bernd l öhr, desy

Bernd Löhr, DESY

DIFFRACTION AT HERA

The HERA Collider and the Experiments

Luminosity and its Measurement

Kinematics of Deep-Inelastic (DIS) and Diffractive Reactions

Diffraction in High-Energy Particle Scattering

Regge Phenomenology versus pQCD

Exclusive Vectormeson Production and Deeply-Virtual Compton Scattering (DVCS)

Inclusive Diffraction and Diffractive Structure Functions

Exclusive Diffractive Reactions: Jets and Heavy Quarks

The HERA Collider

Electron - proton collisions

e p27.5 GeV 920 GeV

Bernd Löhr, DESY

This corresponds to an electron energy in a fixed-target experiment of Ee = 26952 GeV

electronsprotons

Bernd Löhr, DESY

proto

ns

electrons

protons

backward

The H1 Experiment

Tracking :

pp

p 003.0

Liquid-Argon calorimeter :

EM section :

EE

E %12

HAC section :

EE

E %50

HERA I Configuration

A rear view of

the H1 detector

Bernd Löhr, DESY

Bernd Löhr, DESY

protons

backward

The ZEUS Experiment

electrons

protons

Tracking :

T

TT

p

p

pp

T

/0014.0

0065.00058.0

Uranium-scintillator- calorimeter :

EM section :

EE

E %18

HAC section :

EE

E %35

HERA I Configuration

electrons

protons

The ZEUS detector

seen from above

Bernd Löhr, DESY

The Concept of Luminosity

Proton and electron beams are not continuous but they consist of bunches.

Typically 180 proton bunches and electron bunches collided.

Individual bunches from each beam collide

What is the probability that a given process happens ?

L N

N reaction rate ;

cross section ;L (instantaneous) luminosty

The luminosity can be calculated from HERA parameters: yx

iip

ier NNf

2

L

where: rf -beam revolution frequency ; ipeN / -number of electrons/protons in the i-th bunch

2222 ; pepe yyyxxx - transverse size of interaction region

Cross section:

dtL

N L = dtL integrated luminosity

Bernd Löhr, DESY

[cm-2s-1]

[cm-2]

Measurement of the Luminosity

Measure the rate of a process whose cross-section is well known:

Bremsstrahlungin e- collisions

orBethe-Heitler

processproton proton

Measure energy and rate of bremsstrahlung photons in specialized photon detector under very small angles w.r.t. the electron beam

bGeVEepBH 331) 1.0(

very well known cross-section

BHN dtL

epBH (universal) integrated luminosity,

for all cross-section calculations

Bernd Löhr, DESY

initial state radiation final state radiation

ZEUS interaction point

about 100m away from interaction point

photon detectore-- beam

p- beam

Optical diffractionHigh energetic elastic scattering

Generalization in high energy particle interactions :

Diffraction is the exchange of an object with vacuum quantum numbers.

elastic single dissociation

double dissociationdouble Pomeron exchange

Hypothetical object : Pomeron IP

Bernd Löhr, DESY

From Optical Diffraction to High Energy Particle Scattering

Kinematics of DIS and Diffraction

Bernd Löhr, DESY

22 2Q = -q = - k-k virtuality, size of the probe

2Qx =

2p q

2s = k+p center of mass energy squared

22 2HW = M = p+q - proton cms energy squared

x: fraction of the proton carried by the struck partonp q

y=p k

y: inelasticity, fraction of the

electron momentum carried by the virtual photon2Q = x y s

e

q = k - k’

k k’

WZ ,, 0

2t = (p-p )

xMmass of the diffractive system x

four-momentum transfersquared at the proton vertex

2 2M +Q(p-p ) q xx = = IP 2 2p q W +Q

2 2

2 2IP X

Q x Qβ = =

2(p-p ) q x M +Q

For diffractiveevents in addition2 variables

Inclusive nondiffr. DIS events :

Diffractive DIS events :

γ

momentum fraction of the protoncarried by the Pomeron

fraction of the Pomeronmomentum which enters the hard scattering

DIS- and Diffractive Events

Bernd Löhr, DESY

e k k’

WZ ,, 0

Inclusive DIS events :

Diffractive DIS events :

Considerable energy flowin the very forward direction

Large rapidity gap inforward direction

ln tan(2)

Pseudo-Rapidity

is the angle w.r.t.proton direction.

