Exclusive Vector Mesons at HERA

Henri KowalskiDESY

DIS 2006

Tsukuba, April 2006

)2

exp(12*21

0

2*

bddzrdptot

)2/exp(~)(

)exp(~

2 BbbT

tBdt

d diff

GBW - Golec-B, WuesthoffBGBK - Bartels, Golec-B, Kowalski KT - Kowalski, TeaneyKMW - Kowalski, Motyka, Watt

2*1

0

22 |)2

exp(12|16

1*

VM

bip

VM dzebdrddt

d

proton shape

)(),()( 2222

bTxxgrN sC

Glauber Mueller

0)t,(WImAW

1σ 2

el2γptot

Dipole Models equivalent to LO perturbative QCD for small dipoles

x < 10-2

universal rate of rise of all hadronic cross-sections

tottot xWp )/1(~)(~ 2*

Total *p cross-section

6.520

202

2

)1(1

),( xx

Axxg

r

C

g

g

KT

KMW

Inclusive Diffraction-LPS

Dipole cross section determined by fit to F2

simultaneous description of many reactions

F2 C

KT

BGBK

H. Kowalski, L. Motyka, G. Watt

Exclusive Vector Meson Production

Effective modification of Fourier Trans by Bartels, Golec-Biernat, Peters

)1( 2

Real part correction

Skewedness correction Martin, Ryskin Teubner

))2/exp(1(2 2

bd

d)(),()( 222

2

bTRxxgrN gsC

Wave Functions

Boosted Gaussian – NNPZ, FS Gaussian distribution of quark 3-momentum in the meson rest frame

then boosted to LC

Gauss LC - KTGaussian distribution of quark 2-momentum in LC, factorization of r, z components- strong endpoint suppression in T

)2

exp()1(2

),(2

2

2LL

L R

rzz

R

Nzr

)

2exp()1(

2),(

2

222

2TT

T R

rzz

R

Nzr

Parameters of WF fixed by normalization conditions and the values of mesons decay constant, fV

WF Overlaps

Boosted Gaussian - different fV

for T and L

Gaus-LC- different R for T and L

Differences in fV

for Boosted Gaussiansizably smaller thandfferences in R forGaus-LC

Boosted Gaussian more consistentthan Gaus-LC

WF Overlaps integrated over z

KMW

KMW

)2/exp(~)( )exp(~ 2GD

diff

BbbTtBdt

d

KMW

BG BG

))1(( rzbibi ee

Description of the size of interaction region BD

Modification by Bartels, Golec-Biernat, Peters

proton size

KMW

KMW

)2

exp()1()1(2

),(2

2

2,LL

KOMOLT R

rzzzz

R

Nzr

Sensitivity to end points suppression of the wave function

’ ~ 0.1

)(),()( 2222

bTxxgrN sC

))2/exp(1(2 2

bd

d

QCD Evolution within Dipole Sat-Models

DSM with DGLAP (BGBK) + b-dependence (KT, KMW) — b-Sat

DSM with CGC-BFKL (IIM) + b-dependence (KMW+IIM) — b-CGC model

IIM Iancu Itakura Munier

Advantage of b-Sat

Advantage of b-CGC

ρ-meson BD ?

22

12

2

)),(exp()(

SS

s

rQ

ebrbS

Saturation scale (a measure of gluon density) b-frequency

)(),()( 2222

bTRxxgrN gsC

In b-Sat (b-CGC) there are substantial saturation effects in the proton center but only limited part of x-section is in

saturated region

b-independent proton shape?

instead of

J/Psi t-distributions clearly prefer Gaussian proton shape

ρ-meson t-distributions?

Conclusions

we are developing a very good understanding of inclusive and diffractive DIS interactions: F2 , F2

D(3) , F2c , Vector Mesons (J

we obtain a good description of Q2, W and t dependence of and J/ vector meson cross sections with a simple wave function ansatz

HERA measurements suggests presence of Saturation phenomenaSaturation scale determined at HERA, in the proton center,agrees with RHIC

____________________________________________________ Diffractive vector mesons scattering - an excellent probe of nuclear matter, ---- Measure t distribution on polarized nuclei ----- >>>> Obtain holographic picture of nuclei !!!! <<<<<

Possible device: e-RHIC like machine with ~1/3 of HERA energy

Inclusive DIS Hard Diffraction

Optical T

GBW – first Dipole Saturation Model Golec-Biernat, Wuesthoff BGBK – DSM with DGLAP Bartels, Golec-Biernat, Kowalski

IIM - BFKL-CGC motivated ansatz Iancu, Itakura, Munier FS – Regge ansatz with saturation Forshaw and Shaw

....4/))2/exp(1(2 XS Dipole 22

bd

d

Dipole Models equivalent to LO perturbative QCD for small dipoles

Glauber Mueller