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April 4-11, 2003 Frascati Photon 2003 Nucleon-nucleon,  p and  scattering  using factorization: the Aspen Model and analytic.

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Presentation on theme: "April 4-11, 2003 Frascati Photon 2003 Nucleon-nucleon,  p and  scattering  using factorization: the Aspen Model and analytic."— Presentation transcript:

1 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu1 Nucleon-nucleon,  p and  scattering  using factorization: the Aspen Model and analytic amplitude analysis Martin Block Northwestern University

2 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu2 Outline Part I: fitting  tot,  values and B, nuclear slopes of accelerator data--p-p and pbar-p-- using a QCD-inspired model (Aspen Model) M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri Part II: global fit using both cosmic ray and accelerator data simultaneously M.M. Block, F. Halzen & T. Stanev Part III: predictions of forward scattering parameters for LHC (14 TeV)---  tot,  elastic, , and B

3 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu3 Part IV-The factorization hypothesis: relating n-n,  p and  collisions M. M. Block and A. B. Kaidalov Part V-Experimental evidence for factorization, quark counting and vector dominance in n-n,  p and  collisions, using the Aspen Model M. M. Block, F. Halzen, A.B. Kaidalov and G. Pancheri Part VI-Experimental evidence for factorization, using real analytical amplitudes, for n-n,  p and  collisions M. M. Block and K. Kang

4 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu4 Part I: fitting  tot,  values and B, nuclear slopes, of accelerator data--p-p and pbar-p-- using a QCD- inspired model (Aspen Model) Eduardo, Martin, Francis 3 of 4 authors working hard! Giulia, #4 author M.M. Block, E.M. Gregores, F. Halzen & G. Pancheri

5 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu5

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11 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu11

12 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu12 We set

13 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu13

14 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu14 Results of the  2 Fit to  and B data from pp and pbar-p  vs. energy  vs. energy B vs. energy

15 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu15 Part II: global fit using both cosmic ray and accelerator data simultaneously M.M. Block, F. Halzen & T. Stanev Todor thinking? Francis wearing money tie (for ICE CUBE?)

16 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu16 The published cosmic ray data (the Diamond and Triangles) are the problem Accelerator data give good fit

17 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu17 Fig. 7 X max distribution with exponential trailing edge Monte Carlo Example EXPERIMENTAL PROCEDURE Fly’s Eye Shower Profile Fig. 1 An extensive air shower that survives all data cuts. The curve is a Gaisser-Hillas shower- development function: shower parameters E=1.3 EeV and X max =727 ± 33 g cm -2 give the best fit.

18 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu18 Extraction of  tot (pp) from Cosmic Ray Extensive Air Showers

19 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu19 Published Fly’s Eye Result:  tot ( p-air ) = 540 ± 50 mb, at 30 TeV See R. Engel et al, Phys. Rev. D58, 014019 (1998), for  tot (p-air) curves, using Glauber theory

20 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu20  tot (p-p)  vs.  inel (p-air)  inel (p-air) vs. energy Results of Global Fit, Cosmic Ray and Accelerator Data

21 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu21

22 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu22  vs. energy Result of Global fit for  tot (pp) and  tot (pbar-p), using both Accelerator and Cosmic Ray Data

23 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu23

24 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu24

25 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu25 Elastic Scattering at the LHC

26 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu26 A Useful High Energy Parameterization of  inel (p-air) :  inel (p-air) = 177.43 + 15.44 ln s - 0.0204 ln 2 s,  in mb, s in Gev 2  inel (pair), in mb Cms Energy, in GeV

27 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu27  inel (p-air) =  0 [1+ a 0 ln(E lab /1000)],  0 = 297.20 mb, a 0 = 0.04879, E lab in GeV.  inel (p-air), in mb E lab /1000, in GeV A High Energy Parameterization of  inel (p-air), useful for calculating Neutrino Fluxes

28 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu28 Alexei Consequences of the Factorization Hypothesis in nucleon-nucleon,  -p and  Collisions, M. M. Block, Northwestern University A. B. Kaidalov, Moscow University

