small-x and diffraction at hera and lhc henri kowalski desy eds château de blois 2005

Small-x and Diffraction at HERA and LHC

Henri KowalskiDESY

EDS Château de Blois 2005

ZEUS H1

Q2 - virtuality of the incoming photonW - CMS energy of the incoming photon-proton system

x - Fraction of the proton momentum carried by the struck quark x ~ Q2/W2

Liquid Argon Calorimeter Uranium-Scintillator Calorimeter

e 27 GeV

p920GeV

HERA – ep Collider

2

2L

223

224

2em

2

eP2

y)(11Y

)]Q(x,Fy)Q(x,xFY )Q(x,F[Y xQ

απ 2

dxdQ

σd

y – inelasticityQ2 = sxy

Infinite momentum frame

Proton looks like a cloud of non-interacting quarks and gluons

F2 measures parton density in theproton at a scale Q2

Gluon density

Gluon density dominates F2 for x < 0.01

Diffractive Scattering

Non-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

222

20

22222

2

20

221

22222

2

)1(

)}()1(4{2

3

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

3

q

qemf

L

qqemf

T

mQzz

rKzzQe

rKmrKzze

Dipole description of DISequivalent to Parton Picture in perturbative region

),(ˆ 2*1

0

2*

rxdzrd qqp

tot ),(

16

1| 22*

1

0

20

*

rxdzrddt

dqqt

pdiff

)))/,(3

exp(1(),( 20

222

0

2

0 rCxxgrrx sqq

GBW – first Dipole Model only rudimentary evolution

BGBK – DM with DGLAP

Iancu, Itakura, Mounier (IIM) - CGC motivated ansatz Forshaw, Shaw (FS) - Regge type ansatz with saturation, CGC-inspired

Mueller, Nikolaev, Zakharov

GBW

x

x

GeVR

R

rrxqq

02

202

0

2

0

1 ));exp(1(),(

r Q2~1/r2Optical T

Comparison with DataComparison with Data

FS model with/without saturation and IIM CGC model hep-ph/0411337.

Fit F2 and predictxIPF2

D(3)

F2

F2

FS(nosat)

x

CGC

FS(sat)

Diffractive contribution of the total cross sectionDiffractive contribution of the total cross section

tot

pγ

M

M Xdiff

GeV 2.3MXN,pγXdiff tot σ

/dMdσdMr

b

a N

For larger MX, diff has the similar W and Q2 dependences as tot.

• For the highest W bin (200<W<245 GeV), diff (0.28<MX<35 GeV, MN<2.3 GeV) /tot 22

1.21.0 GeV 4Qat %15.8

22

0.70.7 GeV 27Qat %9.6

Proton

b – impact parameter

Impact Parameter Dipole Saturation Model

T(b) - proton shape

Glauber-Mueller, Levin, Capella, Kaidalov…

))(),()(

32exp(12

),( 2222

2bTxxgr

bd

rxds

qq

)2/exp(~)()exp(~ 2 BbbTtBdt

d diff

KowalskiTeaney

x < 10-2

universal rate of rise of all hadronic cross-sections

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

Total *p cross-section

Dipole cross section determined by fit to F2

Simultaneous description of many reactions

Gluon density test? Teubner

*p -> J/ p

*p -> J/ p

IP-Dipole Model

F2 C

IP-Dipole Model

)]4

exp(1[ ),(20

2

0 R

rrxqq

GBW Model

))()/,(32

exp(12 ),( 2

022

2

2bTQrCxxgr

bd

rxds

qq

IP Dipole Model

less saturation (due to IP and charm)

strong saturation

02

20

1)(

x

x

GeVxR

Saturation scale

HERA RHIC

22

22

22

GeV 1

fm 7 1000

1

1

4

S

C

CsS

Q

Rdy

dN

dy

dN

RN

NQ

qSqSF

CgS QQ

C

NQ )(

4

9)()( 222

QSRHIC ~ QS

HERA

22 2

SS r

Q

Saturated state is partially perturbative

p cross-section exhibits the universal rate of growth

Absorptive correction to F2

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

bd

d

Example in Dipole Model

F2 ~ -

Single inclusive pure DGLAP

Diffraction

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

Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

Note: AGK rules underestimate the amount of diffraction in DIS

)exp(!2

kbd

d kk )(),()( 222

2

bTxxgrN s

C

AGK rules in theDipole Model

)2

exp(12 2bd

d qq)exp(

!2

kbd

d kk

)(),()( 2222

bTxxgrN s

C

HERA Result

Unintegrated Gluon Density

)2/exp()( ),,0,()(),,,( 11 BttbQtxftQtxf tgtg

)],(),([ln

)(),( 22

2tt

tg QxxgQT

Qtxf

2

2

)/(

02

22

)(2

)(exp),(

t

tt

Q

kk

ggt

ttSt dzzzP

k

dkkQT

Dipole Model

Example from dipole model

- BGBK

Another approach (KMR)

Active field of study at HERA:

UGD in heavy quark production, new result expected from high luminosity running in 2005, 2006, 2007

Exclusive Double Diffractive Reactions at LHC

2

22114

2

2

22

2

),,,',(),,,',()1(

ˆ

tgtgt

t

c

exclusive

Diff

QtxxfQtxxfQ

dQ

bNO

OSMy

LM

L Diff = hard X-section × Gluon Luminosity

factorization !!!

fg – unintegrated gluon

densities

HiggsHiggs

T

s

Edt

d

ˆ

4

9ˆ4

2

gg Jet+Jet

gg Higgs

low x QCD reactions: pp => pp + gJet gJet ~ 1 nb for ET > 20 GeV , M(jj) ~ 50 GeV ~ 0.5 pb for ET > 60 GeV , M(jj) ~ 200 GeV JET| < 2 KMR Eur. Phys J. C23, p 311

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

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

1 event/sec

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

t – distributions at HERA

|)|4exp(~ tdt

d diffhard

t – distributions at LHC

with the cross-sections of the O(1) nb and L ~ 1 nb-1 s-1 => O(107) events/year are expected.