Regge Phenomenology vs. pQCD

Bernd Löhr, DESY

e e’

p P’

IP, R

X

Regge PhenomenologyPeripheral (soft) processes

IP =Pomeron trajectoryt

IP4(α (t)-1)

b(W) t

0

dσ W e

dt W

00

Wb(W) = b +4α ln

W

shrinkage

IP2(α (0)-1)

tot0

Wσ

W

From fit to hadronic data :

IPα (t) = 1.08+0.25 t

(Donnachie, Landshoff)

=Reggeon trajectory

RI

t(0)(t) IRIR

t(0)(t) IPIP Diffraction

I

δσ(w) W ; δ 0.8 0.16

Diffractive DIS in pQCD

In pQCD the simplest way to describe the exchange of vacuum quantum numbers is the exchange of a colour neutral system of two gluons.

This is realized in the colour dipole picture.

outqqdipole

in

prxQzrdzdrQx

),(),,(),( 222

**

)(

122qqMQ

r

+

higher orders

+

Bernd Löhr, DESY

The wave function of the incoming virtual photon can becalculated from QED.

The outgoing wave function might be known for some exclusiveFinal states, like e.g. vector mesons.

Exclusive Vectormeson Production I

Bernd Löhr, DESY

VDM+Regge

p P’

VM VM*

IP4(α (t)-1)

b t

0

dσ W = e

dt W

00

Wb(W) = b +4α' ln

W

δσ(W) W ; δ 0.22

Shrinkage ; 2b r

pQCD

p P’

VM*

r -12 2 2

qr = z(1-z)Q +m z

1-z

r2 small if Q2 large or MV large

2 2 2 2L s eff effσ α (Q ) |x g(x,Q )| Ryskin : 2 2 2

eff V

1Q = Q +M +|t|

4

fast rise with Wδσ(w) W ; δ 0.8 and 2b 4 GeV α' 0 no or little shrinkage

Do pQCD models describe the data ? Which variables can provide a hard scales ?

KK /J

PHP

DIS 0

0

Exclusive Vectormeson Production II

Bernd Löhr, DESY

Can the Vectormeson Mass be a Hard Scale ? I

Bernd Löhr, DESY

Photoproduction ; Q2=0

ρ, ω, φ, ψ, ψ(2s),

The w-dependence of the “light” vector-meson ( productionis described by Regge phenomenology

δ 0.22

For higher mass vector mesonsthe rise of the production cross sectionwith W gets steeper.

This indicates the onset of hard diffractive scattering

photoproduction

Can the Vectormeson Mass be a Hard Scale ? II

Bernd Löhr, DESY

Photoproduction : Q2=0

-2α' 0.3 0.4 GeV

/J

-2GeV )030.0028.0164.0(

Still some shrinkage seen in J/photoproduction but compatible with pQCD models.

50 100 200 W[GeV]

pQCD models can describe photoproductionof J/ mesons.

[GeV]

W dependence Shrinkage

W

from H1 alone

/J

/J

Can Q2 be a Hard Scale ? I

Bernd Löhr, DESY

For –productionthe W-dependence getssteeper with Q2.

-electroproduction /J

pQCD models can describeexclusive production

-electroproduction

The rise with W is essentially independentof Q2 for production/J

J/

ρ

ρ

J/Ψ

J/Ψ

.

ZEUS

/J

Can Q2 be a Hard Scale ? II

Bernd Löhr, DESY

Slopes of the t-distributions

The b-slope of -production decreases with Q2. At high Q2 it reaches the value of -production./J

The b-slope of -production is independent of Q2 . It is a hard process already at Q2 =0.

/J

ρ J/Ψ

Q2 provides a hard scale

Can |t| be a Hard Scale ? I

Bernd Löhr, DESY

Complication : at high |t|, the vector-meson production proceeds predominantly through proton-dissociative processes.e e’

p

VM

tY

Low mass MY : particles of system Y disappear undetected through the beampipe hole in the detector.

High mass MY : a fraction of the particles from system Y are detected in the calorimeter.

We have to assume vertex factorization :

γ p ρ YY

γ p ρ p

σ = f(M ,W,t)

σ

The ratio should not depend on Q2.

Within experimentaluncertainties :

vertex factorization holds .

Can |t| be a Hard Scale ? II

Bernd Löhr, DESY

pQCD models

Ivanov et al.

