Inclusive Diffraction at HERAMarcella Capua – INFN and Calabria University

Small X and DiffractionFNAL Chicago (USA) 17 – 20 September 2003

on behalf of

• experimental methods and diffractive *p cross section

• Regge phenomenology measurement of t and xIP dependence comparison with inclusive ep cross section • QCD analysis of diffraction - diffractive pdf

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

2

Diffractive γ*p interactions at HERA

IPz

zL x

pp

x 1'

L

t

x

pppt

22)'(

22

22

)'(2 XMQ

Q

ppq

Q

22

22)'(WQ

MQpq

ppqx X

IP

squared 4-momentum transfer to p:

fraction of p momentum:

fraction of the p momentum carried by the IP:

fraction of the IP momentum carried by the struck parton:

- large kinematic range and cross section: the order 10 % of DIS is diffractive- ~4 acceptance (important for * dissociative system)- point-like couplings to probe the Pomeron structure- wide Q2 range: to access the transition region from soft to hard processes

Q2

W

MY

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

3

Large Rapidiy Gap methodX system and e’ measured

System Y not measured, some theoretical and experimental uncertanties

Integrate over t<1GeV2 and MY<1.6 GeV

High acceptance

p tag method o Measurement of t o Free of p-diss backgroundo Lower acceptance

MX methodHigh acceptance t measurement not possible systematics from p-diss

Diffractive peak

z

zL p

px

'

NB: if scattered proton not detected, background from proton dissociative events

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

4

Factorization

Regge factorization - “resolved IP model” (IP with partonic structure):

1)(2/ ),( tIP

Bt

IPpIP xe

txf

(Breit frame)

QCD Hard Scattering factorization (by Collins; Trentadue, Veneziano; Berera, Soper…:)

),(ˆ),,,()( 22** QxQxtxpXpp

pIPpq

),(ˆ),(),()( 22** QQptxfXpp

ppqIPpIP

Regge motivated pomeron flux

At fixed xIP and t diffractive Parton Densities evolve according to DGLAP

Shape of diffractive pdfs independent of xIP and t

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

5

What we know about t-distribution (pTag method)

Exponential fit to t distribution:

Regge phenomenology predicts “shrinkage” of the diffractive peak (b rise as xIP → 0):

no Q2 dependence

For xIP < 10 –2, data

prevent any firm conclusion

We are waiting new data from H1 and ZEUS proton tagger

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

6

• MX < 2 GeV (resonance range) weak W dependance• MX > 2 GeV d/dMX rises with Q2 adiff typically higher then soft

Cross section energy dependence (MX method)

As expected

for soft IP

diffIP aα

XDγ*p Wh)(Wh/dMdσ 222Fit:

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

7

Energy dependence (MX method)

Data (4<MX<8 GeV) consistent with the same W-dependence for the diffractive and the total cross section:

222 IPαX

Dγ*p )(W/dMdσ

total cross section:

diffractive cross section:

102*

IPWtot

p

value of IP diff higher than soft Pomeron

indication of a rise of IPdiff with Q2.

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

8

Ratio diff/tot (MX method)

In DIS diff/tot independent of W !

• low MX: strong decrease of diff/tot

with increasing Q2

• high MX: no Q2 dependence

Regge th: 19.01)0(2

222

*

*

)(

)(/W

W

WdMdIP

IP

totp

XD

p

• at W=220 GeV: diff(MX<35 GeV)/tot

~ 20 % Q2= 2.7 GeV 10 % Q2= 27 GeV

Same results from H1 and ZEUS-LPS

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

9

H1 Measurement of σrD(3)

(LRG method)

FL unknown, FL = 0 or FL = F2 few % error

New low and very high Q2 data!!!

Agreement between measurements

Red sample used for DGLAP QCD interpretation and IP(0) calculation well described by the fit

3-fold differential diffr. struct. func.

)3(

2

2)3(

22)3(

)1(1),,( D

LD

IPDr F

y

yFxQ

Diffractive reduced cross section rD

2)3(2

4

2

2

3

,,2

14

Qxy

yQdQddx

dIP

Dr

IP

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

10

and Q2 dependences

large scaling violation except at high → gluon dominatedsimilar at all xIP → support for Regge factorization

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

11

NLO DGLAP QCD fit

Gluon momentum fraction 75 ±15 % at Q2 = 10 GeV2

and remains large up to high Q2

-Regge factorization

-Singlet Σ and gluon g with Q20=3GeV2

-NLO DGLAP evolution

-Fit medium Q2 (6 < Q2 < 120 GeV2)

-Experimental and theor incertainties

Diff PDF’s:

Extended to large z

Gluon dominate

Σ well constrained

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

12

Test of QCD factorization

Good agreement with prediction with NLO fit at medium Q2 NLO Comparisons with Diff DIS Jets

Marcella Capua, INFN and Calabria University

Small X and Diffraction - FNAL September 2003

13

Summary

• recent data from H1 and ZEUS with improved precision and extended kinematic range

• data prevent any firm conclusion about shrinkage (waiting for new proton tagged data)

• value of diffractive IP higher than soft Pomeron

• W-dependence of diffractive and total cross section similar on DIS

• similar Q2 and dependencies to the inclusive DIS at medium

• NLO QCD fit of inclusive diffractive gives a good description of the data:

- diffractive pdf dominated by gluons

- diffractive pdf predictions well confirmed by tests