters are needed! These anchoring conditions, just above the resonance regions,

Only 3 Free Parameters are needed! These anchoring conditions, just above the resonance regions, are analyticity conditions! However, only 2, c 1 and c 2, are needed in cross section fits ! June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 20

Cross section fits for Ecms > 6 Ge. V, anchored at 4 Ge. V,

Cross section fits for Ecms > 6 Ge. V, anchored at 4 Ge. V, pp and pbar p, after applying “Sieve” algorithm June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 21

r-value fits for Ecms > 6 Ge. V, anchored at 4 Ge. V, pp

r-value fits for Ecms > 6 Ge. V, anchored at 4 Ge. V, pp and pbar p, after applying “Sieve” algorithm June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 22

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

What the “Sieve” algorithm accomplished for the pp and pbar p data Before imposing the “Sieve algorithm: c 2/d. f. =5. 7 for 209 degrees of freedom; Total c 2=1182. 3. After imposing the “Sieve” algorithm: Renormalized c 2/d. f. =1. 09 for 184 degrees of freedom, for Dc 2 i > 6 cut; Total c 2=201. 4. Probability of fit ~0. 2. The 25 rejected points contributed 981 to the total c 2 , an average Dc 2 i of ~39 per point. June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 23

Comments on the “Discrepancy” between CDF and E 710/E 811 cross sections at the

Comments on the “Discrepancy” between CDF and E 710/E 811 cross sections at the Tevatron Collider If we only use E 710/E 811 cross sections at the Tevatron and do not include the CDF point, we obtain: c 2 min/n=1. 055, n=183, probability=0. 29 spp(1800 Ge. V) = 75. 1± 0. 6 mb spp(14 Te. V) = 107. 2± 1. 2 mb If we use both E 710/E 811 and the CDF cross sections at the Tevatron, we obtain: c 2 min/n=1. 095, n=184, probability=0. 18 spp(1800 Ge. V) = 75. 2± 0. 6 mb spp(14 Te. V) = 107. 3± 1. 2 mb, effectively no changes Conclusion: The extrapolation to high energies is essentially unaffected! June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 24

Cross section and r-value predictions for pp and pbar-p LHC prediction Cosmic Ray Prediction

Cross section and r-value predictions for pp and pbar-p LHC prediction Cosmic Ray Prediction The errors are due to the statistical uncertainties in the fitted parameters June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 25

Cross section fits for Ecms > 6 Ge. V, anchored at 2. 6 Ge.

Cross section fits for Ecms > 6 Ge. V, anchored at 2. 6 Ge. V, p+p and p-p, after applying “Sieve” algorithm June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 26

gp log 2(n/m) fit, compared to the pp even amplitude fit F. Damashek and

gp log 2(n/m) fit, compared to the pp even amplitude fit F. Damashek and F. Gilman, Phys. Rev. D 1, 184 (1970). M. Block and F. Halzen, Phys Rev D 70, 091901, (2004) June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 27

Global (Simultaneous) Fit of F 2(x, Q 2) to x and Q 2 Scaling

Global (Simultaneous) Fit of F 2(x, Q 2) to x and Q 2 Scaling Point June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 28

Fitting stot, r values and B, nuclear slopes, of accelerator data-p-p and pbar-p- using

Fitting stot, r values and B, nuclear slopes, of accelerator data-p-p and pbar-p- using a QCDinspired eikonal model (the Aspen Model) Eduardo, Martin, Francis, 3 of 4 authors working hard in Aspen ! Giulia, #4 author, showing above photo at a conference She claims, to this M. M. Block, E. M. Gregores, F. Halzen & G. Pancheri June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 day, that she did not take the picture !! 29

More LHC predictions, from the Aspen Eikonal Model: M. M. Block, Phys. Reports 436,

More LHC predictions, from the Aspen Eikonal Model: M. M. Block, Phys. Reports 436, 71 (2006). Differential Elastic Scattering Nuclear slope B = 19. 39 ± 0. 13 (Ge. V/c)-2 selastic = 30. 79 ± 0. 34 mb June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 30

Cosmic Ray experimental Procedure for Extensive Air Showers: Fly’s Eye to AGASA to Hi.

