Small-x and Diffraction in DIS at HERAII

Henri KowalskiDESY

12th CTEQ Summer School Madison - Wisconsin

June 2004

Proton

b – impact p.

Dipole Saturation Models

T(b) - proton shape 1)( 2

0

bdbT

GlauberMueller

))(),()(

32exp(12

),( 2222

2bTxxgr

bd

rxds

qq

GBW

KT

6.520

202

2

)1(1

),( xx

Axxg

r

C

g

g

BGBK

DGLAP

IIM Model with BFKL & CG evolution

Derivation of the GM dipole cross section

probability that a dipole at b does not suffer an inelastic interaction passing through one slice of a proton1),(

),(),()(1)(

2

2222

zbbdzd

dzzbxxgrN

bP sC

),()(

)(),()(exp)( 2222

2

zbdzbT

bTxxgrN

bS sC

))(),()(32

exp(12

))(Re1(2

2222

2

2

bTxxgrbd

d

bSbd

d

sqq

qq

S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton

<= Landau-Lifschitz

Uncorrelated scatterings

NOTE: the assumption of uncorrelated scatterings isnot valid for BK and JIMWLK equations

Correlations from evolution IIM Dipole fitGM Dipole + DGLAP mimics full evolution

Parameters fitted to HERA DIS data: 2 /N ~ 1 0 = 23 mb = 0.29 x0 = 0.0003

Data precision is essential to the progress of understanding

GBW GBW

GBW

))((22

)/1(~),( reffxxxg

Smaller dipoles steeper rise Large spread of eff characteristic for Impact Parameter Dipole Models (KT)

)()(2 22*

)/1(~)(~ QQp tottot xW

----- universal rate of rise of all hadronic cross-sections

GBW=0.29

)()(2 22*

)/1(~)(~ QQp tottot xW

BGBK

KT

In IP Saturation Model (KT) change of with Q2 is mainly due to evolution effects

GBW

In GBW Model change of with Q2 is due to saturation effects

In BGBK Model change of with Q2 is due to saturation and evolution effects

Analysis of data within Dipole Models

Theory (RV): evolution leads to saturation - Balitzki- Kovchegov and JIMWLK

GBW=0.29

GBW - - - - - - - - - - - - - - - - - - - - -

BGBK ___________________________________

- numerical evaluation

x = 10-6

x = 10-2

x = 10-4

x = 10-2

Evolution increases gluon density => smaller dipoles scatter stronger, gluons move to higher virtualities

Fouriertransform

In Color-Glass gluons occupy higher momentum states

A glimpse into nuclei

Naïve assumption for T(b): Wood-Saxon like, homogeneous, distribution of nuclear matter

)2/exp(~)(

)exp(~

2 BbbT

tBdt

d diff

))(),(

32exp(1

2

),( 222

2bATxxgr

Abd

rxdWSs

Aqq

Smooth Gluon Cloud

Q2 (GeV2) C 0.74 1.20 1.70 Ca 0.60 0.94 1.40

AqqWS

Aqq rxbT

Abd

rxd)/2),()(1(1

2

),(2

Lumpy Gluon Cloud

Q2 (GeV2) C 0.74 1.20 1.70 Ca 0.60 0.94 1.40

qSqSF

CgS QQ

C

NQ )(

4

9)()( 222

1

fm 7 1000

1

1

4

2

22

22

S

C

CsS

Q

Rdy

dN

dy

dN

RN

NQ

Saturation Scale at RHIC

HERASRHICS QQ )()( 22

Diffractive production of a qq pair_

Diffractive production of a qqg system

Inclusive Diffraction

Non-Diffraction Diffraction

Select diffractive events by requirement of no forward energy deposition called max cut

Q: what is the probability that a non-diff event has no forward energy deposition?

e => <=p

p p

Y

log W2 detector detector

log MX 2

MX Method

Non-Diffractive Event Diffractive Event

*p-CMS *p-CMS

Y

non-diff events are characterized by uniform, uncorrelated particle emission along the whole rapidity axis => probability to see a gap Y is ~ exp(-Y) – Gap Suppression Coefficient

since Y ~ log(W2/M2X) – 0

dN/dlogM 2X ~exp( log(M 2

X))

diff events are characterized by exponentially non-suppressed rapidity gap Y

dN/ dM 2X ~ 1/ M 2

X => dN/dlogM2

X ~ const

Y Y

Non-diff

diff

MX Method

Non-diff

Non-diff

diffdiff

Non-DiffractiondN/dM 2

X ~exp( log(M 2X))

Gap suppression coefficient independent of Q2 and W2

for Q2 > 4 GeV2

Diffraction dN/dlog M 2

X ~ const

Gap Suppression in Non-Diff MC---- Generator Level CDM---- Detector Level CDM

dN/dM 2X ~exp( log(M 2

X))

In MC independent of Q2 and W2

~ 2 in MC in data

Detector effects cancel in

Gap Suppression !

