1. Multiplicity Distributions in DIS at HERA
Preliminary Examination
Michele Sumstine
University of Wisconsin
Dec. 19, 2002

2. Outline Introduction HERA and ZEUS Kinematics
Parton Shower & Hadronization Models
Universality of Hadron Production
Data Selection & Simulation of ZEUS Data
Mean Charged Multiplicity vs. Effective Mass
Summary and Plan

3. Particle Scattering Study structure of proton
Scattering via probe exchange
Wavelength
Deep Inelastic Scattering – Q2 large
High energy lepton transfers momentum to a nucleon via probe
h : Plank’s Constant
Q2: related to momentum of photon
probe
lepton
The effective probe of proton is the virtual exchanged photon
The resolving power …
The degree of structure revealed increases…
rp>h/2 = 6.6 E –22 MeV s
Q2=40,000 GeV2 Q=200 GeV = 200e3MeV
Ћc=197 MeV fm 197/200000= fm
Size of proton ~ 1 fm HERA Q2 Range ~ 40,000GeV2 HERA can probe to ~ fm

4. Naïve Quark Parton Model
Proton consists of pointlike non interacting constituents (partons)
Quark Parton Model
3 families of quarks ½ spin particles
In Parton Model proton consists of partons
QCD tells us the partons are quarks

5. QCD Theory QCD Quantum Chromodynamics
Strong force couples to color and is mediated by the gluon
Gluon permits momentum exchange between quarks
Gluons create quarks through pair production
Color confinement: free partons are not observed, only colorless objects -hadrons
Parton distribution function (PDF) gives probability of finding parton with given momentum within proton (experimentally determined)
Experiments--NQPM isn’t whole story
Quarks interact w/each other via strong force
Strong force mediated by gluon
Gluon carries color
No naturally occurring particles have color—
Only observe colorless hadrons
Graphs
The PDF’s are experimentally determained
QCD is non-Abelian theory with SU(3) synmmetry

6. QCD Scale Running of aS Perturbative QCD (pQCD) Nonperturbative QCD
Leading Order (LO)
Next to Leading Order (NLO)
A = A0 + A1aS + A2aS2 +...
HERA DIS Data: Running of aS(m)
Running of aS
As scale m increases, aS(m) decreases (m = ET or Q)
Perturbative QCD (pQCD)
Small aS(m) (hard scale)
Series expansion used to calculate observables
Nonperturbative QCD
Large aS(m) (soft scale)
Series not convergent
The strong coupling constant-not a constant at all…
Scale= time/distance; small scale, short times, small distances, hard process
large scale, long times, large distance, soft process
Each vertex contributes sqrt.
Cross section goes as scattering amplitude squared

7. From Partons to Hadrons
hard scattering  parton showers  hadronization
Hard scattering: large scale (short distance) perturbative process
Parton showers: initial QCD radiation of partons from initial partons
Hadronization: colorless hadrons produced from colored partons                           soft process (large distance) - not perturbatively calculable           phenomenological models and experimental input
PS is governed by pQCD
Parton Showers are QCD predictable once you have set a scale

8. Multiplicity and Energy Flow
The hard scattering process determines the initial distribution of energy
Parton Shower + Hadronization determine the number of charged particles produced
Measure mean number of charged particles produced, (mean charged multiplicity, <nch>), versus the energy available for production of final state hadrons, study the mechanisms of hard scattering, parton showers and hadronization
First I have a hard process that determines…
Then we have the PS and Had that determine…
SO I would like to measure the mean num of charged particles, and see how it depends on the energy available for hadron production.
Hadronization happens at a scale where s becomes large so cannot be treated perturbatively
Studies have led to phenomenological models to describe hadronization which are universal
pQCD & universality of the hadronization process can be tested by comparison with data from e+e- and hadron colliders.

