bernd l öhr, desy
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Bernd Löhr, DESY Page 1
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 Page 2
This corresponds to an electron energy in a fixed-target experiment of Ee = 26952 GeV
electronsprotons
Bernd Löhr, DESY Page 3
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 Page 4
Bernd Löhr, DESY Page 5
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 Page 6
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 Page 7
[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 Page 8
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 Page 9
From Optical Diffraction to High Energy Particle Scattering
Kinematics of DIS and Diffraction
Bernd Löhr, DESY Page 10
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 Page 11
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 Page 12
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 Page 13
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 Page 14
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 Page 15
Can the Vectormeson Mass be a Hard Scale ? I
Bernd Löhr, DESY Page 16
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 Page 17
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 Page 18
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 Page 19
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 Page 20
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 Page 21
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 Page 22
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 Page 23
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 Page 24
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 Page 25
Measured Decay Matrix Elements for Production II
Bernd Löhr, DESY Page 26
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 Page 27
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 Page 28
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 Page 29
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 Page 30
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 Page 31
• 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 Page 32
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 Page 33
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 Page 34
There is no method available to measure directly inclusive diffractive cross-sections
The Proton Detection Method
Bernd Löhr, DESY Page 35
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 Page 36
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 Page 37
Bernd Löhr, DESY Page 38
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 Page 39
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 Page 40
),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 Page 41
Regge-Factorization
Bernd Löhr, DESY Page 42
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 Page 43
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 Page 44
)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 Page 45
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 Page 46
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 Page 47
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 Page 48
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 Page 49
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 Page 50
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 Page 51
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 Page 52
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 Page 53
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 Page 54
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
Page 55Bernd Löhr,
> 400 points 5 parameters/nD = 0.71
ZEUS-MX Diffractive Structure Functions with BEKW(mod.) Fit
Page 56Bernd 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 Page 57
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 Page 58
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 Page 59
H1 and ZEUS: QCD Scaling Violations
H1: DPDF fit ZEUS: BEKW(mod) fit
Bernd Löhr, DESY Page 60
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 Page 61
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 Page 62
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 Page 63
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 Page 64
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 Page 65
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 Page 66
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 Page 67
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
Page 68
Bernd Löhr, DESY Page 69
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 Page 70
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.