Bartels et al.not exponentialat high |t|,predicted bypQCD models.

γp VY -ndσ |t|

d|t|

t-dependence of p-dissociative vector-meson productioncan be described by pQCD models.

Large |t| may provide a hard scale to apply pQCD.

p J/ Y

Bernd Löhr, DESY

The Pomeron Trajectory I

e e’

p P’

IP

t

IP4(α (t)-1)

b(W) t

0

dσ W e

dt W

Measure W-dependence separately for different t-bins Pomeron trajectory

IP(t)= IP(0)+’•t

/J

1.198 + 0.115.t

DIS

1.14 + 0.04.t

photoproduction

1.096+0.125.t

photoproduction

1.081+0.158.t

Soft pomeron (DL)

1.08+.25.t

VM

The Pomeron Trajectory II

Bernd Löhr, DESY

Slope of the Pomeron trajectory at higher |t| :

IPα' depends on t

for high |t| , proton diffractive processes dominate.

In Regge language : IPα (t) is not linear in t

However :

Decay Matrix Density and Ratio of Longitudinal to Transverse Cross-Section for

Production

The is a spin 1 particles. It decays into two pions:

The angular distribution ofthe decay particles and isdescribed by a function of 3 angles: ,,cos W

In total 15 density matrix elements describe the decay angular distribution,which depend on the helicity amplitudes for spin non-flip, single spin-flip, and double spin-flip:

T00, T01, T10, T11, T1-1

S-channel helicity conservation Only non-flip amplitudes T00 and T11 are non-zero

; Notation:

*VM ,T

Bernd Löhr, DESY

Measured Decay Matrix Elements for Production I

If S-channel helicity conservation (SCHC)is valid only the following matrix elements should be different from zero:

Bernd Löhr, DESY

Measured Decay Matrix Elements for Production II

Bernd Löhr, DESY

If S-channel helicity conservation is valid only the following spin density matrix elements should be zero: r1

00 = r111 = r5

00 = r511 = 0

At very small |t| SCHC holds, as |t| grows SCHS is increasingly violated.

A pQCD based model (I.Royen and J.Cudell) is able to describe the SCHC violation.

Bernd Löhr, DESY

A virtual photon has two polarization states:

transverse: helicity 1 (normal light)longitudinal: helicity 0 (only for Q2>0)

LTtot

Ratio of longitudinal to transverse cross-section is function of the photon virtuality:

20400

20400

r1

r1R

04

00

500

r2

r

1

ee

2

sinp2

Q1

If SCHS holds

R is qualitatively described by pQDC models

Ratio of longitudinal to transverse cross-section

Bernd Löhr, DESY

Deeply Virtual Compton Scattering I

Probably cleanest test of pQCD , no hadrons in the final state.

Bethe-Heitler processes lead to the same final state

Interference between QCD and QEDgives access to DVCS-QCD amplitude :

DVCS Bethe-Heitler

Difficult to disentangle experimentally

2DVCS

*BHDVCSBH

*DVCS

2BH |A| )AAA(A |A| d

Generalized parton distributions GPD -> information on transverse distribution of partons

Interference term can be derived from asymmetries, e.g.

Beam-Spin-Asymmetry: p)e(d-p)e(dZ

skewedness

Bernd Löhr, DESY

Deeply Virtual Compton Scattering II

Q2 = 8 GeV2 : = 1.0

~ W

DVCS is a hard process

NLO-QCD calculationscan describe DVCSqualitatively,magnitude of the predictedcross-section depends onused parton-density functions

Deeply Virtual Compton Scattering III

Bernd Löhr, DESY

t-dependence of DVCS measured at several Q2 and W values

For Q2> 5 GeV2: b ~ 5 -6 GeV-2

Compatible with b values for hard production of vector mesons

2GeV 0.34 0.19 5.45 b

Summary of Exclusive Vectormeson Production

Bernd Löhr, DESY

• A high vectormeson mass provides a hard scale. Photoproduction of is described by sof Pomeron exchange, whereas J/photoproduction is a hard process, it can be described by pQCD models.

• Vectormeson production at high Q2 is a hard process, pQCD can be applied.

• The vertex factorization holds.

• Vectormeson production at high |t| is a hard process. The |t|-n dependence is in agreement with pQCD expectations.

• The Pomeron trajectory for photoproduction is compatible with the soft Pomeron trajectory : and shrinkage is observed.

