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The Structure of the Pomeron
I. Y. Pomeranchuk
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Electroweak
Z0, W+, W-
Quantumchromodynamics
8 gluons
Precision measurements and test of higher order correctionsExcellent experimental confirmation
Main assumptions experimentallyverified Predictions so far are limited: QCD is too complicated for our present theoretical and mathematical methods --> limited areas of application Very much work is spendt to enlarge the areas where QCD can be applied.
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Elements of QCD
All particles with color charge participate:
Quarks Antiquarks Gluons
Gluons carry color charge. They interact with each otherThis 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)
s s s
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coupling small for short distances(large scales) ‚hard processes‘
coupling rises stronglyfor large distances (≥ . 2 fm) ‚soft processes‘
Perturbation theory works only for small distances, large scales (>1 GeV2)
~1/r
k*rV(r)
r[fm]1
GeV1 10 100
s
• no free quarks and gluons• at large distances color string
fragmentation
Color dipoles
p
r ~ 1/
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Protons and Predictions of QCD
1. bound state: proton is complicated state of three valence quarks, bound by gluon field (99.9% of mass!). QCD description: lattice theory
p
p
3. p-p scattering at high energies:total X-section and elastic scatteringtot ~ Im [ Ael (t=0)]
Very active new working area! None ofthe established methods works!
2. Parton-Parton scattering ‚hard processes with large scale‘: production of W‘s,Z0,Top, Jets
Successful description by perturbative QCD: S << 1
p p
needs parton distributions
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Experimental facts of p-p scattering at high energiesWe observe a rather simple and universal picture!
Ecm [GeV]
tot
1. total cross sections rise at high energy withs=Ecm
2
tot = a s- + b s
1. Proton has diffuse edge (Gauß profile) 2. it becomes larger with s 3. it is grey!
= 0.0808 determines the rise at high energy
d/dt
t[GeV2]
2. differential X-sectionshows ‘diffraction’picture
d/dt ~ s2 e-btECM
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The Pomeron
high energy scattering is dominated by the exchange of ‚particles‘: ‚Regge trajectories = hadons and their rotational exitations‘
tot s [(0)-1] = s-0.45 for ´Reggeon´
(t) = (0) + ´ t trajectory
d/dt ~ s 2[(t) –1] describes fall of X-sectionat low energiesECM < 20 GeV
p
p X
frajectory
(Reggeon)
X
J
No exhange particle is known for sure which could explain the rise of p-p scattering at high energy! It would carry the quantum numbers of the vacuum P=C = +1 and is colorless!
artificial name : POMERON
QCD: ´Pomeron´ must be composed of qq or gluon-gluon states!
PomeronC=P=+1
p
p
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The best experimental surrounding to study these questionsare not offered by the Tevatron (as might be expected) butby the
Electron-Proton Storage Ring HERA (DESY)
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HERA e p30 GeV 820 (920) GeV
H1
ZEUS
Start of construction 1984Data taking: start 1992 end 30.06.2007ca. 800 physicists at both e-p experiments
construction cost HERA~ 1.2 billion DM2 experiments ~200 MDM
ep
√s =320 GeV
in HH….
DESY
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Deep Inelastic e-p Scattering: Measurement of Parton Structure
pe
e
Spectatorscolor string
Scattering event at HERA (H1)
Evidence for Scattering from pointlikepartoncs ( colored quarks)
• Electron is scattered by large angle ~1/sin4(θ/2
•‚Jets‘ in final state
•Hadrons in proton direction: a colored parton was scattered and left the proton
color string
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Snapshot of Parton Distributionwith time resolution of ~1/Q << 1 fmSnapshot of Parton Distributionwith time resolution of ~1/Q << 1 fm
p
e e
Hard scattering processth ~ 1/Q << 1 fm
fragmentationtF > 1 fm
F2 = Σei2x[qi(x)+qi(x)]
Q2
x pp
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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) = ef
2 x[ qf(x,Q2)+qf(x,Q2) ]
dominant
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Quark und Gluon Densities in the Proton
• Gluon density is determined from the observed scaling violations or directly from 2-jet cross sections
gluon
• Quark densities are directly measured: 50% of proton momentum!
x
Gluon-Momentumdistribution
~ x –g
F2(x) ~
x –
at small x
huge
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• QCD universality: the parton densities are valid for all hard scattering processes, (after corrections for higher order effects in S)
Example: 2 -Jet cross section in pp collisions is predicted!
Universality of Parton distributions: a triumph of QCD LHC
x~0.03 x~0.3
Tevatron
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Hadron-Hadron Scattering at HERA?
Infinite momentum frame
Q2
xp
e
x= Q2/y*s (momentum fraction of parton)
Electrons as probes for quarkStructure-- parton densities, scaling violations ..
Q2 steers the transition from hard collisions( perturbative QCD) to soft hadron physics.We can ‘engineer’ our hadron!
F2(x, Q2) = F2 (W2 , Q2) ≈ 4π2 Q2 * σ*p (W2,Q2)
Proton rest frame
rT~2/Q( size of dipole)
rT
L ~ 1/x
~ 50 fm!~ 1 .01 fm
At low x a color dipole of variable size 2/Q interacts with the proton at high CM energys=W2(p) ≈ Q2/x ≈ 1000 ÷ 90000 GeV2
Low x = high energy scattering!
*p
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the * p cross section at high energies
Another look at deep inelastic scattering: proton rest system
p(W2)~ F2(W2,Q2)/Q2 ~ W2
=0.08
=0.35
W2
low xsoft Pomeron (p-p) intercept
slope depends on Q ~ 1/r: there can be no universal Pomeron!
