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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
)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
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
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
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