• DIS and J/ trajectories are not compatible with a soft Pomeron, little shrinkage is observed.

• pQCD based models are able to describe the features of exclusive hard-production of vector mesons

08.1IP

• At high Q2 the W-dependence of the DVCS cross-section and the slope of the t-distribution are compatible with a hard production process

• DVCS described in terms of generalized parton distributions (GPD) which contain information on transverse distributions of partons in the proton.

• Recently high statistics measurements of DVCS by H1 became available for electron-proton and positron-proton scattering. It is, however, still along way before one can extract GPDs.

• Apologies to HERMES ! The HERMES experiment have measured DVCS to a larger extent, also beam-spin asymmetries. These data are typically at Q2 of 1-2 GeV2. It is not really clear whether pQCD is already applicable at these low Q2.

Summary of Deeply Virtual Compton Scattering

Bernd Löhr, DESY

Definition of Inclusive Diffraction

e e’

p

e e’

P’ p P’

no colour exchange,vacuum quantum numbers

no colour exchange,vacuum quantum numbers

Model of a resolved pomeron

Colour dipole model

Definition of inclusive diffractive scattering:

• The quantum numbers of the vacuum are exchanged between the proton and the virtual photon.• (The proton stays intact.)

Attention: different definitions of diffractive cross-sections, proton dissociative events are (partially) included or not.

Bernd Löhr, DESY

Inclusive Diffraction I

e e’

p

Diffractive/proton dissociative scattering in the parton picture :

MX

MY

Large rapidity gap

t

WxIP

ß2 2M +Qxx

IP 2 2W +Q

2

2 2IP x

x Qβ =

x M +Q

Momentum fraction of the protoncarried by the Pomeron

Momentum fraction of the Pomeroncarried by the struck quark

Two additional variables

Experimentally there are three different methods used to select diffractive events :

1. Detection of outgoing proton : includes reggeon exchange

2. Large rapidity gap : includes reggeon exchange and proton dissociation into small mass

3. MX – method : includes proton dissociation into small mass

Bernd Löhr, DESY

There is no method available to measure directly inclusive diffractive cross-sections

The Proton Detection Method

Bernd Löhr, DESY

1.) Detection of outgoing proton ( H1,ZEUS)

xL= 1-xIP

1xL

2p

L

2L

L

2T M

x

)x1(

x

p- t

Detection of the diffractive proton is the only method to measure the t-distribution

Proton-beam directionZ=96 m

Z=26 m

S1+S2+S3 : horizontal spectrometer

S4+S5+S6 : vertical spectrometer

Fraction of initial proton momentumcarried by the diffractive proton

Silicon strip detectors

The ZEUS Leading ProtonSpectrometer LPS

diffractivepeak

Advantage: no proton dissociatonDisadvantage: small acceptance possible Reggeon contributions

max minη = -ln tan(Θ /2)

No tracks or energy deposits in calorimeter for rapidities greater than max or at angles less than min.

min .

H1 LEPTO : nondiffractice MC-simulation

Requiring a rapidity gap (e.g. max<2) in the events

removes most of the nondiffractive contribution.mostly diffractive

This is equivalent to restrict measurements to low xIP .

)ln(1/x IP

max

Bernd Löhr, DESY

Advantage: large acceptance -> high statistics

Disadvantage: contains contributions from nondiffractive and proton dissociative reactions and Reggeon contributions

The Rapidity Gap Method

Rapidity

z

z

E+p1y = ln

2 E-p

Uncorrelated particle emission between incoming p-direction and scattered quark.

partdN = λ = const.

dy

Poisson distr. for y innondiffractive events

-λΔyP(0)=e

max miny -y20W =c e limit miny -y2

X 0M =c e

The MX-Method (I)

Non diffractive events

Property of a produced particle

Idealised rapidity distribution

Length of rapidity distribution is given by cms-energy

minmax2 y-y Wln

Rapidity gap as a statistical fluctuation

2Xb ln Mnondiff

2X

dN = c e

d ln M

Bernd Löhr, DESY

Bernd Löhr, DESY

The MX-Method (II)

0.025t2dMdt

σd2

< 0.1

diff2 2X X

dN 1

dM (M )n

Experimentally at high energies and not too low MX

n 1

diff2X

dN const.

d lnM

Cortousy of K.Goulianos

with

This follows also from a triple Regge model

]lnM)2)0(1exp[(Mlnd

d2Xjk2

X

diff

Xpp

1)0(k

t-averaged j1

const. Mlnd

d2X

diff

Xpp

Nondiffractive + diffractive contributions 2Xb ln M

2X

dN = D + c e

d ln M

for 2 2X 0ln M ln W

Fit slope b, c and D

D is the diffractive contributionTwo approaches for fit to the data

1.) take D=const. for a limited range in ln M2

X

2.) take D from a BEKW-model (see later) parametrization which describes the measured data. This is an iterative procedure.