9. Unique opportunity to study hadron-lepton collisions
HERA Description
920 GeV p+
(820 GeV before 1999)
27.5 GeV e- or e+
318 GeV cms
Equivalent to a 50 TeV Fixed Target
Instantaneous luminosity max: 1.8 x 1031 cm-2s-1
220 bunches
96 ns crossing time
IP~90mA p
Ie~40mA e+ H1
ZEUS
HERA Circumference: 6336 m
Synchrotron radiation is lin. pol. in plane of acceleration.
Mean energy loss per revolution: for Electrons: ~8MeV
Fixed target: ECM=S=2E1m2
Colliding Beam: ECM = S=4E1E2
Luminosity: L =f n1 n2/4 xy
N1,n2 number of particles in bunch
f=frequency
xy characterize beam profiles in horizontal and vertical direction
~1011 Protons/Bunch
~3.5x1010 e/Bunch
Current: 1.6x10-19 q/C
Vacuum Pressure: 3x10-11 Torr
e+ beam: T B field
P beam: 4.65 T B field
Spaces left in beam so kicker magnets can dump beam, study beamgas
Sokholov-Ternov Effect: e- polarized with spin antiparallel to dir. of bending field (transverse)
DESY Hamburg, Germany
Unique opportunity to study hadron-lepton collisions

10. ZEUS Luminosities (pb-1)
HERA Data
Luminosity upgrade
5x increase in Luminosity
 expect 1 fb-1 by end of
For this beginning study I looked at the 96 data, which is ~12pb-1
ZEUS Luminosities (pb-1)
# events (106)
Year
HERA
ZEUS on-tape
Physics
e-: 93-94, 98-99
27.37
18.77
32.01
e+: 94-97, 99-00
165.87
124.54
147.55

11. General Purpose Detector
ZEUS Detector
Electron
27.5GeV
Missing ET implies a 
E loss by heavy charged particles
Inelastic w/ e- of atoms
Elastic w/ nuclei
E loss by e-
Collision – ionization
Radiative loss – bremsstrahlung
1/(m2c4)
General Purpose Detector
Almost hermetic
Measure ep final state particles: energy, particle type and direction

12. Central Tracking Detectorp
View Along Beam Pipe
Side View
Drift Chamber inside 1.43 T Solenoid
Can resolve up to 500 charged tracks
Average event has ~20-40 charged tracks
Determine interaction vertex of the event
Measure number of charged particles (tracks)
R= p/qB
R=mv/qB relativistic
Filled with Ar(84.3%)
CO2(8.4%)
ethane(6.8%)
ethanol(0.5%)

13. Uranium-Scintillator Calorimeter
alternating uranium and scintillator plates (sandwich calorimeter)
 =  = 5.7o
 = -3.0  = 174.3o
Positrons
27.5 GeV
Protons
820 GeV
compensating - equal signal from hadrons and electromagnetic particles of same energy - e/h = 1
Energy resolution  e/Ee= 18% / E h/Eh= 35% / E , E in GeV
Rapidity important because changes in rapidity are invariant under Lorentz boosts along the beam direction.
Pseudorapidity  Rapidity for m=0, =1.
Rapidity. Calculate angles from the Energy and longitudinal momenta
Y=1/2 log (E + pz/E – pz)
Depleted Uranium, is 99.8% U238, 0.25% U235, and 0.001% U234 by Mass, Natural U has 0.72%U235
So ours is depleted of U235
e/h = 1 Important for me, don’t need a lot of corrections to get energy flow
Calorimeter: EMC Depth : HAC Depth
FCAL : 1 : 6 (6 nuclear interaction lengths)
BCAL : 1 : 4
RCAL : 1 : 3
=1 absorption length = 25 radiation lengths for electromagnetic particles
Depth of FCAL > RCAL due to Ep > Ee
Used for measuring energy flow of particles.
covers 99.6% of the solid angle

