Overview of low-x and diffraction at HERA

Henri KowalskiDESY

Rencontres de Moriond La Thuile, March 2006

0)t,(WImAW

1σ 2el2

γptot

2

22Pγ

totem

2

22

2 WQx)Q(W,σ

α π4 Q)Q(x,F

*

F2 is dominated by single ladder exchange

ladder symbolizes a QCD evol. process( DGLAP or others )

Gluon density

Gluon density dominates F2 for x < 0.01

Diffractive ScatteringNon-Diffractive Event ZEUS detector

Diffractive Event

MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter

Non-Diffraction Diffraction

- Rapidity

uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap Y is ~ exp(-<n>Y) <n> - average multipl. per unit of Y

Diffractive Signature

dN/dM2X ~ 1/M2

X => dN/dlog M2

X ~ const

Non-diff

diff

~ Y= log(W2/M2X)

Observation of diffraction indicates that single ladder may not be sufficient(partons produced from a single chain have exponentially suppressed rap. gaps)

Inclusive DIS Hard Diffraction

Optical T

GBW – first Dipole Saturation Mode Golec-Biernat, Wuesthoff BGBK – DSM with DGLAP Bartels, Golec-Biernat, Kowalski

IIM - BFKL-CGC motivated ansatz Iancu, Itakura, Munier FS – Regge ansatz with saturation Forshaw and Shaw

....4/))2/exp(1(2 XS Dipole 22 bd

d

Dipole Models equivalent to LO perturbative QCD for small dipoles

Glauber Mueller

Impact Parameter Dipole Saturation Model

)2

exp(12*21

0

2*

bddzrdptot

)2/exp(~)(

)exp(~

2 BbbT

tBdt

d diff

KT - Kowalski TeaneyKMW – Kowalski, Motyka, Watt

2*1

0

22 |)2

exp(12|16

1*

VM

bip

VM dzebdrddt

d

proton shape )(),()( 222

2

bTxxgrN s

C

x < 10-2

universal rate of rise of all hadronic cross-sections

tottot xWp )/1(~)(~ 2*

Total *p cross-section

6.520

202

2

)1(1),( xx

Axxg

rC

g

g

KT KMW

Inclusive Diffraction

from fit to tot predict diff

GBW, BGBK, ….

-LPS

Dipole cross section determined by fit to F2

Simultaneous description of many reactions

F2 C

KMW

KT

KMW

)2/exp(~)( )exp(~ 2GD

diff

BbbTtBdt

d

KMW

BG BG

))1(( rzbibi ee

Description of the size of interaction region BD

Modification by Bartels, Golec-Biernat, Peters

proton size

Diffractive Di-jets Q2 > 5 GeV2

-RapGap

Satrap

Saturation scale (a measure of gluon density)

HERA RHIC

22

22

22

GeV 1

fm 7 1000

11

4

S

C

CsS

Q

RdydN

dydN

RNNQ

qSqSF

CgS QQ

CNQ )(

49)()( 222

QSRHIC ~ QS

HERA

22

12

2

)),(exp()(

SS

s

rQ

ebrbS

)(20

2 xRQ

Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski

02

20

1)(xx

GeVxR

GS is an effective property of HERA data

b-Dipole Model analysis: GS seen in the center of the proton

Theoretical importance: property of non-linear evolution in QCD BK, JIMWLK

2-Pomeron exchange in QCD

Final States(naïve picture)

0-cut

1-cut

2-cut

Diffraction

<n>

<2n>

Multiple Interactions and Long Range Correlation

QCD diagrams

Note: AGK rules underestimate the amount of diffraction in DIS

)exp(!2

kbdd k

k )(),()( 2222

bTxxgrN s

C

AGK rules in theDipole Model

)2

exp(12 2bdd qq

)exp(!2

kbdd k

k

)(),()( 2222

bTxxgrN s

C

Exclusive Double Diffractive Reactions at LHC

low x QCD reactions: pp => pp + gJet gJet ~ 1 nb for M(jj) ~ 50 GeV ~ 0.5 pb for M(jj) ~ 200 GeV JET| < 1

xIP = p/p, pT xIP ~ 0.2-1.5%

High momentummeasurementprecision

pp => pp + Higgs 3) fb SM O(100) fb MSSM

1 event/sec

xIP = p/p, pT xIP ~ 0.2-1.5%

OSMyLM

LDiff

22

2

ˆ

2

214

2

2 ),(),()1(

tgtgt

t

c

exclusive QxfQxfQdQ

bNO

Absorptive corrections from BK equation Resummation of BFKL pomeron fan diagrams

Conclusions We are developing a very good understanding of inclusive and diffractive DIS interactions: F2 , F2

D(3) , F2c , Vector Mesons (J/Psi

HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC

Observation of diffraction indicates multi-gluon interaction effects -> Underlying events at LHC may be process dependent

Diffractive LHC ~ pure Gluon Collider => investigations of properties of the gluon cloud in the new region Gluon Cloud is a fundamental QCD object - SOLVE QCD!!!!

_____________________________________________________ Diffractive vector mesons scattering - an excellent probe of nuclear matter

Ideal device: e-RHIC like machine with ~1/3 of HERA energy