Determine diffractive events by subtracting nondiffractive events from measured data bin by bin as calculated from fitted values b and c.

Both approaches give the same results

Bernd Löhr, DESY

The MX-Method (III)

Advantage: no nondiffractive contribution large acceptance -> high statistics

Disadvantage: contains contribution from proton dissociation

Diffractive Cross-Section and Diffractive Structure Functions

Bernd Löhr, DESY

),x,t,Q()y1(1Q

2

ddtdxdQ

dIP

2)4(Dr

2

2em

IP2

4

),xt,,Q(Fy)-(11

y - ),xt,,Q(F ),xt,,(Q IP

2)4(DL2

2

IP2D(4)

2IP2)4(D

r

sizeable only at high y, can safely be neglected in the range of HERA measurements.

If t is not measured, i.e. integrated over

),x,Q()y1(1Q

2

ddxdQ

dIP

2)3(Dr

2

2em

IP2

3

and anlogously ),x,Q(F IP2D(3)

2

H1 uses ),x,Q( IP2)3(D

r , ZEUS neglects the longitudinal part and uses ),x,Q(F IP2D(3)

2

Diffractive DIS Factorization

In the same way as for DIS, diffractive deep inelastic cross sections can be expressedas a convolution of diffractive parton densities with a deep inelastic cross section.

diffractive parton distribution function (dpdf)

number density of a parton i in the protonunder the condition that it undergoes a diffractive reaction

dpdfs at fixed t and xIP evolve with Q2

according to DGLAP

hard universal DIS cross section

DDIS factorization rigorously proven:Collins ; Berera, Soper ; Trentadue, Veneziano

dpdfs are universal for all hard diffractive processes

Bernd Löhr, DESY

Regge-Factorization

Bernd Löhr, DESY

Regge theory originally developed for eleastich 2-body scatteringExtension to inclusive diffraction:

Triple-Regge formalism

This expression allows the decomposition into aflux factor and a cross section:

Based on the triple-Regge formalism the diffractive parton distribution functionsare factorized accordingly:

with

This Regge- or vertex-factorization cannot be proven in pQCD

Separation of Pomeron from Reggeon Contributions

Bernd Löhr, DESY

Results obtained with LPS/FPS method and the LRG method may contain nondiffractive contributions from Reggeon exchanges.

They are fitted by a sum of Pomeron and Reggeon contributions.From the fit the Pomeron contribution can be extracted.

)Q,(Ft),x(fn )Q,(Ft),x(f)Q,,,x(F 2IR2IPIRIR

2IP2IPIP

2IP

D(4)2 t

)Q,(F 2IR2 is taken from a parametrization of the pion structure function

The fluxes are normalized according to: 003.0at x 1dt)t,x(fx IPIPIR/IP

t

1IPmin

Fitted values are )Q,(F 2IP2 and IRn , the normalization of the Reggeon contribution

Other parameters, like , are also fitted or taken from other measurements.

IRIP,IR,IPIR,IP B , , )0(

with )x1/(xm |t| IP2IP

2pmin

Bernd Löhr, DESY

)Q,( )Q,(F 2Di

i

2IP2 f

gluon , s , d , u , s , d ,u ; speciesparton i

)Q,( 2Di f

Parametrization at a starting value Q02 as :

z-1

0.01-CB

i20 ez)1(zA )Q,(z ii zf i

z is the longitudinal momentum fraction of the parton entering the hard sub-process.

z = for lowest order quark-parton modell process,0 < < z for higher order processes.