14. ZEUS Trigger First Level Second Level Third Level
107 Hz Crossing Rate,105 Hz Background Rate, 10 Hz Physics Rate
First Level
Dedicated custom hardware
Pipelined without deadtime
Global and regional energy sums
Isolated m and e+ recognition
Track quality information
Second Level
“Commodity” Transputers
Calorimeter timing cuts
E - pz cuts
Vertex information
Simple physics filters
Third Level
Commodity processor farm
Full event info available
Refined Jet and electron finding
Advanced physics filters
Commodity = bought from a store, as opposed to CFLT’s custom hardware
Pipelined without deadtime:
A perfect data acquisition system would be able to readout all the data from all the detectors w/o any deadtime due to inability to read the data from a previous event before the next event is taken. The ZEUS system buffers the data from each event in a pipeline for 5us before the level one decision. Because every event is pipelined the FLT can select events with almost no deadtime

15. Kinematic Variables Virtuality of exchanged photon
remnant
e(k)
e’(k’)
p(P)
  (q) q’
Virtuality of exchanged photon
Inelasticity: 0  y  1
Fraction of proton momentum carried by struck parton x  1
= Center of mass energy of the ep system
Virtuality is square of four momentum transferred from the scattered positron to the photon.
Larger Q2 means more virtual photon
In proton rest frame, y is fraction of energy lost by interacting positron
Y=0: completely elastic, electron gives no energy to proton, final state hadrons low energy, low angle
Y=1; completely inelastic
X is fraction of proton momentum carried by the part of the proton that participated in the interaction
s = (p + k)2 , 4 momentums, so this equals 2p dot k = 4EeEp
Center of mass energy of the *P system
Only two independent quantities

16. Kinematic Reconstruction
Four Measured Quantities: Ee’, e, Eh, h.
(p,E) conservation  
DIS Event
Variable
Electron Method (Ee’,)
Jacquet-Blondel (Eh,)
Double Angle (,) Q2 X y
Electron Method:
Angles can be measured precisely
E’ can’t be measured so precisely due to detector resolution, and dead material
--Q2el --good at high Q2 (higher E’s which don’t rely so much on resolution)
--yel—good at higher y
--not good for x anywhere
Hadron Method
--Q2—not as good due to indirect measurement of E
--y --good at lower y’s (opposite of el)
--x—slightly better
DA method
All are better because this uses only angles
Separate page for Reconstruction calculations

17. Deep Inelastic Scattering
Proton remnant missed
Scattered quark is manifested as a jet in detector
The electron is scattered out and is manifested as an Em shower in the det.
In low Q2 the positron is scattered much more towards the rear calorimeter.

18. 50 TeV Fixed Target Experiment
HERA Kinematic Range
Q2 = sxy
0.1 < Q2 < GeV2
10-6 < x < 0.9
Equivalent to a
50 TeV Fixed Target Experiment
SVX- shifted vertex: shift vtx toward FCAL,a lower angle track will still hit the RCAL so can go into lower Q2
BPT-Beam Pipe Tracker: Cal behind the RCAL, if e scatters at low angle & misses the RCAL can still go into the beam pipe calorimeter, so can go to lower Q2
Also added Beam Rotators
Curved portions follow a line of constant scatterd electron angle for yellow
green: follow a line of constant E (27.5)

19. Modeling Multi-parton Production
Model multiple parton emissions from partons produced in hard scattering
Not possible to perform exact matrix element calculations
Two approaches: Parton Shower and Color Dipole Model
Parton Shower Model
successive splitting process
cascade of partons with decreasing virtuality
cascade continues until a cut-off ~ 1 GeV2
How do we model emissions from partons produced in hard scattering?
Two approaches:
Radiations can also produce additional partons

20. Color Dipole Model Chain of independently radiating color dipoles
ep: first dipole between struck quark and proton remnant
gluon induced processes are added in "by hand“
Subsequent gluon radiation eminates from dipoles spanned btwn the newly created color charges …
Gluon induced hard scale processes are added in by hand
DON’T SAY THIS: (just notes)
or the gluon induced processes, half the time they assume q half time qbar.
In contrast to the PS model it is not possible to distinguish from initial and state radiation, i.e. can’t reconstruct an evolution path