29 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu29 all s

30 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu30

31 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu31

32 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu32 B c.m.s. energy

33 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu33

34 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu34 Forward Compton Scattering, using Real Analytic Amplitudes  + p   +p, with  E  C subtraction =f + (0) = -  /m, Thompson scattering limit, A, , c, s 0 and  are real constants to be fit.  =0.5 corresponds to a descending Regge trajectory Forward high energy (real analytic) scattering amplitude, f +

35 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu35  2 /d.f.=0.98, for 40 d.f., for log 2 (s) fit Using optical theorem,

36 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu36

37 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu37  fitted with log 2 s  2 /d.f.=0.06, for 9 d.f

38 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu38  , using Real Analytic Amplitudes

39 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu39 Compton Scattering, using Real Analytic Amplitudes  p   p, using real analytic amplitudes  E  (lab), in GeV

40 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu40

41 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu41

42 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu42

43 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu43 Does factorization depend on using a dipole- dipole form factor? Could we also use a monopole-monopole for , with a monopole-dipole for  -p?

44 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu44 dipole-dipole dipole-monopole monopole-monopole set nn =  Fourier transforms yields energy –independent relation:  /  2

45 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu45 W(b), dipole-dipole, dipole-monopole, monopole-monopole

46 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu46 nn uses dipole-dipole,  p uses monopole-dipole,  uses monopole-monopole Total cross section and the ratio of elastic to total cross section

47 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu47 Kyungsik Kang, In Paris To test factorization, we will utilize real analytical amplitudes Part VI: Experimental evidence for factorization, using real analytical amplitudes, for n-n,  p and  collisions M. M. Block and K. Kang

48 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu48 Real Analytic Amplitudes even: odd:

49 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu49 Real analytic amplitudes for  p and 

50 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu50  , using either PHOJET or PYTHIA--data are from L3 and OPAL M. Acciari et al, Phys. Lett. B519, 33 (2001), G. Abbiendi et al, Eur. Phys. J. C14,199 (2000).

51 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu51 GOOD GLOBAL FIT BAD

52 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu52  pp,  pbar-p vs.  s

53 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu53  pp,  pbar-p vs.  s

54 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu54   -p =(2/3*P had )  nn

55 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu55   =(2/3*P had ) 2  nn, L3 and OPAL data, uncorrected with PYTHIA and PHOJET

56 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu56 curve:   =(2/3*P had ) 2  nn data: L3 and OPAL, renormalized by factor 0.929, using PHOJET

57 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu57 solid line:  nn =   p =   dotted line:  nn from QCD-Inspired Fit (Aspen Model)

58 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu58

59 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu59

60 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu60

61 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu61

62 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu62 d  /dt, for “Elastic” Scattering  +p  +p  +p  +p  +p  +p

63 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu63

64 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu64 Form Factors W(b), for same

65 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu65 Total cross sections  tot and  el /  tot, for dipole-dipole (n-n), dipole- monopole (  -p) and monopole-monopole (  ) form factors, for same

66 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu66 Toy eikonal  W, for n-n,  p and  scattering where

67 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu67 Survival Probability of Large Rapidity Gaps in nucleon-nucleon,  p and  Collisions M.M. Block, Northwestern University F. Halzen, Wisconsin University Francis, at the table

68 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu68

69 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu69

70 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu70 To Prove: Survival is process-independent, i.e., nn =  p = 

71 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu71 Survival is process-independent !  nn =  p = 

72 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu72 Gap Survival Probability for pbar-p and pp Collisions Gap Survival (%) for nucleon-nucleon,  p and  Collisions c.m.s. energy

73 April 4-11, 2003 Frascati Photon 2003 mblock@northwestern.edu73 Alexei Consequences of the Factorization Hypothesis in nucleon- nucleon,  -p and  Collisions, M. M. Block, Northwestern University A. B. Kaidalov, Moscow University Survival Probability of Large Rapidity Gaps in nucleon-nucleon,  p and  Collisions M.M. Block, Northwestern University F. Halzen, Wisconsin University Francis, at the table

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