QCD DGLAP Fits

In a picture where the Pomeron has a partonic structure (Ingelmann-Schlein Model)

)Q,(F 2IP2 can be interpreted as the Pomeron structure function

Pomeron structure function expressed as a sum ofuniversal Pomeron parton distribution functions :

Pomeron pdfs obey DGLAP evolution

A DGLAP fit and the Regge fit are usually carried out simultaneously

Results from Proton Detection Method

Bernd Löhr, DESY

H1: Forward Proton Spectrometer (FPS) ZEUS: Leading Proton Spectrometer (LPS)

combined Regge and DGLAP fit --- extrapolation to nonmeasured Q2

..... Pomeron contribution only

Regge fit at two t-values

Bernd Löhr, DESY

Comparison FPS with LPS data

Both datasets have systematic uncertainties from the beam divergence

H1: +/- 10% ZEUS: +12%/-10%

They are not shown in the figures.

Fair agreement in shapebetween the FPS and LPSresults

Bernd Löhr, DESY

H1 LRG Results

DGLAP fit toH1 data

Regge fit to ZEUS data

Both data show qualitatively the samefeatures

Data contain contributions from proton dissociation

Bernd Löhr, DESY

Comparison between H1 and ZEUS LRG Results

The ZEUS data are normalized to the H1 data

Reason : The H1 dataset and the ZEUS dataset contain different amounts of proton dissociation. The data are not corrected for that.

Good agreement in shape

Bernd Löhr, DESY

Comparison between H1 FPS and LRG Results

The LRG data contain contributions from proton dissociation up to massesof 1.6 GeV.

The FPS data are multipliedby a factor 1.23 such that they correspond to the LRG data

Singlet Structure function

Bernd Löhr, DESY

H1 DPDF Fits

)z(s)z(d)z(u)z(sd(z)u(z)Σ(z)

z-1

0.01-CB

i20 ez)1(zA )Q,(z ii zf i

Differences between fit A and fit B

)z(s)z(d)z(u)z(sd(z)u(z)

Gluon structure function )z(g

Fit A:

For both fits only data with Q2>8.5 GeV2

have been used.

Bg is set to zero

Qo2 = 1.75 GeV2

Fit B: Qo2 = 2.5 GeV2

Aq, Bq, Cq are always fitted

Bg, Cg is set to zero

The gluon density is only weakly constraint by the data

For fit A the fraction of exchanged momentum carried by gluons in the range 0.0043<z<0.8 is around 70% throughout the studied Q2 range. For fit B it is a little less but compatible with fit A.

Bernd Löhr, DESY

Results from the MX-Method : ddiff/dMX

ZEUS results: FPC I published 2005 , FPC II preliminary 2007

1.2 GeV < MX < 30 GeV FPC I: 2.7 GeV2 < Q2 < 55 GeV2FPC II: 2.7 GeV2 < Q2 < 320 GeV2

Data contain contributions from proton dissociation with MN<2.3 GeV

Fit of W-dependence of inclusive DIS and inclusive diffractive DIS cross sections

Inclusive DIS:

Bernd Löhr, DESY

For small x, F2 rises rapidly as x-> 0

-2 xc F

1)0( IP x

1 W

Inclusive diffractive DIS:

diffaX

0X

Np

W

Wh

dM

d *

4

a 1

diff

IP

2

0IP W

Wln)1)(2(

ef(t) dt

d

t t )0( )t( IPIPIP

tAe dt

d

29.0

5.0- GeV syst.)( 0.5(stat.) 7.9 A

e.g.measured by ZEUS LPS

Inclusive DIS and inclusive diffractive DIS are not describedby the same ‘Pomeron’.

<<<

From W dependence, averaged over t :

;

With

4

a

A1)0(

diffIP

IP

Ratio of total diffractive cross-section to total DIS cross-section

Ratio plotted at W=220 GeV because only there the full MX range is covered by measurments

Mx 98-99

Mx 99-00 (prel.)

Within the errors of the measurementsr is independent of W.

At W=220 GeV, r can be fitted by

r = diff(0.28<MX<35 GeV)/tot

r = 0.22 – 0.034.ln(1+Q2)

This logarithmic dependence of the ratioof total diffractive cross-section to the total DIS cross section indicates thatdiffraction is a leading twist process for not too low Q2.

