gluons in the proton and exclusive hard diffraction

$: Gluons in the proton and exclusive hard diffraction$
Nov 13, 2007 Aharon Levy - Oxford seminar 1

Gluons in the proton and exclusive hard diffraction

Aharon LevyTel Aviv University and DESY

• Introduction

• soft, hard interactions

• gluons

• data on exclusive vector meson electroproduction

• sizes of gluon cloud

• sizes of photon configurations

• effective Pomeron trajectory

• comparison to theory


LHeC


Deep Inelastic kinematics

Spin

[20 fb-1 /point]


McAllister, Hofstadter Ee=188 MeV rmin=0.4 fmBloom et al. 10 GeV 0.05 fmCERN, FNAL fixed target 500 GeV 0.007 fmHERA 50 TeV 0.0007 fm

HERA Kinematics

Ee=27.5 GeVEP=920 GeVs=(k+P)2 = (320 GeV)2 0.2

( )

c fmr

Q Q GeV

e

p

* r b

Transverse distance scale:

Impact parameter:c

bt

where t is the square of the 4-momentumtransferred to the proton


Proton momentum framePartons frozen during time of interaction. Virtual photon samples the quark distribution.

Assume that partons form incoherent beam. The parton density distributions are meant to be universal quantities.


Proton rest-frame

e

p

* r bq

q

Photon fluctuates into , , ….. states, which interact with the proton.

r large interaction soft, r small interaction hard.

qq qqg

soft and hard – studied by W (or x~1/W2) dependence of the cross section.


high energy behavior tot s0.08

,pp pp,p p

Donnachie and Lanshoff – universal behavior of total hadron-hadron cross section :

(0) 1 (0) 1( ) IP IRtot h h As Bs

soft


Regge trajectories

IP - Pomeron

( ) (0) 't t

( ) 1.08 0.25IP t t

( ) 0.45IR t t

(0) 1 (0) 1( ) IP IRtot h h As Bs


hard

The rise of F2 with decreasing x is strongly dependent on Q2.

2*

22( )tot

dF p

dxdQ

DIS:

2( )2

QF x at small x


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

s0.08

soft hard

2( )2

QF x


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.


arXiv:0711.1721Date: Mon, 12 Nov 2007 07:49:56 GMT (288kb)

Title: Status of Deeply Inelastic Parton DistributionsAuthors: Johannes Bl\"umlein From EDS07


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)


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


(W) - , J/,


(Q2+M2) - VM


(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)


b(Q2) – ρ0,

pp 0*

Fit||tbe

dt

d

:


b(Q2+M2) - VM

2 2( )r b c

‘hard’

gg


Frankfurt - Strikman

Kornelija Passek-Kumaricki - EDS07

DVCS


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

0400

0400

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.


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 - 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).


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.


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).

• 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 are 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.

gluons in the proton and exclusive hard diffraction

Documents

hard transition

parton density distributions

exclusive hard processes

hard interactions gluons

theoryf2 parton densities

gluon density

hadronhadron interactions

decreasing x