13th International Conference on Elastic & Diffractive Scattering
description
Transcript of 13th International Conference on Elastic & Diffractive Scattering
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
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
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
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
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
Second part of scattering amplitude
1 22 1 2
0 0
( , ) [ ( ) ( ) ) ( )grs sT s t h h A b
s s
ASSUMPTION
1 2( ) ( ); ( ) ( );em grf b F b f b A b
General Parton Distributions -GPDs
Electromagnetic form factors(charge distribution)
Energy momentum tensor form factors (matter distribution)
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
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
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)
F1p *t2
Gep/Gd
GMp/(pGd)
GEn
GMn
Gravitational and Dirac form-factors
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
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.
( 52.8 GeV )pp p sm l tp s al
( 52.8 GeV ) argpp p l e tp s
( 62.1 GeV )p p sp p
( 52.8 GeV )pp p sm l tp s al
( 53 GeV )spp pp
( 62.7 GeV )p p sp p
( 541 GeV )spp pp
( 541 546 GeV )s andpp pp
( 1800 GeV )p p sp p
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
Lower energy
There is a small place for the secondary reggeons (with the intercept > 0,5 )
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;
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
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).
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.
END
END
THANKSFOR YOUR ATTANTION
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)
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