Bernd Löhr, DESY

The ZEUS data support taking nT(Q2)=ng(Q2)=nL(Q2)= n1`ln(1+Q2/Q20)

Taking x0= 0.01 and Q20= 0.4 GeV2 results in the modified BEKW model

with the 5 free papameters :

cT , cL , cg , n1T,L,g ,

Bernd Löhr, DESY

ZEUS BEKW(mod) Fit

Dipole Model

BEKW-fit : transverse qq contribution

longitudinal qq contribution transverse qqg contribution

sum of all contributions

FPC I FPC II

Bernd Löhr,

> 400 points 5 parameters/nD = 0.71

ZEUS-MX Diffractive Structure Functions with BEKW(mod.) Fit

Bernd Löhr,

ZEUS-MX Diffractive Structure Functions

Relation between differential diffractive cross section and diffractive structure function

F2D(3) specifies the probability to find a in diffractive reaction a quark in a proton

carrying a fraction x=xIP of the proton momentum.

rises approximately proportional to .

This rise reflects the increase of the diffractive cross section with W.

At small xIP the development of the diffractive cross section is governed by theincrease of the gluon density as W increases or xIP decreases.

Bernd Löhr, DESY

ZEUS-MX Diffractive Structure Function and the BEKW(mod) Fit

-

-

Towards low values the qqg contribution rises strongly due to the increase in gluon density.

The longitudinal qqL contribution is sizeable only at very high and is responsible for a finite value of the diffractive structure function at

For fixed Q2 and fixed xIP the data show a broad maximun around =0.5 which originates from the dependence of the tansverse qqT contribution.

Bernd Löhr, DESY

ZEUS MX : QCD Scaling Violations

ZEUS BEKW(mod) fit

xIPF2D(3) in fixed (xIP,)-bins

xIPF2D(3) shows considerablescaling violations:

from positive scaling violations over near constancy tonegative scaling violations.

Scaling violations well describedby BEKW model -> effective DGLAPevolution present in this model.

Bernd Löhr, DESY

H1 and ZEUS: QCD Scaling Violations

H1: DPDF fit ZEUS: BEKW(mod) fit

Bernd Löhr, DESY

Summary of Inclusive Diffraction

1.) Three experimental methods to measure inclusive diffraction at HERA : PS/LPS, LRG, and MX. All include contributions of different magnitude from

proton dissociation or from Reggeon exchange or from both.

2.) Inclusive diffraction is a leading twist reaction.

2.) The diffractive cross-section can be expressed in terms of diffractive structure functions.

3.) Assuming Regge factorization H1 separated Pomeron and Reggeon contributions

and extracted DPDFs from the LRG data.

4.) QCD inspired dipole models can describe inclusive diffraction as well. The ZEUS MX data are described rather precisely over the whole kinematic

range by the BEKW(mod) parametrization.

5.) The BEKW modell explains the diffractive structure function F2D(3) in terms of

transverse and longitudinal quark-antiquark and quark-antiquark-gluon contributions.

6.) The diffractive structure function F2D(3) shows large scaling violations. This points to a large gluon fraction in the colourless exchange.

Inclusive diffraction

Exclusive diffractive processes

Bernd Löhr, DESY

Semi-Inclusive DiffractionAnd Tests of QCD Factodization

exclusive vector meson production transition from soft to hard diffractive reactions

diffractive structure functions description by quark-dipole models universal diffractive parton densities

Semi-inclusive diffractive processes diffractive final states with special properties: jets, heavy quarks, ....

Semi-inclusive diffractive processes are a testing ground for the universality of the diffractive parton distributions derived from inclusive reactions.

P’p

VM VM*

p

VM* z

1-z

P’

e e’

p P’

e e’

p P’

Bernd Löhr, DESY

Semi-Inclusive Diffractive DIS D*(2010) Production

Kinematical selection:max<3, xIP < 0.035, < 0.8

ACTW fit (Alvero et al.):Combined fit of DPDFs to H1 and ZEUSinclusive diffractive data and to ZEUSdiffractive di-jet photoproduction data,all data up to 1998.

The pQCD fit using the DPDFs from inclusive diffraction gives acceptable descriptions of diffractive D*(2010) Production.

Confirmation of the universality ofDPDFs from inclusive diffraction.

c

c

- D*

c

Bernd Löhr, DESY

Semi-Inclusive Diffractive DIS Di-Jet Production

jet

jet

zIP: part of the Pomeron momentum that goes into the hard interaction

Diffractive di-jet production is sensitive to the gluon DPDF

Diffractive photon-gluon fusion

H1 fits A and B used in NLO calculation (Z.Nagy)

Fit B gives an acceptable description of the data

diffractiveSystem

X

Fit A Fit B

Confirmation of the universality ofDPDFs from inclusive diffraction.