Cosmic Ray experimental Procedure for Extensive Air Showers: Fly’s Eye to AGASA to Hi. Res Fly’s Eye Shower Profile Monte Carlo Example Logarithmic slope, Lm, is measured Fig. 1 An extensive air shower that survives all data cuts. The curve is a Gaisser-Hillas showerdevelopment function: shower parameters E=1. 3 Ee. V and Xmax =727 ± 33 g cm-2 give the best fit. June 28 -July 2, 2010 Fig. 7 Xmax distribution with exponential trailing edge M. M. Block, ISVHECRI 2010 31

Extraction of stot(pp) from Cosmic Ray Extensive Air Showers by Fly’s Eye and AGASA

Extraction of stot(pp) from Cosmic Ray Extensive Air Showers by Fly’s Eye and AGASA k is very model-dependent Need good fit to accelerator data June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 32

Hi. Res Measurement of Xmax Distribution: Xmax = X 1 + X’ June 28

Hi. Res Measurement of Xmax Distribution: Xmax = X 1 + X’ June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 33

Ingredients needed for Glauber Model B, from Aspen (eikonal) Model s, from ln 2

Ingredients needed for Glauber Model B, from Aspen (eikonal) Model s, from ln 2 s fit June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 34

Glauber calculation with inelastic screening, M. Block and R. Engel (unpublished) B (nuclear slope)

Glauber calculation with inelastic screening, M. Block and R. Engel (unpublished) B (nuclear slope) vs. spp, as a function of sp-air spp from ln 2(s) fit and B from QCD-fit June 28 -July 2, 2010 Hi. Res Point M. M. Block, ISVHECRI 2010 35

To obtain spp from sp-air June 28 -July 2, 2010 M. M. Block, ISVHECRI

To obtain spp from sp-air June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 36

sp-air as a function of Ö s, with inelastic screening kexpt = 1. 264

sp-air as a function of Ö s, with inelastic screening kexpt = 1. 264 ± 0. 033 ± 0. 013 k. Hi-Res = 1. 21+ 0. 14 - 0. 09, a direct measurement June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 37

A table of k-values, used in experiments and from Monte Carlo simulation k’s that

A table of k-values, used in experiments and from Monte Carlo simulation k’s that were actually used by the experimenters: Note historical diminishing in time! Monte Carlo: More current k’s, found by Monte Carlo, from popular models World average of our fitted k: kexpt = 1. 264 ± 0. 033 ± 0. 013 June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 38

CONCLUSIONS 1) The Froissart bound for pp collisions is saturated at high energies. 2)

CONCLUSIONS 1) The Froissart bound for pp collisions is saturated at high energies. 2) At the LHC, stot = 107. 3 ± 1. 2 mb, r = 0. 132± 0. 001. 3) At cosmic ray energies, we have accurate estimates of spp and Bpp from collider data. 4) The Glauber calculation of sp-air from spp and Bpp is reliable. 5) The Hi. Res value (almost model-independent) of sp-air is in reasonable agreement with the collider prediction. 6) We now have a good benchmark, tying together colliders with cosmic rays. June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 39

Saturating the Froissart Bound: spp and spbar-p log 2(n/m) fits, with world’s supply of

Saturating the Froissart Bound: spp and spbar-p log 2(n/m) fits, with world’s supply of data Original cosmic ray points & QCDfit from Block, Halzen and Stanev: Phys. Rev. D 66, 077501 (2000). Todor thinking? June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 40

THANK YOU FOR YOUR PATIENCE! Thanks, Peter Mazur and Larry Jones, For going out

THANK YOU FOR YOUR PATIENCE! Thanks, Peter Mazur and Larry Jones, For going out of your way to make it possible for me to “be” Any here. questions? June 28 -July 2, 2010 M. M. Block, ISVHECRI 2010 41