Physical meaning of the Gap Suppression Coefficient

Uncorrelated Particle Emission (Longitudinal Phase Space Model) – particle multiplicity per unit of rapidity

Feynman (~1970): depends on the quantum numbers carried by the gap

2 for the exchange of pion q.n. for the exchange of rho q.nfor the exchange of pomeron

q.n

is well measurable provided good calorimeter coverage

exp(- Y ) = exp(-log(W2/M2X)= (W2/M2

X)

from Regge point of view ~ (W2)

SR = SATRAP: MC based on the Saturated Dipole Saturation Model

~ H1 approach

A. Martin M. Ryskin G. Watt

BEKW

A. Martin M. Ryskin G. Watt

Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt

Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt

Absorptive correction to F2

from AGK rules

....4/))2/exp(1(2 22

bd

d Example in Dipole Model

F2 ~ -

Single inclusive pure DGLAP

Diffraction

)(),()( 2222

bTxxgrN s

C

A. Martin M. RyskinG. Watt

A. Martin M. Ryskin G. Watt

AGK Rules

)(

)!(!

!2)1( mm

km

kmk F

kmk

m

The cross-section for k-cut pomerons:Abramovski, Gribov, KancheliSov. ,J., Nucl. Phys. 18, p308 (1974)

1-cut

1-cut

2-cut

QCD Pomeron

F (m) – amplitude for the exchange of m Pomerons

Color singlet dominates over octet in the 2-gluon exchange amplitude at high energies

3-gluon exchange amplitude is suppressed at high energies

2-gluon pairs in color singlet (Pomerons) dominate the multi-gluon QCD amplitudes at high energies

Pomeron in QCD t-channel picture

2-Pomeron exchange in QCD Final States(naïve picture)

0-cut

1-cut

2-cut

p*p-CMS

Y

detector

p*p-CMS

p*p-CMS

detector

<n>

<2n>

Diffraction

0-cut

1-cut

2-cut

3-cut

AGK Rules in the Dipole Model

)(

1

1)1(2 m

m

mtot F

!

1

2)1(2))2/exp(1(2

1

12 mbd

dm

m

m

Total cross section Mueller-Salam (NP B475, 293)

Dipole cross section

)(),()( !

1

2222

2)( bTxxgr

NmF s

C

mm

Amplitude for the exchange of m pomerons in the dipole model

KT model

)(2 )!(!

!2)1( mm

km

kmk Fkmk

m

bd

d

AGK rules

Dipole model

)!()1(

!!

1

2)!(!

!2)1(

2 kmkmkmk

m

bd

d km

km

kmkm

m

km

kmk

)exp(!2

kbd

d kk

Diffraction from AGK rules

2

1222

))2/exp(1()exp()2/exp(21

))exp(1())2/exp(1(2

k

kqqdiff

bd

d

bd

d

bd

d very simple but not quite right

)2

exp(12 2bd

d qq)exp(

!2

kbd

d kk

)(),()( 2222

bTxxgrN s

C

22220

22222

22

20

221

22222

22

22,

1

00

22,

)1( )}()1(4{2

3),,(

)}()(])1({[2

3),,(

),(),,(),(*

qqemf

L

qqemf

T

qqf

fLT

PLT

mQzzrKzzQeQzr

rKmrKzzeQzr

rxQzrdzrdQx

Q2~1/r2

1for /1)(1 rrrK

1for ) exp(2/)(1 rrxrK

exp(-mq r)

All quarks Charmed quark

GeV 3.1 MeV 100

),(),,(2

,,

22,

1

0

csdu

qqf

fLT

mm

rxQzrdzr

GeV 3.1

),,(),(2 22,

1

0

c

cLTqq

m

Qzrrxdzr

),,()exp(!

),,(

),,()2

exp(12),,(

22*1

0

22

22*1

0

22

*

*

rzQk

rzQdzbdrd

rzQrzQdzbdrd

ff

k

fp

k

ff

fp

Note: AGK rules underestimate the amount of diffraction in DIS

Conclusions

We are developing a very good understanding of inclusive and diffractive *p interactions: F2 , F2

D(3) , F2c , Vector Mesons (J/Psi)….

Observation of diffraction indicates multi-pomeron interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one

Saturation effects in ep are considerably increased in nuclei

Thoughts after CTEQ School

George Sterman: Parton Model Picture (in Infinite Momentum Frame) is in essence probabilistic, non-QM. It is summing probabilities and not amplitudes

F2 = f e2f x q(x,Q2)

Parton Model Picture is extremely successful, it easily carries information from process to process, e.g. we get jet cross-sections in pp from parton densities detemined in ep

Dipole Models (Proton rest Frame) are very successful carrying information from process to process within ep. They are in essence QM, main objects are amplitudes:

0)t,(WImAW

1σ 2

el2γptot

In DM Picture diffraction is a shadow of F2 . Many other multi-pomeron effects should be present

Several attempts are underway to build a bridge over the gap between Infinite Momentum Frame and Proton Rest Frame Pictures

Jochen Bartels, Lipatov & Co: Feynman diagrams for multi-pomeron processes…

Raju Venogopulan & Co, Diffraction from Wilson loops, fluctuations from JIMWLK… ……………………………………..

A new detector to study strong interaction physics

e

p

HadronicCalorimeter

EM CalorimeterSi tracking stations

Compact – fits in dipole magnet with inner radius of 80 cm.Long - |z|5 m

e 27 GeV

p920GeV

ForwardDetector

Increase of kinematic range by over 4 order of magnitude in x at moderate Q2 and 6 order of magnitude in Q2

HERA InteractionsCollisions of e+ (e-) of 27.5 GeV with p of 920 GeV