21. Hadronization Models
Use phenomenological models because these processes aren’t calculable in pQCD – low scale
Lund String Model and Cluster Fragmentation Models
Start at low cut-off scale – set of partons from parton shower transformed into colorless hadrons
Local parton-hadron duality
Long distance process involving small momentum transfers
Hadron level flow of momentum and quantum numbers follows parton level
Flavor of quark initiating a jet found in a hadron near jet axis
The hadronization process must be phe-nom–en-o-locically modeled due to the low scale of these processes, i.e. as is large and so they are not calculable in pQCD.
Hadronization starts at low cut off scale…
The models follow Local hadron parton duality,
Proposes that the observed hadron distributions are proportional to the calculated parton distributions
If your leading parton is a strange quark, then after the long distance hadronization process you will find a strange hadron within some small angular region in the direction on the original strange quark.

22. Lund String Fragmentation
color "string" stretched between q and q moving apart
confinement with linearly increasing potential (1GeV/fm)
string breaks to form 2 color singlet strings, and so on., until    only on-mass-shell hadrons.
Hadrons are formed when the string energy is too small to create further qqbar pairs

23. Cluster Fragmentation Model
preconfinement of color (after parton shower)
non-perturbative
splitting after parton shower
color-singlet clusters of
neighboring partons formed
We group colored partons ion to colorless clusters, then these clusters decay into hadrons.
Gluons are split non perturbatively into qqbar pairs, color neutral clusters are formed which decay into hadrons
clusters decay into hadrons

24. Universality of Hadron Production
Can look at just part of the string: assumed to give final state particles proportional to logarithm of mass
Similarity of particle production at ee, ep and pp colliders
If you look at hadron production in e+e-, ep and ppbar, what you see is there is a section of the process where the hadrons get produced through a similar process.
If you compare e+e- and ep, you see the difference is that in ep I have the proton remnant to contend with.
I can test hpw similar the process is by studying the universality. This can be done by measuring…
Aim: Test the universality of hadronization in QCD nch ~ length of the string(s) ~ ln of energy available for hadron production

25. e+e- & ep : Breit Frame
Phase space for e+e- annihilation evolves with Q/2 = s/2
Current hemisphere of Breit frame evolves as Q/2
For testing the universality, I need a frame where I can compare e+e- and ep directly
So move to Breit frame…
Z=0 separates current from target region, Longitudinal momentum = 0
ZEUS data must be multiplied by 2 when comparing to e+e-, because in e+e- there are two quarks hadronizing, in ep just 1.
So my current region in BF is same as either hemisphere for e+e-. (in e+e- both hemispheres are same)
Current region  e+e- annihilation

26. Early Experimental Evidence for Universality
Mean charged multiplicity vs. Q in e+e- and current region of Breit frame at HERA
Linear dependence vs. ln Q observed
Data in e+e- and ep agree universality of hadronization process observed
Also look at <nch> as a function of energy available for particle production (slide to follow)
e+e- ep
Here we have EARLY measurement of mean charged multiplicity vs. Q for e+e- and current region of BF at HERA.