For hard diffraction this allows to follow the t – distribution to tmax ~ 4 GeV2 For soft diffraction tmax ~ 2 GeV2

Saturated gluons

Non-Saturated gluons

t-distribution of hard processesshould be sensitive to the evolution and/or saturation effects

see: Al Mueller dipole evolution, BK equation, and the impact parameter saturation model for HERA data

Dipole form double eikonal single eikonal

KhozeMartinRyskin

t – distributions at LHC

Effects of soft proton absorption modulate the hard t – distributions

t-measurement will allow to disentangle the effects of soft absorption from hard behavior

Survival Probability S2

Soft Elastic Opacity

bdbsM

bdebsMS

bs

22

2),(2

2

),(

),(

),(/

)()(),( 21

220

222

21

2

21 tttt ppSbS

ttppF

2

22114

2

2),,,',(),,,',(

)1(

tgtg

t

t

c

exclusive QtxxfQtxxfQ

dQ

bNO

L. Motyka, HKpreliminary

Gluon Luminosity

QT2 (GeV2)

Dipole Model

F2

Exclusive Double Diffraction

Conclusions

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

D(3) , F2c , Vector Mesons (J/Psi)….

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

HERA determined properties of the Gluon Cloud

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!!!!

))((22

)/1(~),( reffxxxg

Smaller dipoles steeper rise Large spread of eff characteristic for IP Dipole Models

)()(2 22*

)/1(~)(~ QQp tottot xW

universal rate of rise of all hadronic cross-sections

The behavior of the rise with Q2

)]4

exp(1[ ),(20

2

0 R

rrxqq

GBW Model

))()/,(32

exp(12 ),( 2

022

2

2bTQrCxxgr

bd

rxds

qq

KT-IP Dipole Model

less saturation (due to charm)

strong saturation

Unintegrated Gluon Densities

Exclusive Double Diffraction

)2/exp()( ),,0,',()(),,,',( 1111 BttbQtxxftQtxxf tgtg

)],(),([ln

)(),,,',( 22 ttt

gtg QxxgQTQ

RtQtxxf

2

2

)/(

02

22

)(2

)(exp),(

t

tt

Q

kk

ggt

ttSt dzzzP

k

dkkQT

Note: xg(x,.) and Pgg drive the rise of F2 at HERA and Gluon Luminosity decrease at LHC

Dipole Model

Saturation Model Predictions for Diffraction

Absorptive correction to F2

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

bd

d

Example in Dipole Model

F2 ~ -

Single inclusive pure DGLAP

Diffraction

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

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

Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

),,()exp(!

),,(

),,()2

exp(12),,(

22*1

0

22

22*1

0

22

*

*

rzQk

rzQdzbdrd

rzQrzQdzbdrd

ff

k

fp

k

ff

fp

Probability of k-cut in HERA data

DipoleModel

Problem of DGLAP QCD fits to F2

CTEQ, MRST, …., IP-Dipole Model

0 ,~),( 20 xxxg at small x

valence like gluon structure function ?

Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT

),(),(ln

),( 221

2

2

z

xgzP

z

dz

d

xdg

x

gg

Cs N

gg xxP

2ln41

~

BFKL ------

from Gavin Salam - Paris2004

As

gg CxP 22

)(~

2

LO DGLAP ---

at low x

Next to leading logs NLLx -----

from Gavin Salam - Paris 2004

Ciafalloni, Colferai, Salam, Stasto

Similar results byAltarelli, BallForte, Thorn

)())(,())((3

2 222

bTrxxgrD s Density profile

2exp

22 r

DS

grows with diminishing x and r

approaches a constant value Saturated State - Color Glass Condensate

multiple scattering

S – Matrix => interaction probability Saturated state = high interaction probability S2 => 0

rS - dipole size for which proton consists of one int. length

12 eS

Saturation scale = Density profile at the saturation radius rS 22 2

SS r

Q 2SQ

S = 0.15

S = 0.25

Saturated state is partially perturbative

cross-sectiom exhibits the universal rate of growth

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

RHIC

HERASRHICS QQ )()( 22

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-gluon interaction effects at HERA Open problems: valence-like gluon density? absorptive corrections low-x QCD-evolution HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one

HERA+NMC data => Saturation effects are considerably increased in nuclei

Diffractive Scattering

Non-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 multiplicity per unit of rapidity

Diffractive Signature

dN/ dM 2X ~ 1/ M 2

X => dN/dlog M 2

X ~ const note : Y ~ log(W2 / M 2

X)

Non-diff

diff

fm 10001011

qq

xmE p

Slow Proton Frame

Transverse size of the quark-antiquark cloud

is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV)

Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state , J/ or X = two quarks

incoming virtual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons

0)t,(WImAW

1σ 2

el2γptot )Q(x, F

Q

α π4 )Q(W,σ 2

2 2em

22Pγ

tot

*

Rise of ptot with W is a measure of radiation intensity