13th international conference on elastic & diffractive scattering
DESCRIPTION
13th International Conference on Elastic & Diffractive Scattering ( 13th "Blois Workshop") CERN, 29th June - 3rd July 2009. GPDs and hadron elastic scattering. O.V. Selyugin Dubna, JINR. Contents. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
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13th International Conference on Elastic & Diffractive Scattering (13th "Blois Workshop") CERN, 29th June - 3rd July 2009
GPDs and hadron elastic scattering
O.V. SelyuginDubna, JINR
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Contents
1. Introduction
2. GPDs and hadrons form-factors
3. t-dependence of the GPDs
6. Conclusion
4 Unitarization of the elastic scattering amplitude
5. The differential cross sections
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Elastic scattering amplitude
pp pp pp pp
( )0,577... the Euler constant 1 2and are small correction terms
2 2 2 2 21 2 3 4 5
dσ=2π[|Φ| +|Φ| +|Φ| +|Φ| +4|Φ| ]
dt( , ) ( , ) ( )h e i
i i is t s t t e
1 2( , ) [ ln ( B (s, t) | t | / 2 ) ]s t
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Unitarity
0
0
( , ) ( ) (1 exp[ ( , )])T s t is bdb J bq i s b
Factorization
( , ) ( ) ( );s b h s f b ( )h s s
4
Impact parameters dependence
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Soft and hard Pomeron
Donnachie-Landshoff model;
Schuler-Sjostrand model
1 01 ln( / )1 1
0
( , ) [ ( ) t s ssT s t h e
s
2 02 ln( / ) 22
0
( ) ] ( )t s ssh e F t
s
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Second part of scattering amplitude
1 22 1 2
0 0
( , ) [ ( ) ( ) ) ( )grs sT s t h h A b
s s
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ASSUMPTION
1 2( ) ( ); ( ) ( );em grf b F b f b A b
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General Parton Distributions -GPDs
Electromagnetic form factors(charge distribution)
Energy momentum tensor form factors (matter distribution)
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Fallowing to A. Radyushkin
Phys.ReV. D58, (1998) 114008GPDs
0limit
1
1 1( ) , , ;q qF t dx H x t
1
2 1( ) , , ;q qF t dx E x t
q(x;t) = Hq(x,0,t) + H
q(-x,0,t) q(x;t) = Eq(x,0,t) + E
q(-x,0,t)
1
1 0( ) , , ;q qF t dx x t H
1
2 0( ) , , ;q qF t dx x t ε
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Energy-momentum tensor
1 2 2
1[ , , , , ] ( ) ( ) ;q q
q qdx x H x t E x t A B
1
0( ) , ;q qA t dx x x t H
1
0( ) , ;q qB t dx x x t ε
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Our ansatz
2
0.4
(1 ), ( ) ex ;p[ ]q x
x t q x a tx
H
q(x) is based on the MRST2002 and A. Radyushkin (2005)
0.69 3.50 0.5( ) 0.262 (1 ) (1 3.83 37.65 );u x x x x x 0.65 4.03 0.5( ) 0.061 (1 ) (1 49.05 8.65 );d x x x x x
1. Simplest;
2. Not far from Gaussian representation
4. Valid for large t
3. Satisfy the (1-x)n (n>= 2)
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F1p *t2
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Gep/Gd
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GMp/(pGd)
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GEn
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GMn
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Gravitational and Dirac form-factors
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1 2 2
0( ) , ( 1.8, )q q
DA t dx x x t G GeV H
2 3
2 2 2 21 2
( ) ( ) ( )
*(1 ) / ( );
grf b A b K b
r b r b
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PARAMETERS
Fixed:
1 1 2 2( , ) ( , ) ( , );s b k s b k s b
1 2 1 20.08; 0.45; 0.25; 0.1;
1 2/ 0.008 / 4.47.h h Free:
1 2 1 21.09; 1.57; 2.4 30.9.6;k k r r
2 2731/ 947 3.
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( 52.8 GeV )pp p sm l tp s al
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( 52.8 GeV ) argpp p l e tp s
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( 62.1 GeV )p p sp p
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( 52.8 GeV )pp p sm l tp s al
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( 53 GeV )spp pp
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( 62.7 GeV )p p sp p
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( 541 GeV )spp pp
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( 541 546 GeV )s andpp pp
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( 1800 GeV )p p sp p
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PREDICTIONS ( 10, 14 TeV )pp pp s
1.8 TeV; (0) 0.208; 80.3 ;tots mb
10 TeV; (0) 0.2 1 ;38; 32tots mb
14 TeV; (0) 0.2 1 ;35; 46tots mb
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Lower energy
There is a small place for the secondary reggeons (with the intercept > 0,5 )
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Non-linear equation (K-matrix)
(1 );dN
N Ndy
[ ] ( ,0);N y s
( , )[ ] ;
1 ( , )
i s bN y
s b
31
0ln( / );y s s
( )[ ] ;
1 ( )
y
y
s f bN y
s f b
2 5400 / 947 6;
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Interpolating form of unitarization
( , ) / [1 (1 ( , ) / ) ];G s b i s b
1; 1 ( , )( , ) 1 ;
(1 ( , )) 1 ( , )
s bG s b
s b s b
.
( , ) 1 ( ( , );G s b exp s b
1/(1 [1 ] ) (1 );dN
N Ndy
32
Fit:
;
Experiment data choose the eikonal form
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Summary
1. Proposed a new simple model of proton-proton and
proton-antiproton elastic scattering .
3 . Both distributions are obtained from our model of GPDs of the
hadrons. The corresponding electromagnetic and gravitational form factors of
the proton are calculated with our proposed t-dependence of the GPDs.
2. The model is based on the assumption that the scattering amplitude is a sum of terms proportional to the charge distribution of the hadron (dominant at small t) and terms proportional
to the matter distribution of the hadron (dominant at large t).
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Summary
4. The model includes the contributions of the soft and hard pomerons with intercepts = 1+0.08 and 1+0.45 and slopes = 0.25 and 0.1 GeV-2.
5, The model describes all high-energy experimental data beginning from sqrt(s)=52.8 GeV in the Coulomb hadron interference region and at large |t| =10 GeV2.
(with 4 free parameters , 2 = 3 per point)6. We note the essential contribution of the hard pomeron at the LHC energy at small and large t. This leads to a large value of rho at small t.
7. We do not see the odderon contribution at small and large t.
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END
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END
THANKSFOR YOUR ATTANTION
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Saturation bound
37
00( , ) 2 ( ) ( , )Bs b q J bq M s q dq
2 21( , ) [ ]
2s b dzV z b
k
G(s,b)
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1 1 2 2( , ) ( , ) ( , );s b k s b k s b
1 1 2 2( , ) ( , ) ( ); ( , ) ( ) ( );s b h s b f b s b h s f b
1 21 2
0 0
( ) [ ( ) ( ) ]s s
h s h hs s