The Structure of the Pomeron

I. Y. Pomeranchuk

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.

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

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/

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

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

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

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)

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

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

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

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

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

• 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

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

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!

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

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!

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

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?

• 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

22Diffractive Parton Distributions (best set)

CombindedQCD analysisof F2

D and2-jet X-crosssectionsassumingfactorisation

z =

can we usethem?

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

Central diffractive particle production at pp Colliders

Central Higgs production at LHC? Test at Tevatron: central 2-jet

CDF

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

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

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

the dipole –p cross section: the saturation model

r~2/QR0(x)

qq

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!

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

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 ?

Free parameters (few) are determined by a fitof the predictions to F2(x,Q2)Diffractive distributionsare predicted.

description of F2D

is ‘acceptable’

• 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

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