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June 13, 2008 Aharon Levy - Torino seminar 1

Gluons in the proton and exclusive hard diffraction

Aharon LevyTel Aviv University

• Introduction

• data on exclusive vector meson electroproduction• sizes of gluon cloud

• sizes of photon configurations

• comparison to theory


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)

F2 parton densities. * ‘sees’ partons. parton density increases with decreasing x.


From Pumplin, DIS05

There are signs that DGLAP (Q2

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 FL will provide an important test.

all is not well …

Can also get information on gluon density from exclusive hard processes.


Exclusive VM electroproduction

(V0 = DVCS)

* 0

0 , , , / ,

p V p

V J


soft to hard transition

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)


Below Q2 0.5 GeV2, see same energy dependence as observed in hadron-hadron interactions. Start to resolve the partons.

s0.096

soft hard

2( )2

QF x


soft to hard transition

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)


ingredients

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


Mass distributions KK

/J


Photoproduction

W process becomes hard as scale (mass) becomes larger.


(W) – ρ0 Fix mass – change Q2


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)

pp 0* 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,

pp 0*

Fit||tbe

dt

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)

pp 0*

When r0004 close to 1, error on R large and asymmetric

advantageous to use r0004 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 seems to be suppressed

qq

qq

qq


L/tot(t)

TL bb

size of *L *T

large configuration seems to be ssuppressed

qq


(W) - DVCS* p p

Final state is real T

using SCHC initial * is *T

but W dep of steep

large *T configurations seem to be 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 trajectoryρ0 electroproduction

' 1

Tk

‘hard’

gg


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• HERA data shows transition from soft to hard interactions.• 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. 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 Q2, 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.

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