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 )
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
)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
Diffractive production of a qq pair_
~ probability to find a Pomeron(2g) in p
~ probability for a Pomeron(2g) to couple to a quark
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
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)
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
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
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
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
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
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
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
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
))((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
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
Absorptive correction to F2
....4/))2/exp(1(2 22
bd
d
Example in Dipole Model
F2 ~ -
Single inclusive pure DGLAP
Diffraction
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
),,()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
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
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