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Anna MastroberardinoCalabria University

On behalf of the H1 & ZEUS Collaborations

Diffraction at HERA

HSQCD 2004St. Petersburg, Russia

18 – 22 May 2004

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Outline

Introduction to diffraction

Diffractive structure function of the proton

QCD fits of diffractive data

Test of QCD factorization with jets and charm

Exclusive vector mesons

Summary

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What is diffraction?

XW

Q2e (k)e’(k’)

P (p) P’(p’)t

IPxIP

*(q)

Diffraction: exchange of colour singlet (IP) producing a rapidity GAP in the particle flow

Q2

WThe struck quark carries fraction x Q2/W2 of the proton momentum

W = photon-proton centre of mass energy

The pomeron carries fraction xIP of the initial proton momentum The struck parton carries fraction β of the Pomeron momentum

Standard DIS in a frame in which the proton is very fast (Breit frame):

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Why diffraction ?

),()],(1[2

14 2

22

2

4

2

2

2

QxFQxR

yy

xQdxdQ

d

i

ii x,QxfeF 222

),,,()1(2

14 2)4(

2)4(

2

4

2

2

4

txQFR

yy

QdtdxdQd

dIP

DD

IP

Diffractive DIS probes the partonic structure of colour singlet exchange

DIS probes the partonic structure of the proton

Diffractive structure function Diffractive cross section

920 GeV proton 27.5 GeV electron

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252

10

GeV10

GeV 300

x

Q

W

~ 10% of low-x DIS diffractive at HERA What role does it play?

HERA has opened up the small x domain

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Selection methods

Large Rapidity Gap MX – Method Proton Tagging

ln MX2

-2 0 2 4 6 8

Two systems X and Y well separated in phase space with low masses MX ,MY << W

Y : proton or p-dissociation carries most of the hadronic energy

X : vector meson, photon or photon-dissociation

Diffractive peak

no forward energy deposition

Diffractive events are characterized by:

flat vs ln MX2 distribution

scattered proton almost intact

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Factorization in Diffractive DIS

QCD factorization for diffractive DIS holds (Collins, Bereira & Soper, Trentadue & Veneziano)

),(),( 22/

)4(2 QFtxfF IP

IPpIPD

iD

i/pD fF ̂ ~ 2 universal partonic cross section

(same as in inclusive DIS)

diffractive parton distribution function – evolve according to DGLAPuniversal for diffractive ep DIS (inclusive, dijets, charm)

If in addition postulate Regge factorization (Ingelman & Schlein)

equations DGLAPfollowing evolves ),( 22 QF IP

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New results from ZEUS

Transition from very low Q2 to DIS (0.03 <Q2<100 GeV2)

MN < 2.3 GeV

Proton tagging method MX method

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Recent results from H1

)4(

2

2)4(

2)4(

)2

1(2

DL

DDr F

yy

yF

0 if

low yat

2

2

D

LDD

r

DDr

FF

F

Integrate over t )3(Dr

22 GeV 16005.1 Q

high precision measurement of and Q2 dependences

QCD fit (DGLAP evolution of diffractive pdfs) (coming later)

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Measurement of & Q2 dependences

Regge factorization holds for xIP< 0.01

Weak dependence: looks like a photon more than a proton

Scaling violations positive up to large : large gluon contribution

DGLAP evolution based fit describes the data

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H1 NLO QCD fit – diffractive PDFs

Parametrize Flavour Singlet (quarks + antiquarks) and gluons at Q2 = 3 GeV2

Evolve according to NLO DGLAP and fit Determine quark sea and gluon distribution

Integrated fraction of exchanged momentum carried by gluons

(75 15)%

Diffractive interactions gluon dominated

Diffractive data fitted in similar way to proton F2 data

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QCD fit describes data

fractional gluon momentum

shape of pdfs not well constrained

))%(9)(882( sysstat

)36/9.37/( 2 ndf

[F2D(3)cc from DESY-03-094]

(LPS)

ZEUS NLO QCD fit to F2D and charm

• xIP <0.01

• QCDNUM

• Regge factorisation assumption possible for this small data set

• DL flux

• initial scale Q2=2 GeV2

• zf(z)=(a1+a2z+a3z2)(1-x)a4

• other PDFs parametrisation tried

• Thorne-Robert variable-flavour- number-scheme

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If QCD factorization holds diffractive parton densities are universal

- Test: use diffractive pdfs obtained so far from inclusive data to predict other final state cross sections

diffractive DIS ?

hadron – hadron scattering?

Factorization in Diffractive DIS – experimental test

iD

i/pD fF ̂ ~ 2 universal partonic cross section

(same as in inclusive DIS)

diffractive parton distribution function – evolve according to DGLAPuniversal for diffractive ep DIS (inclusive, dijets, charm)

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A test of QCD factorization: jets and charm (H1)

Use results of NLO QCD fit to predict the rate of diffractive production of

dijets and charm in DIS

NLO calculations based on H1 pdfs describe data well

QCD factorization in DDIS holds

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diffractive DIS ?

factorization breaking

Diffractive structure function of antiproton

understood in terms of (soft) rescattering corrections of the spectator partons (Kaidalov, Khoze, Martin, Ryskin) But several other approaches …

also a suppression of resolved processes, supposed to be similar to pp ?

Factorization in Diffractive DIS – experimental test

It holds

Factorization not expected to work - Indeed it does not:

hadron-hadron scattering ?

diffractive dijets at the Tevatron: suppression by a factor of 10

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Diffractive dijets in photoproductionReal photon (Q2~ 0) can develop hadronic structure

photoproduction similar to

hadron-hadron interaction

LO comparison: no evidence for a suppression of resolved with respect to direct

NLO comparison ?

X= partonic momentum for dijet production

photon remnant energy 1 - x

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Diffractive dijets in photoproduction

NLO comparison: agreement between data and MC found if resolved contribution suppressed by a factor of 0.34 rate of suppression expected from theoretical models

NLO calculations compared to preliminary H1 data (Klasen and Kramer, DESY 04-011)

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Vector Meson production

(JPC=1--): JIP

p p

V

pp

V

W

cross section:

226

2

),( ~ effS QxxG

Q

2

22

~W

MQx V

8.0~ ~

~),( /for 2.02

W

xQxxGJ eff

rise with W: increasing with hard scale

probability of finding 2 gluons in the proton

2-gluon exchange Exclusive VM production calculable in pQCD

NLO calculation available for J/photoproduction

Sensitivity to gluons in proton

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Vector Meson production

(p Vp), Q2=0

W x

MV

p centre-of-mass energy

Small MV (MV2 1 GeV2):

Incoming dipole behaves like a normal-size hadron. Flat vs W reflects flat gluon distribution for Q2 0

Large MV :

Fast growth of with W reflects growth of gluon distribution with decreasing x

Soft regime

Hard regime

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Exclusive J/ Meson production

- pQCD models describe data

- strong sensitivity to (generalized) gluon

- need NLO to constrain gluon density

L/T vs Q2

Pomeron trajectory

0<Q2<100 GeV2

IP(t) not consistent with

soft diffractive measurement

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Summary

Non perturbative phenomenology

HERA–II: a lot of more data coming

Need to discriminate models

pQCD

New high precision HERA data have improved our understanding of diffraction:

Diffractive processes are dominated by gluons

Regge factorization works to a good approximation

Diffractive pdfs are universal within HERA - QCD factorization holds in diffractive DIS

Vector mesons: steep W dependence - Pure pQCD approach successful

- On the way to understanding the large breaking of factorization at Tevatron – soft re-scattering