Exclusive Diffraction at HERA

Henri KowalskiDESY

Ringberg

October 2005

0)t,(WImAW

1σ 2

el2γptot

2

22Pγ

totem

2

22

2 W

Qx)Q(W,σ

α π4

Q)Q(x,F

*

F2 is dominated by single ladder exchange

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

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

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 produce exponentially suppressed rap. gaps)

Diffractive Structure Function Dipole Model

Study of exclusive diffractive states may clarify which pattern is right Only few final states present in DiMo: qq, qqg (aligned and as jets) VM

______________ Initial Diff. SF Q2

0 ~ 4 GeV2

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 the perturbative region

),(ˆ 2*1

0

2*

rxdzrd qqp

tot

),(16

1| 22*

1

0

20

*

rxdzrddt

dqqt

pdiff

Mueller, Nikolaev, Zakharov

r Q2~1/r2

Optical T

momentum space

configuration space

dipole preserves its size during interaction.

2222*1

0

20 |),,(),(),,(|

16

1|

*

rzQrxrzQdzrddt

dqqVMt

pVM

qq ~ r2xg(x,) for small r

Iancu, Itakura, Munier - BFKL-CGC motivated ansatz

Forshaw and Shaw - Regge ansatz with saturation

Dipole description of DIS

)))/,(3

exp(1(),( 20

222

0

2

0 rCxxgrrx sqq

GBW – first Dipole Saturation Mode (rudimentary evolution) Golec-Biernat, Wuesthoff

BGBK – DSM with DGLAP Bartels, Golec-Biernat, Kowalski

GBW

x

x

GeVR

R

rrxqq

02

202

0

2

0

1 ));exp(1(),(

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

22222

2*1

0

22 |),,())(),(32

exp(1),,(|16

1*

rzQbTxxgrrzQdzebdrddt

dsVM

bip

VM

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

r

C

g

g

from fit to tot predict diff

GBW, BGBK …

Ratio of tot to diff

diff is not a square of tot !

Diffractive production of a qq pair_

~ probability to find a Pomeron(2g) in p

~ probability for a Pomeron(2g) to couple to a quark

spin 1/2 spin 1

~ s => dN/dlog M2X ~ const

Diffractive production of a qqg state

Inclusive Diffraction LPS

— BGBK Dipole

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)

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

WVM ~

WVM ~

Exclusive production

22222

2*1

0

22 |),,())(),(32

exp(1),,(|16

1*

rzQbTxxgrrzQdzebdrddt

dsVM

bip

VM

)exp(~ tBdt

dD

diff

))1(( rzbibi ee

Modification by Bartels, Golec-Biernat, Peters, (first proposed byNikolaev, Zakharov)

H. Kowalski, L. Motyka, G. Watt preliminary

Diffractive Di-jets Q2 > 5 GeV2

-RapGap

Satrap

Diffractive Di-jets Q2 > 5 GeV2

Diffractive Di-jets Q2 > 5 GeV2

Dijet cross section factor 3-10 lower than expected using HERA Diffractive Structure Functions

suppression due to secondary interactions ?

Diffractive Di-jets at the Tevatron

H1 and ZEUS:NLO overestimates data by factor 1.6.

Kaidalov et al.: resolved part needs to be rescaled by 0.34

scaled by factor 0.34

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

ZEUS-LPS

H1 VFPS at HERA

Conclusions

Inclusive diffraction, exclusive diffractive VM and jet production can be successfully derived from the measured F2

(Dipole Model with u. gluon densities obtained from F2 ) Detailed VM-data from HERA should allow to pin down VM wave functions

Diffractive Structure Function analysis describes well the inclusive diffractive processes and the exclusive diffractive jet production although it has some tendency to amplify small differences of the input distributions

Exclusive diffractive processes give detailed insight into DIS dynamics

                                 

 

Press Release: The 2005 Nobel Prize in Physics4 October 2005The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2005 with one half toRoy J. GlauberHarvard University, Cambridge, MA, USA"for his contribution to the quantum theory of optical coherence"

Glauber wrote his formula for heavy nuclei and for deuteron. He was the first who realized that his formula in the case of deuteron describes both the elastic cross section and the diffractive dissociation of the deuteron. Genya Levin

Roy Glauber's recent research has dealt with problems in a number

of areas of quantum optics, a field which, broadly speaking, studies the quantum electrodynamical interactions of light and

matter. He is also continuing work on several topics in high- energy collision theory, including the analysis of hadron collisions, and the

statistical correlation of particles produced in high-energy reactions.

Specific topics of his current research include: the quantum mechanical behavior of trapped wave packets; interactions of light with trapped ions; atom counting-the statistical properties of free

atom beams and their measurement; algebraic methods for dealing with fermion statistics; coherence and correlations of bosonic

atoms near the Bose-Einstein condensation; the theory of continuously monitored photon counting-and its reaction on

quantum sources; the fundamental nature of “quantum jumps”; resonant transport of particles produced multiply in high-energy

collisions; the multiple diffraction model of proton-proton and proton-antiproton scattering

Roy Glauber’s Harvard Webpage

Saturation and Absorptive corrections

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

bd

d Example in Dipole Model

F2 ~ - Single inclusive linear QCD evolution

Diffraction

High density limit —> Color Glass Condensate McLerran

coherent gluon state Venogopulan

2-Pomeron exchange in QCD

Final States(naïve picture)

0-cut

1-cut

2-cut

Diffraction

<n>

<2n>

QCD diagrams

)2

exp(12 2bd

d qq)exp(

!2

kbd

d kk

)(),()( 2222

bTxxgrN s

C

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

)]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 (a measure of gluon density)

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

)(20

2 xRQ

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

02

20

1)(

x

x

GeVxR

Geometrical Scaling can be derived from traveling wave solutions of non-linear QCD evolution equations

Velocity of the wave front gives the energy dependence of the saturation scale Munier, Peschanski L. McLerran +… Al Mueller + ..

Question: Is GS an intrinsic (GBW) or effective (KT) property of HERA data?

Dipole X-section

—— BGBK---- GBW

2-Pomeron exchange in QCD

Final States(naïve picture)

0-cut

1-cut

2-cut

Diffraction

<n>

<2n>

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

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%

OSMy

LM

LDiff

22

2

ˆ

2

214

2

2),(),(

)1(

tgtgt

t

c

exclusive QxfQxfQ

dQ

bNO

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

OSMy

LM

LDiff

22

2

ˆ

fg – unintegrated gluon

densities

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!!!!

J. Ellis, HERA-LHC Workshop

Higher symmetries (e.g. Supersymmetry) lead to existence of several scalar, neutral, Higgs states, H, h, A . . . . Higgs Hunter Guide, Gunnion, Haber, Kane, Dawson 1990

In MSSM Higgs x-section are likely to be much enhanced as compared to Standard Model (tan large because MHiggs > 115 GeV) CP violation is highly probable in MSSM all three neutral Higgs bosons have similar masses ~120 GeV can ONLY be RESOLVED in DIFFRACTION Ellis, Lee, Pilaftisis Phys Rev D, 70, 075010, (2004) , hep-ph/0502251

Correlation between transverse momenta of the tagged protons give a handle on the CP-violation in the Higgs sector Khoze, Martin, Ryskin, hep-ph 040178

Precise measurementof the Higgs Mass

Gluon density

Gluon density dominates F2 for x < 0.01

))((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