June 10, 2008A. Levy: Exclusive VM, GPD08, Trento1 Exclusive VM electroproduction Aharon Levy Tel Aviv University on behalf of the H1 and ZEUS collaborations

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento2 Why are we measuring IP ‘soft’ ‘hard’ gg Expect  to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q 2 ) 2 ) Expect b to decrease from soft (~10 GeV -2 ) to hard (~4-5 GeV -2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento3   s 0.096

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento4 Why are we measuring IP ‘soft’ ‘hard’ gg Expect  to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q 2 ) 2 ) Expect b to decrease from soft (~10 GeV -2 ) to hard (~4-5 GeV -2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento5 Why are we measuring Use QED for photon wave function. Study properties of VM wf and the gluon density in the proton.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento6 Mass distributions PHP DIS

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento7 Photoproduction process becomes hard as scale (mass) becomes larger. real part of amplitude increases with hardness.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento8  (W) – ρ 0

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento9 Proton dissociation MC: PYTHIA pdiss : 19 ± 2(st) ± 3(sys) %

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento10  (W) – ρ 0, 

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento11  (W) - , J/ , 

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento12  (Q 2 +M 2 ) - VM

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento13 Kroll + Goloskokov:  = ln (Q 2 /4) (close to the CTEQ6M gluon density, if parametrized as xg(x)~x -  /4 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento14  (Q 2 ) Fit to whole Q 2 range gives bad  2 /df (~70) VMncomments ρ2.44±0.09Q 2 >10 GeV 2  2.75±0.13 ±0.07 Q 2 >10 GeV 2 J/  2.486±0.080 ±0.068 All Q 2  1.54±0.09 ±0.04 Q 2 >3 GeV Q 2 (GeV 2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento15  (Q 2 ) (for Q 2 > 1 GeV 2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento16 Proton vertex factorisation photoproduction proton vertex factorisation Similar ratio within errors for  and   proton vertex factorisation in DIS IP Y elastic p-dissociative

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento17 b(Q 2 ) – ρ 0,  Fit:

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento18 b(Q 2 +M 2 ) - VM ‘hard’ gg

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento19 Information on  L and  T Use  0 decay angular distribution to get r density matrix element  - ratio of longitudinal- to transverse- photon fluxes ( = 0.996) using SCHC

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento20 R=  L /  T (Q 2 ) When r close to 1, error on R large and asymmetric  advantageous to use r rather than R.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento21 R=  L /  T (Q 2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento22 R=  L /  T (M ππ ) Why??

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento23 R=  L /  T (M ππ ) Possible explanation: example for  =1.5

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento24 Photon configuration - sizes small k T large k T large config. small config.  T : large size small size strong color forces color screening large cross section small cross section  *:  * T,  * L  * T – both sizes,  * L – small size Light VM: transverse size of ~ size of proton Heavy VM: size small  cross section much smaller (color transparency) but due to small size (scale given by mass of VM) ‘see’ gluons in the proton   ~ (xg) 2  large 

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento25  L /  tot (W)   L and  T same W dependence  L  in small configuration  T  in small and large configurations small configuration  steep W dep large configuration  slow W dep  large configuration is suppressed

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento26  L /  tot (t)  size of  * L   * T  large configuration suppressed

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento27  (W) - DVCS Final state  is real   T using SCHC  initial  * is  * T but W dep of  steep  large  * T configurations suppressed

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento28 Effective Pomeron trajectory ρ 0 photoproduction Get effective Pomeron trajectory from d  /dt(W) at fixed t Regge:

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento29 Effective Pomeron trajectory ρ 0 electroproduction

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento30 Comparison to theory All theories use dipole picture Use QED for photon wave function Use models for VM wave function – usually take a Gaussian shape Use gluon density in the proton Some use saturation model, others take sum of nonperturbative + pQCD calculation, and some just start at higher Q 2 Most work in configuration space, MRT works in momentum space. Configuration space – puts emphasis on VM wave function. Momentum space – on the gluon distribution. W dependence – information on the gluon Q 2 and R – properties of the wave function

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento31 ρ 0 data (ZEUS) - Comparison to theory Martin-Ryskin-Teubner (MRT) – work in momentum space, use parton-hadron duality, put emphasis on gluon density determination. Phys. Rev. D 62, (2000). Forshaw-Sandapen-Shaw (FSS) – improved understanding of VM wf. Try Gaussian and DGKP (2- dim Gaussian with light-cone variables). Phys. Rev. D 69, (2004). Kowalski-Motyka-Watt (KMW) – add impact parameter dependence, Q 2 evolution – DGLAP. Phys. Rev. D 74, (2006). Dosch-Ferreira (DF) – focusing on the dipole cross section using Wilson loops. Use soft+hard Pomeron for an effective evolution. Eur. Phys. J. C 51, 83 (2007).

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento32 ρ 0 data (H1) - Comparison to theory Marquet-Peschanski-Soyez (MPS): Dipole cross section from fit to previous ,  and J/  data. Geometric scaling extended to non-forward amplitude. Saturation scale is t-dependent. Ivanov-Nikolaev-Savin (INS): Dipole cross section obtained from BFKL Pomeron. Use k t -unintegrated PDF and off-forward factor. Goloskokov-Kroll (GK): Factorisation of hard process and proton GPD. GPD constructed from standard PDF with skewing profile function.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento33 Q2Q2 KMW – good for Q 2 >2GeV 2 miss Q 2 =0 DF – miss most Q 2 FSS – Gauss better than DGKP

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento34 Q2Q2 Data seem to prefer MRST99 and CTEQ6.5M

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento35 W dependence KMW - close FSS: Sat-Gauss – right W-dep. wrong norm. MRT: CTEQ6.5M – slightly better in W-dep.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento36  L /  tot (Q 2 )

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento37  L /  tot (W) All models have mild W dependence. None describes all kinematic regions.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento38  L,  T (Q 2 +M 2 ) Different Q 2 +M 2 dependence of  L and  T (  L  0 at Q 2 =0) Best description of  L by GK;  T not described.

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento39 Density matrix elements - ,  Fair description by GK r 5 00 violates SCHC

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento40  VM /  tot

June 10, 2008A. Levy: Exclusive VM, GPD08, Trento41 Summary and conclusions New high statistics measurements on ρ 0,  electroproduction and on DVCS. The Q 2 dependence of  (  *p  ρp) cannot be described by a simple propagator term. The cross section is rising with W and its logarithmic derivative in W increases with Q 2. The exponential slope of the t distribution decreases with Q 2 and levels off at about b = 5 GeV -2. Proton vertex factorisation observed also in DIS. The ratio of cross sections induced by longitudinally and transversely polarised virtual photons increases with Q 2, but is independent of W and t. The effective Pomeron trajectory has a larger intercept and smaller slope than those extracted from soft interactions. All these features are compatible with expectations of perturbative QCD. None of the models which have been compared to the measurements are able to reproduce all the features of the data.