Smallx and Diffraction at HERA and LHC Henri Kowalski DESY EDS Chteau de Blois 2005

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Small-x and Diffraction at HERA and
LHCHenri KowalskiDESY EDS Château de
Blois 2005
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HERA ep Collider
ZEUS
H1
e 27 GeV
p 920 GeV
Liquid Argon Calorimeter
Uranium-Scintillator Calorimeter
Q2 - virtuality of the incoming photon W -
CMS energy of the incoming photon-proton system
x - Fraction of the proton momentum
carried by the struck quark x
Q2/W2
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y inelasticity Q2 sxy
Infinite momentum frame Proton looks like a
cloud of non-interacting quarks and gluons
F2 measures parton density in the proton at a
scale Q2
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Gluon density
Gluon density dominates F2 for x lt 0.01
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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
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Dipole description of
DIS equivalent to Parton Picture in perturbative
region
erltlt1 Q21/r2
Optical T
Mueller, Nikolaev, Zakharov
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
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Comparison with Data
FS model with/without saturation and IIM CGC
model hep-ph/0411337.
Fit F2 and predict xIPF2D(3)
FS(nosat)
F2
CGC
FS(sat)
F2
x
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Diffractive contribution of the total cross
section

• For larger MX, sdiff has the similar W and Q2
  dependences as stot.
• For the highest W bin (200ltWlt245 GeV),
• sdiff (0.28ltMXlt35 GeV, MNlt2.3 GeV) /stot

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Kowalski Teaney
Impact Parameter Dipole Saturation Model
Proton
b impact parameter
Glauber-Mueller, Levin, Capella, Kaidalov
T(b) - proton shape
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Total gp cross-section
universal rate of rise of all hadronic
cross-sections
x lt 10-2
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Dipole cross section determined by fit to F2
Simultaneous description of many reactions
F2 C
Gluon density test? Teubner
IP-Dipole Model
gp -gt J/y p
gp -gt J/y p
IP-Dipole Model
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GBW Model
IP Dipole Model
less saturation (due to IP and charm)
strong saturation
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Saturation scale
HERA RHIC
QSRHIC QSHERA
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Saturated state is partially perturbative
gp cross-section exhibits the universal
rate of growth
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Absorptive correction to F2
Example in Dipole Model
F2
-
Diffraction
Single inclusive pure DGLAP
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2-Pomeron exchange in QCD
Final States (naïve picture)
detector
Diffraction
0-cut
DY
g
p
gp-CMS
ltngt
1-cut
g
p
gp-CMS
detector
lt2ngt
2-cut
g
p
gp-CMS
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Feynman diagrams QCD amplitudes J.
Bartels
A.
Sabio-Vera

H. K.
0-cut
1-cut
2-cut
3-cut
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AGK rules in the Dipole Model
Note AGK rules underestimate the amount of
diffraction in DIS
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HERA Result Unintegrated Gluon Density
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
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Exclusive Double Diffractive Reactions at LHC
xIP Dp/p, pT xIP 0.2-1.5
xIP Dp/p, pT xIP 0.2-1.5
1 event/sec
low x QCD reactions pp gt pp gJet gJet s
1 nb for ET gt 20 GeV , M(jj) 50 GeV


s 0.5 pb for ET gt 60 GeV , M(jj) 200 GeV

hJET lt 2 KMR Eur. Phys J.
C23, p 311


sDiff hard X-section Gluon Luminosity
factorization !!!
gg JetJet gg Higgs
pp gt pp Higgs s O(3) fb
SM O(100) fb MSSM
fg unintegrated gluon densities
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t distributions at HERA
t distributions at LHC with the
cross-sections of the O(1) nb and L 1 nb-1
s-1 gt 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
Non-Saturated gluons
t-distribution of hard processes should 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
Saturated gluons
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Survival Probability S2

