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Small-x 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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Small-x and Diffraction in DIS atHERAIIHenri KowalskiDESY 12thCTEQ 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


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

  • NOTE: the assumption of

  • uncorrelated scatterings is

  • not valid for BK and JIMWLK

  • equations

  • Correlations from evolution

  • IIM Dipole fit

    GM Dipole + DGLAP mimics

    full evolution

<= Landau-Lifschitz


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 cross-sections

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 = 10-6

BGBK ___________________________________

x = 10-2

Evolution increases gluon density =>

smaller dipoles scatter stronger,

gluons move to higher virtualities

Fourier

transform

x = 10-4

- numerical evaluation

x = 10-2

In Color-Glass gluons occupy higher

momentum states


A glimpse into nuclei

Naïve assumption for T(b):

Wood-Saxon like, homogeneous, distribution of nuclear matter


Smooth Gluon Cloud

Q2 (GeV2)

C 0.74 1.20 1.70

Ca 0.60 0.94 1.40


Lumpy Gluon Cloud

Q2 (GeV2)

C 0.74 1.20 1.70

Ca 0.60 0.94 1.40



_

Diffractive production of a qq pair




Non-DiffractionDiffraction

<=p

e =>

Select diffractive events by requirement of

no forward energy deposition

called hmaxcut

Q: what is the probability that a non-diff event

has no forward energy deposition?


MX Method

Non-Diffractive Event Diffractive Event

detector

detector

log W2

log MX2

DY

Y

Y

DY

g*

g*

p

p

g*p-CMS

g*p-CMS

non-diff 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 non-suppressed

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

Non-Diffraction

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


Gap suppression in non diff mc
Gap Suppression in Non-Diff MC

---- 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


Physical meaning of the gap suppression coefficient l

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 l

exp(- lDY ) = exp(-llog(W2/M2X)= (W2/M2X)-l

from Regge point of view ~ (W2)-2(1-a)



~ ModelH1 approach






Absorptive correction to F Model2

from AGK rules

  • Martin

  • M. Ryskin

  • G. Watt

Example in Dipole Model

F2 ~

-

Single inclusive

pure DGLAP

Diffraction


A. Martin M. Ryskin Model

G. Watt


Agk rules
AGK Rules Model

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


Pomeron in QCD Model

t-channel picture

Color singlet dominates over octet

in the 2-gluon exchange amplitude

at high energies

3-gluon exchange amplitude is suppressed

at high energies

2-gluon pairs in color singlet (Pomerons)

dominate the multi-gluon QCD amplitudes

at high energies


2-Pomeron exchange in QCD Model

Final States

(naïve picture)

detector

Diffraction

0-cut

DY

g*

p

g*p-CMS

<n>

1-cut

g*

p

g*p-CMS

detector

<2n>

2-cut

g*

p

g*p-CMS


0-cut Model

1-cut

2-cut

3-cut


Agk rules in the dipole model
AGK Rules in the Dipole Model Model

Total cross section Mueller-Salam (NP B475, 293)

Dipole cross section

Amplitude for the exchange of m pomerons in the dipole model

KT model


AGK rules Model

Dipole model

Diffraction from AGK rules

very simple

but not quite

right


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 multi-pomeron 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, non-QM. 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 cross-sections 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 multi-pomeron

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 multi-pomeron processes…

Raju Venogopulan & Co,

Diffraction from Wilson loops, fluctuations from JIMWLK…

……………………………………..


A new detector to study strong interaction physics
A new detector to study strong interaction physics gap

p

Si tracking stations

EM Calorimeter

Hadronic

Calorimeter

Compact – fits in dipole magnet with inner radius of 80 cm.

Long - |z|5 m

e


Forward gap

Detector

e

27

GeV

p

920

GeV


HERA Interactions gap

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


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