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diffractive scattering 1. elastically scattered Proton! (would be best )
2. no ‚forward energy‘ (rapidity gap event ) ca. 10% of all events
xP
q
Rapidity gap
DIS
gap
p
Large Q
e
Events first seen by ZEUS
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Electron Scattering from the Pomeron
• we measure the diffractive structure function F2D(, Q2, xP)
in inclusive scattering: Quark structure of the Pomeron
e
xP
q
Rapidity gap
Experimental Facts: 1. F2
D(, Q2, xP) = xP-2[(t)-1]*F2
D(Q2)Pomeron flux * Quark distribution of Pomeron 2. = 1.16±.03 = 1.08 ! (not soft Pomeron)2. We scatter from pointlike partons - scaling - Jets
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
F2DQ2)
QCD analysis of scaling violations:
• The Pomeron is dominated bydominated by Gluons Gluons (~75 % of Pomeron momentum )
• Gluons have high average momenta but badly known at high
• Quark distribution is directly measured
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Direct Measurement of the Pomeron Gluon Distribution
-jet
-jet
2-Jetevents measuregluons in the Pomeron!
Factorisation? Are diffractive parton distributions universal for all diffractive processes? Do we get the same gluon distribution?
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• 2-Jet cross section shows same Pomeron flux with (0)=1.2 and agrees with resoved Pomeron model.
• Gluon density is in agreement with F2
D but only with Fit B 2-jets discriminate between solutions
• Pomeron is dominated by gluons
• qqg fluctuationen in the Photon dominate
QCD factorisation is valid forDiffractive Deep Inelastic Scatteringthis is required by QCD -> Collins
222-Jet cross section in diffractive DIS
NLO QCD prediciton based on factorisation
ß
ß
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22Diffractive Parton Distributions (best set)
CombindedQCD analysisof F2
D and2-jet X-crosssectionsassumingfactorisation
z =
can we usethem?
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Diffractive Parton Densities in p-p Collisions (Tevatron)
p p
p p
jet
jet
Faktor 10
gap
Predicted cross sectionusing diffractive partonDensities from HERA
Diffractive X-sections in pp
do not factorise! ???????
Diffractive processes in hadron reactions are more difficult to describe.What destroys factorisation? study HERA p (controversial..)
Several models on the market to explain this fact:
•Multiple interactions including ‚spectator partons destroy the rapidity gapor• color neutralisation by soft gluons depends on parton final state and CM energy
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Central diffractive particle production at pp Colliders
Central Higgs production at LHC? Test at Tevatron: central 2-jet
CDF
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Main experimental results
1. ‚Pomeron‘ is (dominantly) a gluon state
• rise of γ*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. σ γ*p
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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: S(t) = 1.008 + 0.25 * t
Phenomenological description of total X-sections by Pomeron trajectory
glueball candidates J=2
Soft Pomeron
E xperiment: intercept (0) of the ‚trajectory‘ changes with Q2 resp. the size of the hadrons. There can be no universal Pomeron trajectory!
Model describes datarather well and is economic!
hard Pomeron: H(t) = 1.44 + 0.10 * t p(W2,Q2) at high Q2
(98): Use 2 Pomeron trajectories
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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
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?
r~1/Q
dipole-p cross-section
dipole WF inthe photon (calc.)
diffraction (F2D)
F2
σ *p (x,Q2)~ F2(x,Q2)/Q2
σT,Ldiffr
B
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the dipole –p cross section: the saturation model
r~2/QR0(x)
perturbative QCD predicitionfor small dipole sizes ~r2
R0(x) ~ (1/x)λ: average gluon distance at which saturation sets in. Depends also on transverse gluon profile T(b).
~r2 (perturbative) saturation
simplest version: Golec-Biernat ,
Wüsthoff 99 : R0(x)= (x/x0)λ * 1 GeV2
improvements: + Bartels, Kowalski
proton
Ψ
diffractive Ψproductiondescribable by2-gluon exchange(LO only so far)
Ψ
confront to data: Fits to F2 at x<10 -2
to determine free parameters: x0 = 3 10-4, λ= 0.15 ,
describes transition to soft physics!
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successes of dipole saturation model
τ = Q2* R02(x)
1. describes F2 at small x and moderate Q2
2. predicts ‘geometric scaling’ of F2
at small x F2(x,Q2) = F2 ( Q2* R0
2(x) ) eqiv.
σ*p = σ*p (Q2*R02(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)
This is of course no proof of saturation but several disconnectedeffects 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 scatteredfrom the color field of theProton and is neutralized statistically.
How does the gluon field look likein the proton ?
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Free parameters (few) are determined by a fitof the predictions to F2(x,Q2)Diffractive distributionsare predicted.
description of F2D
is ‘acceptable’
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• Models exhibit approximatefactorisation of Pomeron flux Normalisation off by factors 2
BUT: only leading order(no progress recently)
Diffractive 2-Jet events
Models with color neutralisation by soft gluons (non pertubative)
Color dipole models: 2gluon-exchange and ‚saturation‘
2gluon
Res. Pomeron
saturation
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S= Ecm2 edge area increases due to the evolution
of soft gluons which becomevisible (active) at high energy
proton gets blacker and inceases its size with increasing CM energy
b_‚ black‘
example:model of Pirner, Shoshi, Steffen ‚2002
HERA energy
how does the proton look like at high energy?
Profile function
LHC
could be consolidated much betterby HERA measurements and their theoretical interpretation