Soft Elastic Opacity
t distributions at LHC Effects of soft
proton absorption modulate the hard t
distributions
Khoze Martin Ryskin
Dipole form double eikonal
t-measurement will allow to disentangle the
effects of soft absorption from hard behavior
single eikonal
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Gluon Luminosity
F2
Exclusive Double Diffraction
Dipole Model
L. Motyka, HK preliminary
QT2 (GeV2)
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Conclusions We are developing a very good
understanding of inclusive and diffractive gp
interactions F2 , F2D(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 gt investigations of properties of the
gluon cloud in the new region Gluon Cloud is
a fundamental QCD object - SOLVE QCD!!!!
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The behavior of the rise with Q2
universal rate of rise of all hadronic
cross-sections
Smaller dipoles ? steeper rise Large spread of
leff characteristic for IP Dipole Models
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GBW Model
KT-IP Dipole Model
less saturation (due to charm)
strong saturation
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Unintegrated Gluon Densities
Dipole Model
Exclusive Double Diffraction
Note xg(x,.) and Pgg drive the rise of F2 at
HERA and Gluon Luminosity decrease at LHC
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Saturation Model Predictions for
Diffraction
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Absorptive correction to F2
Example in Dipole Model
F2
-
Diffraction
Single inclusive pure DGLAP
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Fit to diffractive data using MRST Structure
Functions A. Martin M. Ryskin
G. Watt
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A. Martin M. Ryskin G. Watt
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AGK Rules
QCD Pomeron
The cross-section for k-cut pomerons Abramovski,
Gribov, KancheliSov. ,J., Nucl. Phys. 18, p308
(1974)
1-cut
F (m) amplitude for the exchange of
m Pomerons
1-cut
2-cut
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2-Pomeron exchange in QCD
Final States (naïve picture)
detector
Diffraction
0-cut
DY
g
p
gp-CMS
ltngt
1-cut
g
p
gp-CMS
detector
lt2ngt
2-cut
g
p
gp-CMS
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Feynman diagrams QCD amplitudes J.
Bartels
A.
Sabio-Vera

H. K.
0-cut
1-cut
2-cut
3-cut
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Probability of k-cut in HERA data
Dipole Model
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Problem of DGLAP QCD fits to F2
CTEQ, MRST, ., IP-Dipole Model
at small x
valence like gluon structure function ?
Remedy Absorptive corrections? MRW

Different evolution? BFKL,

CCSS, ABFT
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from Gavin Salam - Paris2004
at low x
LO DGLAP ---
BFKL ------
Next to leading logs NLLx -----
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Ciafalloni, Colferai, Salam, Stasto
Similar results by Altarelli, Ball Forte,
Thorn
from Gavin Salam - Paris 2004
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Density profile
grows with diminishing x and r
approaches a constant value
Saturated State - Color Glass Condensate
S Matrix gt interaction probability
Saturated state high interaction probability
S2 gt 0
multiple scattering
rS - dipole size for which proton consists of
one int. length
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Saturation scale Density profile at the
saturation radius rS
lS 0.25
lS 0.15
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Saturated state is partially perturbative
cross-sectiom exhibits the universal rate of
growth
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RHIC
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Conclusions We are developing a very good
understanding of inclusive and diffractive gp
interactions F2 ,
F2D(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
HERANMC data gt Saturation effects are
considerably increased in
nuclei
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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
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Diffractive Signature
diff
Non- diff
Non-Diffraction
Diffraction
- Rapidity
uniform, uncorrelated particle emission along
the rapidity axis gt probability to see a gap
DY is exp(-ltngtDY) ltngt - average multiplicity
per unit of rapidity

dN/ dM 2X 1/ M 2X gt dN/dlog M 2X const
note DY log(W2 / M 2X)

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Slow Proton Frame
incoming virtual photon fluctuates into a
quark-antiquark pair which in turn emits a
cascade-like cloud of gluons
Transverse size of the quark-antiquark cloud is
determined by r 1/Q 2 10-14cm/ Q (GeV)
Rise of sgptot with W is a measure of
radiation intensity
Diffraction is similar to the
elastic scattering replace the outgoing
photon by the diffractive final state
r , J/Y or X two quarks