Exclusive Vector Mesons at HERA Henri Kowalski DESY DIS 2006 Tsukuba, April 2006

GBW - Golec-B, Wuesthoff BGBK - Bartels, Golec-B, Kowalski KT - Kowalski, Teaney KMW - Kowalski, Motyka, Watt proton shape Glauber Mueller Dipole Models equivalent to LO perturbative QCD for small dipoles

x < universal rate of rise of all hadronic cross-sections Total  * p cross-section KT KMW

Inclusive Diffraction -LPS Dipole cross section determined by fit to F 2 simultaneous description of many reactions F 2 C KT BGBK

H. Kowalski, L. Motyka, G. Watt Exclusive Vector Meson Production Effective modification of Fourier Trans by Bartels, Golec-Biernat, Peters Real part correction Skewedness correction Martin, Ryskin Teubner

Wave Functions Boosted Gaussian – NNPZ, FS Gaussian distribution of quark 3-momentum in the meson rest frame then boosted to LC Gauss LC - KT Gaussian distribution of quark 2-momentum in LC, factorization of r, z components - strong endpoint suppression in  T Parameters of WF fixed by normalization conditions and the values of mesons decay constant, f V WF Overlaps

Boosted Gaussian - different f V for T and L Gaus-LC - different R for T and L Differences in f V for Boosted Gaussian sizably smaller than dfferences in R for Gaus-LC Boosted Gaussian more consistent than Gaus-LC WF Overlaps integrated over z

KMW

BGBG BGBG Description of the size of interaction region B D Modification by Bartels, Golec-Biernat, Peters proton size

KMW

Sensitivity to end points suppression of the  wave function

 ’ ~ 0.1

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 B D ?

Saturation scale ( a measure of gluon density) b-frequency 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: F 2, F 2 D(3), F 2 c, Vector Mesons (J  we obtain a good description of Q 2, W and t dependence of  and J/  vector meson cross sections with a simple wave function ansatz HERA measurements suggests presence of Saturation phenomena Saturation 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 Dipole Models equivalent to LO perturbative QCD for small dipoles Glauber Mueller