Bernd Löhr, DESY

Combined Fit to DIS Inclusive Diffractive and Diffractive Di-Jet Production

Experimental validation of universality of DPDFs make combined fit

The information from diffractive di-jet production improves the fit of the gluon density in particular at high zIP.

Bernd Löhr, DESY

HERA DPDFs and Predictions for the Tevatron

Do the DIS-DPDFs from HERA also describe diffraction in hadron-hadron interactions ?

Note: QCD factorization has not been proven for hadron-hadron interactions

Diffracitve di-jet production at CDF

jethard scattering

IPLRG

jet

jet

Convolution of 2 structure functions

Predictions from DIS diffractive structure functions fail by factor 5-7.

Final state interaction between proton remnent and antiproton possible : gap survival probability is not one.

Bernd Löhr, DESY

Semi-Inclusive Diffractive Photoproduction at HERA

What is special about photoproduction (Q20 GeV2) ?

Direct photoproduction

Photon takes part directly in hard interaction

X

Resolved photoproduction

Photon fluctuates into a hadronic state of which only a part enters the hard interaction

X < 1

operational definition:

X > 0.7 direct

X < 0.7 resolved

Resolved photoproduction is similar to hadron-hadron interactions

Is diffractive resolved photoproduction also suppressed ?

Do final state interactions play a role also in photoproduction ?

Bernd Löhr, DESY

Diffractive D*(2010) Photoproduction at HERA

NLO calculations:Frixione et al. FMNR-codeand H1 DPDFs

Qualitative good agreement with NLO QCD calculations using inclusive DPDFs

Bernd Löhr, DESY

Diffractive Di-Jet Photoproduction at HERA

H1: Q2 1 GeV2 ; 165 < W < 242 GeV

max= 3.2 ; xIP < 0.03

ET*,jet1 > 5 GeV ; ET

*,jet2 > 4 GeV

-1 < jetlab < 2

ZEUS: Q2 < 1 GeV2 ;

max = 2.8 ; xIP < 0.028

ETjet1 > 7.5 GeV ; ET

jet2 > 6.5

GeV

-1.5 < jetlab < 1.5

Note : NLO predictions scaled by 0.5Note : H1 and ZEUS are quoting results for different kinematical regions

Bernd Löhr, DESY

Diffractive Di-Jet Photoproduction at HERA : cont.

Results from H1 and ZEUS separately for direct and resolved photoproduction

H1: data for all x in NLO calculation xPL > 0.9 no scaling factor xPL < 0.9 scale factor 0.44 -> unacceptable fit

Fit with 2 free normalizations

for x,PL < 0.9 and x,PL > 0.9 yielded

0.47 +/-0.16 and 0.53+/-0.14

ZEUS diffractive di-jet photoproduction

direct enrichedXobs < 0.75resolved enriched X

obs > 0.75

Agreement within errors between data and NLO calculations with inclusive DPDFs

Note, however, that kinematic regions forH1 and ZEUS data are different -> may not be a contradiction

Bernd Löhr, DESY

Summary of Semi-Inclusive Diffractionand Tests of QCD Factorization

1.) QCD inspired models using the DPDFs determined from inclusive diffractive DIS describe at least qualitatively semi-inclusive diffractive production of heavy quarks and di-jets.

2.) The QCD factorization scheme in DIS is experimentally verified in diffractive DIS.

3.) Although theoretically not expected, Regge factorization seems to hold in practice.

4.) These are experimental indications that DPDFs might be universal in DIS.

5.) QCD factorization does not hold for diffractive hadron-hadron interactions. Using HERA DPDFs leads to a gross overestimation of dijet production at the Tevatron. The survival probability of diffractive gaps is smaller than one.

6.) The situation in semi-inclusive diffractive photoproduction needs further clarification. For heavy quark production the QCD factorization seems to hold also for the resolved photon contribution. For di-jet production there are indications from H1 that QCD factorization might not be valid whereas ZEUS results confirm QCD factorization although in a slightly different kinematical regime.

bernd l öhr, desy

Documents

electron energy

diffractive eventsbernd

gevelectronsprotonsbernd

abovebernd lhr

diffractionbernd lhr

electron bunches

pomeron ipbernd lhr

integrated luminositybernd