Smallx and Diffraction in DIS at HERA II Henri Kowalski DESY 12 th CTEQ Summer School Madison  Wisconsin June 2004. Dipole Saturation Models. Proton. GBW. b – impact p. BGBK. DGLAP. IIM Model with BFKL & CG evolution. KT. Glauber Mueller. T(b)  proton shape.
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Proton
GBW
b – impact p.
BGBK
DGLAP
IIM Model with BFKL & CG evolution
KT
Glauber
Mueller
T(b)  proton shape
Derivation of the GM dipole cross section
probability that a dipole at b
does not suffer an inelastic
interaction passing through
one slice of a proton
Uncorrelated scatterings
S2 probability that a dipole
does not suffer an inelastic
interaction passing through
the entire proton
GM Dipole + DGLAP mimics
full evolution
<= LandauLifschitz
Data precision is essential to the progress of understanding
GBW
GBW
GBW
Parameters fitted to HERA DIS data: c2 /N ~ 1
s0 = 23 mb l = 0.29 x0 = 0.0003
lGBW=0.29
 universal rate of rise of all
hadronic crosssections
Smaller dipoles steeper rise
Large spread of leff characteristic for
Impact Parameter Dipole Models (KT)
Analysis of data within Dipole Models
BGBK
lGBW=0.29
KT
GBW
In GBW Model change of l with Q2 is
due to saturation effects
In IP Saturation Model (KT) change
of l with Q2 is mainly due to
evolution effects
In BGBK Model change of l with Q2 is
due to saturation and evolution effects
Theory (RV): evolution leads to saturation  Balitzki Kovchegov and
JIMWLK
GBW                     
x = 106
BGBK ___________________________________
x = 102
Evolution increases gluon density =>
smaller dipoles scatter stronger,
gluons move to higher virtualities
Fourier
transform
x = 104
 numerical evaluation
x = 102
In ColorGlass gluons occupy higher
momentum states
Naïve assumption for T(b):
WoodSaxon like, homogeneous, distribution of nuclear matter
Diffractive production of a qq pair
NonDiffractionDiffraction
<=p
e =>
Select diffractive events by requirement of
no forward energy deposition
called hmaxcut
Q: what is the probability that a nondiff event
has no forward energy deposition?
MX Method
NonDiffractive Event Diffractive Event
detector
detector
log W2
log MX2
DY
Y
Y
DY
g*
g*
p
p
g*pCMS
g*pCMS
nondiff events are characterized by
uniform, uncorrelated particle emission
along the whole rapidity axis =>
probability to see a gap DY is
~ exp(lDY)
l – Gap Suppression Coefficient
diff events are characterized by
exponentially nonsuppressed
rapidity gap DY
since DY ~ log(W2/M2X) – h0
dN/dlogM 2X ~exp( l log(M 2X))
dN/ dM 2X ~ 1/ M 2X =>
dN/dlogM2X ~ const
MX Method
diff
diff
diff
Non
diff
Non
diff
Non
diff
NonDiffraction
dN/dM 2X ~exp( l log(M 2X))
Gap suppression coefficient l
independent of Q2 and W2
for Q2 > 4 GeV2
Diffraction
dN/dlog M 2X ~ const
 Generator Level CDM
 Detector Level CDM
Detector effects
cancel in
Gap Suppression !
dN/dM 2X ~exp( llog(M 2X))
In MC l independent of Q2 and W2
l~ 2 in MC
l~ 1.7 in data
Uncorrelated Particle Emission (Longitudinal Phase Space Model)
l – particle multiplicity per unit of rapidity
Feynman (~1970): l depends on the quantum numbers carried by the gap
l = 2 for the exchange of pion q.n. (a=0)
= 1 for the exchange of rho q.n. (a=1/2)
= 0 for the exchange of pomeron q.n. (a=1)
l is well measurable provided good calorimeter coverage
Physical meaning of the Gap Suppression Coefficient lexp( lDY ) = exp(llog(W2/M2X)= (W2/M2X)l
from Regge point of view ~ (W2)2(1a)
~ ModelH1 approach
A. Martin M. Ryskin G. Watt Model
BEKW
Fit to diffractive data using MRST Structure Functions Model
A. Martin M. Ryskin G. Watt
Fit to diffractive data using MRST Structure Functions Model
A. Martin M. Ryskin G. Watt
Absorptive correction to F Model2
from AGK rules
Example in Dipole Model
F2 ~

Single inclusive
pure DGLAP
Diffraction
A. Martin M. Ryskin Model
G. Watt
QCD
Pomeron
The crosssection for kcut pomerons:
Abramovski, Gribov, KancheliSov. ,J., Nucl. Phys. 18, p308 (1974)
1cut
F (m) – amplitude for the exchange of
m Pomerons
1cut
2cut
Pomeron in QCD Model
tchannel picture
Color singlet dominates over octet
in the 2gluon exchange amplitude
at high energies
3gluon exchange amplitude is suppressed
at high energies
2gluon pairs in color singlet (Pomerons)
dominate the multigluon QCD amplitudes
at high energies
2Pomeron exchange in QCD Model
Final States
(naïve picture)
detector
Diffraction
0cut
DY
g*
p
g*pCMS
<n>
1cut
g*
p
g*pCMS
detector
<2n>
2cut
g*
p
g*pCMS
Total cross section MuellerSalam (NP B475, 293)
Dipole cross section
Amplitude for the exchange of m pomerons in the dipole model
KT model
Q Model2~1/r2
exp(mq r)
All quarks Model
Charmed quark
Conclusions DIS
We are developinga very good understanding of inclusive and
diffractive g*p interactions:
F2 , F2D(3) , F2c , Vector Mesons (J/Psi)….
Observation of diffraction indicates multipomeron interaction
effects at HERA
HERA measurements suggests presence of Saturation phenomena
Saturation scale determined at HERA agrees with the RHIC one
Saturation effects in ep are considerably increased in nuclei
Thoughts after CTEQ School DIS
George Sterman: Parton Model Picture (in Infinite Momentum Frame)
is in essence probabilistic, nonQM. It is summing probabilities and
not amplitudes
F2 = f e2f x q(x,Q2)
Parton Model Picture is extremely successful, it easily carries information
from process to process, e.g. we get jet crosssections in pp from
parton densities detemined inep
Dipole Models (Proton rest Frame) are very successful carrying information
from process to process within ep. They are in essence QM, main objects
are amplitudes:
In DM Picture diffraction is a shadow of F2 . Many other multipomeron
effects should be present
Several attempts are underway to build a bridge over the gap
between
Infinite Momentum Frame and Proton Rest Frame Pictures
Jochen Bartels, Lipatov & Co:
Feynman diagrams for multipomeron processes…
Raju Venogopulan & Co,
Diffraction from Wilson loops, fluctuations from JIMWLK…
……………………………………..
p
Si tracking stations
EM Calorimeter
Hadronic
Calorimeter
Compact – fits in dipole magnet with inner radius of 80 cm.
Long  z5 m
e
Collisions of e+ (e) of 27.5 GeV with p of 920 GeV
Increase of kinematic range by over 4 order of magnitude
in x at moderate Q2 and6 order of magnitude in Q2