Exclusive VM electroproduction

June 10, 2008 A. Levy: Exclusive VM, GPD08, Trento 1

Exclusive VM electroproduction

Aharon LevyTel Aviv University

on behalf of the H1 and ZEUS collaborations

* 0

0 , , , / ,

p V p

V J


Why are we measuring

IP

‘soft’

WW )(

‘hard’

gg||tbe

dt

d

• Expect to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q2)2)

• Expect b to decrease from soft (~10 GeV-2)

to hard (~4-5 GeV-2)


s0.096

2( )2

QF x



IP

‘soft’

WW )(

‘hard’

gg||tbe

dt

d

• Expect to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q2)2)

• Expect b to decrease from soft (~10 GeV-2)

to hard (~4-5 GeV-2)



Use QED for photon wave function. Study properties of VM wf and the gluon density in the proton.


Mass distributions

KK /J

PHP

DIS 0

0


Photoproduction

W process becomes hard as scale (mass) becomes larger. real part of amplitude increases with hardness.


(W) – ρ0


Proton dissociationMC: PYTHIA

pdiss: 19 ± 2(st) ± 3(sys) %


(W) – ρ0,


(W) - , J/,


(Q2+M2) - VM


Kroll + Goloskokov: = 0.4 + 0.24 ln (Q2/4) (close to the CTEQ6M gluon density, if parametrized as xg(x)~x-/4)


(Q2) nMQ

22

Fit to whole Q2 range gives bad 2/df (~70)

VM n comments

ρ 2.44±0.09 Q2>10 GeV2

2.75±0.13 ±0.07

Q2>10 GeV2

J/ 2.486±0.080±0.068

All Q2

1.54±0.09 ±0.04

Q2>3 GeV2

101Q2(GeV2)


(Q2)

* 2

2

2 2 ( )

1( )

( )p n QQ

Q M

2 2( ) 2.15 0.007n Q Q

(for Q2 > 1 GeV2)


Proton vertex factorisation

photoproduction

proton vertex factorisation

Similar ratio within errors for and

proton vertex factorisation in DIS

IP IP

Yelastic p-dissociative


b(Q2) – ρ0, Fit

||tbedt

d

:


b(Q2+M2) - VM

2 2( )r b c

‘hard’

gg


Information on L and T

Use 0 decay angular distribution to get r0400 density matrix

element 04 04 200 00(cos ) (1 ) (3 1)cosh hf r r

04000400

1

1L

T

rR

r

- ratio of longitudinal- to transverse-photon fluxes ( <> = 0.996)

0400

L L

L T tot

r

using SCHC


R=L/T (Q2)When r00

04 close to 1, error on R large and asymmetric advantageous to use r00

04 rather than R.


R=L/T (Q2)


R=L/T (Mππ)

Why??


R=L/T (Mππ)

Possible explanation:

2

1R

M

example for =1.5


Photon configuration - sizessmall kT large

kTlarge 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

qq

qq


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

qq

qq

qq


L/tot(t)

TL bb

size of *L *T

large configuration suppressed

qq


(W) - DVCS* p p

Final state is real T

using SCHC initial * is *T

but W dep of steep

large *T configurations suppressed


Effective Pomeron trajectory

ρ0

photoproduction

Get effective Pomeron trajectory from d/dt(W) at fixed t

2[2 ( ) 2]( ) ( ) IP td

W F t Wdt

Regge:


Effective Pomeron trajectory

ρ0 electroproduction


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 Q2

• 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

• Q2 and R – properties of the wave function


ρ0 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, 014022 (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, 094013 (2004).

• Kowalski-Motyka-Watt (KMW) – add impact parameter dependence, Q2 evolution – DGLAP. Phys. Rev. D 74, 074016 (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).


ρ0 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 kt-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.


Q2

KMW – good for Q2>2GeV2 miss Q2=0

DF – miss most Q2

FSS – Gauss better than DGKP


Q2

Data seem to prefer

MRST99 and CTEQ6.5M


W dependence

KMW - close

FSS:

Sat-Gauss – right W-dep.

wrong norm.

MRT:

CTEQ6.5M – slightly better in W-dep.


L/tot(Q2)


L/tot(W)

All models have mild W dependence. None describes all kinematic regions.


L,T (Q2+M2)

• Different Q2+M2 dependence of L and T (L0 at Q2=0)

• Best description of L by GK; T not described.


Density matrix elements - ,

• Fair description by GK

• r500 violates SCHC


VM/tot


Summary and conclusions• New high statistics measurements on ρ0,

electroproduction and on DVCS.• The Q2 dependence of (*pρp) cannot be described by a

simple propagator term.• The cross section is rising with W and its logarithmic

derivative in W increases with Q2.• The exponential slope of the t distribution decreases with Q2

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 Q2, 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.

Exclusive VM electroproduction

Documents

vm wave function

study properties of

soft pomeron value

dipole picture use qed

cteq6m gluon density

r large

t configurations

lt mwhy