Martin Block Northwestern University

April 4-11, 2003 Frascati Photon 2003

mblock@northwestern.edu 1

Nucleon-nucleon, p and scatteringusing factorization: the Aspen Model and analytic amplitude

analysis

Martin BlockMartin Block

Northwestern Northwestern UniversityUniversity

April 4-11, 2003 Frascati Photon 2003

mblock@northwestern.edu 2

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

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• Part IV-The factorization hypothesis: relating n-n, p and collisionsM. 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

April 4-11, 2003 Frascati Photon 2003

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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

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We set

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Results of the 2 Fit to and B data from pp and pbar-p

vs. energy vs. energy

B vs. energy

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Part II: global fit using both cosmic ray and accelerator data simultaneously

M.M. Block, F. Halzen & T. Stanev

Todor Todor thinking?thinking?

Francis Francis wearing wearing money money tie (for tie (for ICE ICE CUBE?)CUBE?)

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1e+1 1e+2 1e+3 1e+4 1e+5

, in

mb.

0

20

40

60

80

100

120

140

160

180

200

220

s, in GeV

(pbar-p)(pp)

1e+1 1e+2 1e+3 1e+4 1e+5

, in

mb.

0

20

40

60

80

100

120

140

160

180

200

220

s, in GeV

AGASA Air Shower Data

Fly's Eye Air Shower Data

(pbar-p)(pp)

The The publishedpublished cosmic ray data cosmic ray data (the Diamond and Triangles) (the Diamond and Triangles) are the problemare the problem

Accelerator data give good fit

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Fig. 7 Xmax 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 Xmax =727 ± 33 g cm-2 give the best fit.

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Extraction of tot(pp) from Cosmic Ray Extensive Air Showers

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Published Fly’s Eye Result:

tot(p-air) = 540 ± 50 mb, at 30 TeV

tot(pp), in mb

40 50 60 70 80 90 100 110 120 130 140 150 160

B, i

n (G

eV/c

)-2

15

20

25

30

35

40440 mb

440 mb

490 mb

490 mb 540 mb

540 mb

590 mb

590 mb

640 mb

See R. Engel

et al,

Phys. Rev. D58,

014019 (1998),

for tot(p-air)

curves, using

Glauber theory

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vs. energy

Result of Global fit for tot(pp) and tot(pbar-p), using

both Accelerator and Cosmic Ray Data

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Alexei

Consequences of the Factorization Hypothesis in

nucleon-nucleon, -p and Collisions,

M. M. Block, Northwestern University

A. B. Kaidalov, Moscow University

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all s

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B

c.m.s. energy

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Does factorization depend on using a dipole-dipole form factor?

Could we also use a monopole-monopole for , with a monopole-dipole for -p?

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dipole-dipole

dipole-monopole

monopole-monopole

set <b2>nn = <b2>

Fourier transforms

yields energy –independent relation: /2

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nn uses dipole-dipole, p uses monopole-dipole, uses monopole-monopole

Total cross section and the ratio of elastic to total cross section

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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

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Real Analytic Amplitudes

even:

odd:

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Real analytic amplitudes for p and

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mblock@northwestern.edu 5010 100

, in

nb

0

500

1000

1500

s, in GeV

L3, using PHOJETOPAL, using PHOJET

OPAL, using PYTHIAL3, using PYTHIA

, 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).

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mblock@northwestern.edu 51GOODGOOD

GLOBAL FITGLOBAL FIT

BADBAD

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10 100 1000 100000

50

100

150

200

pppbar-p

pp, log2(s) analytic amplitude fit

pbar-p, log2(s) analytic amplitude fit

s, in GeV

, in

mb.

pp , pbar-p vs. s

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pp , pbar-p vs. s

s, in GeV

10 100 1000 10000

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

pppbar-p

pp, log2(s) analytic amplitude fit

pbar-p, log2(s) analytic amplitude fit

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10 100 1000

p,

in

b

0

100

200

300

400

500

p=(2/3*Phad)nn

s, in GeV

-p =(2/3*Phad)nn

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10 100

, in

nb

0

500

1000

1500

OPAL, using PHOJET, renormalized L3, using PHOJET, renormalized

Phad)2nn

s, in GeV

curve: =(2/3*Phad)2 nn

data: L3 and OPAL, renormalized by factor 0.929, using PHOJET

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solid line: nn=p=

dotted line: nn from QCD-Inspired Fit (Aspen Model)

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