The Structure of the Pomeron

1
The Structure of the Pomeron
I. Y. Pomeranchuk ( 1913 -1966 )
2
SM
Quantumchromodynamics 8 gluons
Electroweak g, Z0, W, W-
Precision measurements and test of
higher order corrections Excellent experimental
confirmation
Main assumptions experimentally verified
Predictions so far are limited QCD is too
complicated for our present theoretical and
mathematical methods --gt limited areas of
application Very much work is spendt to
enlarge the areas where QCD can be applied.
3
Elements of QCD
All particles with color charge
participate Quarks
Antiquarks
Gluons
Gluons carry color charge. They interact with
each other This is all the difference to QED!!
Experimental Status

• Gluons exist and carry spin 1
• Gluons carry color charge tripel gluon
  vertex exists
• There are 8 gluons (the gauge group is
  SU(3)C)

4
Color dipoles

• no free quarks and gluons
• at large distances color string

r 1/m
V(r)
kr
as
rfm
1
0.4
1/r
m2 GeV2
1 10 100
Perturbation theory works only for small
distances, large scales (gt1 GeV2)
5
Protons and Predictions of QCD
6
Experimental facts of p-p scattering at high
energies We observe a rather simple and
universal picture!
1. total cross sections rise at high energy
with sEcm2 stot a s-a b sl
stot

• l 0.0808
• determines the rise at
• high energy

Ecm GeV
1. Proton has diffuse edge (Gauß profile) 2. it
becomes larger with s 3. it is grey!
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The Pomeron
high energy scattering is dominated by the
exchange of particles Regge trajectories
hadons and their rotational exitations
stot s a(0)-1 s-0.45 for
Reggeon

describes fall of X-section at low energies ECM lt
20 GeV
ds/dt s 2a (t) 1
trajectory
a (t) a (0) a t
J
8
The best experimental surrounding to study
these questions are not offered by the Tevatron
(as might be expected) but by the
Electron-Proton Storage Ring HERA (DESY)
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30 GeV 820 (920) GeV
HERA e
p
vs 320 GeV
Start of construction 1984 Data taking start
1992 end 30.06.2007 ca. 800 physicists at
both e-p experiments
construction cost HERA 1.2 billion DM 2
experiments 200 MDM
p
e
H1
ZEUS
DESY
in HH.
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Deep Inelastic e-p Scattering Measurement of
Parton Structure
Evidence for Scattering from pointlike partoncs (
colored quarks)

• Electron is scattered by large
• angle 1/sin4(?/2)

Spectators color string

• Jets in final state

e

• Hadrons in proton direction a
• colored parton was scattered and
• left the proton

p
e
color string
Scattering event at HERA (H1)
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e
e
Q2
g
x pp
p
Hard scattering process th 1/Q ltlt 1 fm
F2 Sei2xqi(x)qi(x)
fragmentation tF gt 1 fm
Snapshot of Parton Distribution with time
resolution of 1/Q ltlt 1 fm
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Q2-Evolution of Strukturfunktionen

• Electrons scatter only from Quarks
• F2 changes with Q2, because resolution improves
  the rise of F2 at small x depends on the gluon
  density

F2ep(x,Q2) Sef2 x qf(x,Q2)qf(x,Q2)
dominant

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Quark und Gluon Densities in the Proton
F2(x) x l at small x
huge
Gluon- Momentum distribution x lg
x
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Universality of Parton distributions
a triumph of QCD ? LHC

• QCD universality the parton densities are
  valid for all hard scattering processes,
• (after corrections for higher order effects in
  aS)
• Example 2 -Jet cross section in pp collisions
  is predicted!

Tevatron
x0.3
x0.03
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Hadron-Hadron Scattering at HERA?
Infinite momentum frame
e
Q2
x
p
x Q2/ys (momentum fraction
of parton)
Electrons as probes for quark Structure -- parton
densities, scaling violations ..
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the g p cross section at high energies
Another look at deep inelastic scattering proton
rest system
l0.08
l0.35
W2
low x

• gp(W2) F2(W2,Q2)/Q2 W2l

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DIS
gap
e
Large Q2
p
Events first seen by ZEUS
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Electron Scattering from the Pomeron

• we measure the diffractive structure function
  F2D(b, Q2, xP)
• in inclusive scattering Quark structure of the
  Pomeron

Experimental Facts 1. F2D(b, Q2, xP)
xP-2a(t)-1F2D(b,Q2) Pomeron flux Quark
distribution of Pomeron 2. a(0) 1.16.03
1.08 ! (not soft

Pomeron) 2. We scatter from pointlike partons
- scaling - Jets
e
q
b
xP
Rapidity gap
Resolved Pomeron Model -The wave function of
the Protons contains a Pomeron
component. -The electron scatters from the
quarks in the Pomeron. -The Pomeron flux
factor is not described by the soft Pomeron!
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Diffractive Parton Distributions

