June 13, 2008Aharon Levy - Torino seminar1 Gluons in the proton and exclusive hard diffraction Aharon Levy Tel Aviv University Introduction data on exclusive vector meson electroproduction sizes of gluon cloud sizes of photon configurations comparison to theory

June 13, 2008Aharon Levy - Torino seminar2 QCD based fits can follow the data accurately, yield parton densities. BUT: many free parameters (18-30) (only know how parton densities evolve) form of parameterisation fixed by hand (not given by theory) F 2  parton densities.  * ‘sees’ partons. parton density increases with decreasing x.

June 13, 2008Aharon Levy - Torino seminar3 From Pumplin, DIS05 There are signs that DGLAP (Q 2 evolution) may be in trouble at small x (negative gluons, high  2 for fits). Need better data to test whether our parton densities are reasonable. The structure function F L will provide an important test. all is not well … Can also get information on gluon density from exclusive hard processes.

June 13, 2008Aharon Levy - Torino seminar4 Exclusive VM electroproduction (V 0 =   DVCS)

June 13, 2008Aharon Levy - Torino seminar5 soft to hard transition 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 13, 2008Aharon Levy - Torino seminar6 Below Q 2  0.5 GeV 2, see same energy dependence as observed in hadron- hadron interactions. Start to resolve the partons.   s soft  hard

June 13, 2008Aharon Levy - Torino seminar7 soft to hard transition 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 13, 2008Aharon Levy - Torino seminar8 ingredients Use QED for photon wave function. Study properties of V-meson wf and the gluon density in the proton.

June 13, 2008Aharon Levy - Torino seminar9 Mass distributions

June 13, 2008Aharon Levy - Torino seminar10 Photoproduction process becomes hard as scale (mass) becomes larger.

June 13, 2008Aharon Levy - Torino seminar11  (W) – ρ 0 Fix mass – change Q 2

June 13, 2008Aharon Levy - Torino seminar12 Proton dissociation MC: PYTHIA pdiss : 19 ± 2(st) ± 3(sys) %

June 13, 2008Aharon Levy - Torino seminar13  (W) – ρ 0, 

June 13, 2008Aharon Levy - Torino seminar14  (W) - , J/ , 

June 13, 2008Aharon Levy - Torino seminar15  (Q 2 +M 2 ) - VM

June 13, 2008Aharon Levy - Torino seminar16 Kroll + Goloskokov:  = ln (Q 2 /4) (close to the CTEQ6M gluon density, if parametrized as xg(x)~x -  /4 )

June 13, 2008Aharon Levy - Torino seminar17  (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 13, 2008Aharon Levy - Torino seminar18  (Q 2 ) (for Q 2 > 1 GeV 2 )

June 13, 2008Aharon Levy - Torino seminar19 Proton vertex factorisation photoproduction proton vertex factorisation Similar ratio within errors for  and   proton vertex factorisation in DIS IP Y elastic p-dissociative

June 13, 2008Aharon Levy - Torino seminar20 b(Q 2 ) – ρ 0,  Fit:

June 13, 2008Aharon Levy - Torino seminar21 b(Q 2 +M 2 ) - VM ‘hard’ gg

June 13, 2008Aharon Levy - Torino seminar22 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 13, 2008Aharon Levy - Torino seminar23 R=  L /  T (Q 2 ) When r close to 1, error on R large and asymmetric  advantageous to use r rather than R.

June 13, 2008Aharon Levy - Torino seminar24 R=  L /  T (Q 2 )

June 13, 2008Aharon Levy - Torino seminar25 R=  L /  T (M ππ ) Why??

June 13, 2008Aharon Levy - Torino seminar26 R=  L /  T (M ππ ) Possible explanation: example for  =1.5

June 13, 2008Aharon Levy - Torino seminar27 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 13, 2008Aharon Levy - Torino seminar28  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 seems to be suppressed

June 13, 2008Aharon Levy - Torino seminar29  L /  tot (t)  size of  * L   * T  large configuration seems to be ssuppressed

June 13, 2008Aharon Levy - Torino seminar30  (W) - DVCS Final state  is real   T using SCHC  initial  * is  * T but W dep of  steep  large  * T configurations seem to be suppressed

June 13, 2008Aharon Levy - Torino seminar31 Effective Pomeron trajectory ρ 0 photoproduction Get effective Pomeron trajectory from d  /dt(W) at fixed t Regge:

June 13, 2008Aharon Levy - Torino seminar32 Effective Pomeron trajectory ρ 0 electroproduction ‘hard’ gg

June 13, 2008Aharon Levy - Torino seminar33 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 13, 2008Aharon Levy - Torino seminar34 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 13, 2008Aharon Levy - Torino seminar35 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 13, 2008Aharon Levy - Torino seminar36 Q2Q2 KMW – good for Q 2 >2GeV 2 miss Q 2 =0 DF – miss most Q 2 FSS – Gauss better than DGKP

June 13, 2008Aharon Levy - Torino seminar37 Q2Q2 Data seem to prefer MRST99 and CTEQ6.5M

June 13, 2008Aharon Levy - Torino seminar38 W dependence KMW - close FSS: Sat-Gauss – right W-dep. wrong norm. MRT: CTEQ6.5M – slightly better in W-dep.

June 13, 2008Aharon Levy - Torino seminar39  L /  tot (Q 2 )

June 13, 2008Aharon Levy - Torino seminar40  L /  tot (W) All models have mild W dependence. None describes all kinematic regions.

June 13, 2008Aharon Levy - Torino seminar41  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 13, 2008Aharon Levy - Torino seminar42 Density matrix elements - ,  Fair description by GK r 5 00 violates SCHC

June 13, 2008Aharon Levy - Torino seminar43  VM /  tot - ???

June 13, 2008Aharon Levy - Torino seminar44 Summary and conclusions HERA data shows transition from soft to hard interactions. 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. Transverse size of gluon density (0.6 fm) inside the charge radius of the proton (0.8 fm). 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 large configurations of the transversely polarised photon seem to be suppressed. 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. Precision measurements of exclusive vector meson electroproduction can help determine the gluon density in the proton.