• approximate scaling

F2D(b,Q2)
b
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Direct Measurement of the Pomeron Gluon
Distribution
2-Jet events measure gluons in the Pomeron!
Factorisation? Are diffractive parton
distributions universal for all diffractive
processes? Do we get the same gluon distribution?
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222-Jet cross section in diffractive DIS

• 2-Jet cross section shows same
• Pomeron flux with a(0)1.2 and
• agrees with resoved Pomeron
• model.
• Gluon density is in agreement with
• F2D but only with Fit B? 2-jets
• discriminate between solutions
• Pomeron is dominated by gluons
• qqg fluctuationen in the Photon
• dominate

ß
QCD factorisation is valid for Diffractive Deep
Inelastic Scattering this is required by QCD -gt
Collins
ß
NLO QCD prediciton based on factorisation
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22Diffractive Parton Distributions (best set)
Combinded QCD analysis of F2D and 2-jet
X-cross sections assuming factorisation
z b
can we use them?
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Diffractive Parton Densities in p-p Collisions
(Tevatron)
p
Predicted cross section using diffractive
parton Densities from HERA
gap ?
Faktor 10
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Central diffractive particle production at pp
Colliders
Central Higgs production at LHC?
Test at Tevatron central 2-jet
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Main experimental results

• Pomeron is (dominantly) a gluon state
• rise of ?p cross section is not universal but
  depends on Q2
• The diffractive gluon density is universal for
  DIS
• It cannot be applied directly to Hadron-Hadron
  scattering

These facts must be reproduced by any theoretical
description!
Next Theoretical models which try to describe
more aspects of diffractive
scattering - flux factors -
parton densities resp. s ?p
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Phenomenological description of total X-sections
by Pomeron trajectory
Could Pomeron be a Regge trajectory which is
exchanged in diffractiven processes? The bound
states on this trajectory could be
glueballs! Model of Donnachie und Landshoff
soft Pomeron aS(t) 1.008 0.25 t

E xperiment intercept a(0) of the trajectory
changes with Q2 resp.
the size of the hadrons.
There can be no universal
Pomeron trajectory!
glueball candidates J2
Soft Pomeron
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from hard to soft physics do we see saturation?

• We measure high energy scattering
• of a color dipole with the proton
• We can choose the transverse size
• of the dipole via Q2

r1/Q
s ?p (x,Q2) F2(x,Q2)/Q2

• The only unknown in
• principle is the dipole-p cross section which
  depends on
• x 1/t
• the transverse size of the
• dipole
• the distribution profile of
• the gluons in the proton
• can it be calculated?

F2
dipole WF in the photon (calc.)
dipole-p cross- section
sT,Ldiffr
B
diffraction (F2D)
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the dipole p cross section the saturation model
r2 (perturbative)
saturation
?qq
simplest version Golec-Biernat , Wüsthoff 99
R0(x) (x/x0)? 1 GeV2 improvements Bartels,
Kowalski
?
R0(x) (1/x)? average gluon distance at
which saturation sets in. Depends also on
transverse gluon profile T(b).
proton
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successes of dipole saturation model
1. describes F2 at small x and moderate
Q2 2. predicts geometric scaling of F2 at
small x F2(x,Q2) F2 ( Q2 R02(x) ) eqiv.
s?p s?p (Q2R02(x) )
3. predicts the ratio DIS diffractive/ DIS
constant vs. energy ? this was one of the
simple messages of the data which are not
easily explained 4. detailed predictions
concerning diffractive processes (needs
more theoretical work)
t Q2 R02(x)
This is of course no proof of saturation but
several disconnected effects are successfully
predicted ? very appealing though not compelling
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soft color interaction ,calculation
of dipole cross section in
semiclassical model
The qq color dipole is scattered from the color
field of the Proton and is neutralized
statistically.
How does the gluon field look like in the proton
?
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Free parameters (few) are determined by a fit of
the predictions to F2(x,Q2) ? Diffractive
distributions are predicted.
description of F2D is acceptable
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Diffractive 2-Jet events
Models with color neutralisation by soft gluons
(non pertubative)
Color dipole models 2gluon-exchange and
saturation
2gluon Res. Pomeron saturation

• Models exhibit approximate
• factorisation of Pomeron flux
• Normalisation off by factors 2
• BUT only leading order
• (no progress recently)

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how does the proton look like at high energy?
edge area increases due to the evolution of soft
gluons which become visible (active) at high
energy
S Ecm2
proton gets blacker and inceases its size with
increasing CM energy
Profile function
HERA energy
black
LHC
example model of Pirner, Shoshi, Steffen 2002