27. 96-97 Data Sample Event Selection Track Selection
Scattered positron found with E > 12 GeV
longitudinal vertex cut: |Zvtx| < 50 cm
scattered positron position cut: |x| > 15 cm or |y| > 15cm (in RCAL) “Box cut”
40 GeV < E-pz < 60 GeV
Track Selection
Tracks associated with primary vertex
|| < 1.75
pT > 150 MeV
Physics and Kinematic Requirement
Q2 (from double angle) > 12 GeV2
y (from scattered positron) < 0.95
y (from hadrons) > 0.04
For this initial study, I have looked at part of the 1996 data,
And I used the following criteria to select my events.
EVENT SELECTION:
To ensure that the kinematic variables can be reconstructed with sufficient accuracy,
I required a good positron be found coming from the vertex,
I used a box cut to ensure that the positron is fully contained in the detector,
And required the total E-pz to be near 55 Gev
TRACK SELECTION:
Trks associated with primary vtx,
<1.75, ensure tracks are in a region of high CTD acceptance, where detector response & systematics are well understood
Pt>150, to ensure the track makes it thru the layers of the CTD
KINEMATIC:
Yel<.95 removes photoproduction
Yjb>0.04 to guarentee accuracy for DA method (which is used to reconstruct Q2)
The hadron angle depends on yjb, and the measurement of yjb is distorted bu Uranium noise in the cal for low yjb
NOTES:
E-pz. For e+ E=27.5, pz = since E2-p2=m2 and m=0, so = 55, for the proton, Ep=920, p=920, =0
Total e-pz = 55 GeV
E-pz removes photoproduction (scattered e is missing, q2 is low=0, electron goes in beam pipe, Ee=0.)
removes evnts w/ large radiative corrections (electron looses energy by radiating a big photon, so Ee is less than 27.5)
95842 events before cuts
4798 events
after all cuts

28. Event Simulation Ariadne ’96 v2.0 Q2 > 10 GeV2
Matrix elements at LO pQCD O(s)
Parton showers: CDM
Hadronization: String Model
Proton PDF’s: GRV94 HO parameterization of experimental data*
Q2 > 10 GeV2
Detector Simulation: software package based on GEANT
Proton PDF’s are parameterized from experimental data
Detector simulation besed on JAY-AUNT
19990 events before cuts
7058 events
after all cuts
*M.Glück, E.Reya and A.Vogt, Phys. Lett. B306 (1993) 391

29. Work done by M.Sumstine Summer 2002
Zeus ’96 Data vs. Ariadne
Vertex Position
X & Y vertex
MC simulates transverse vertex well
Z vertex
Here I am comparing only a small part of the 1996 data, to the simulation of the Zvtx which is averaged over the full year, Because the event vertex can shift over time, the Zvtx appears shifted here, this will come into better agreement when I increase statistics.
Longitudinal vertex is shifted due to partial data
Work done by M.Sumstine Summer 2002

30. Energy & Theta of Scattered Positron
Scattered Positron Energy
Polar Angle of Scattered Positron
Ariadne
’96-’97 Data
Energy Corrections for dead material (the uranium)
material through which particles travel before they reach our detector, for example: magnets, cables (as far as the uranium calorimeter is concerned, also CTD is dead material . . .).  While travelling through this materialthe particles loose some energy, so the one we measure in the CAL is less than we would expect. This has to be corrected for. for non-uniformities in the calorimeter (there is the beampipe, etc)
- the detector is not perfect, there are gaps betwee modules and other different boundaries between different sections/parts/etc. of the CAL. These caus the detector response not to be uniform all over the (spatial) angle. That's why the correction for them is called non-uniformities correction.
Positron energy corrections needed – under study.

31. Position of Scattered Positron at RCAL
x position
y position
Important for reconstruction of Q2
Cut: |x| or |y| > 15cm : Eliminates events close to beam pipe

32. Kinematics: Virtuality
Q2 electron method
Energy corrections not yet applied
Good agreement on 2 orders of magnitude

33. Kinematics: Inelasticity
Y electron method
Y hadron method
needs electron energy corrections
uses hadronic system variables

34. Tracking: # of Charged Tracks
Number of tracks well described by Ariadne model over two orders of magnitude
Validation of model & CTD tracking simulation
Pause: OK I have showed the kinematic variables associated with the calorimeter,
Now I need to look at tracking.
Here we have….

35. Tracking:  & pT
First look at tracking, acceptable for use to correct for detector effects

36. Effective Mass Study: <nch> vs. Meff
CAL within the CDT acceptance
Study: <nch> vs. Meff
CTD
Hadronic final state within 
Charged part seen as tracks
Energy measured by calorimeter
Ok I need a variable that describes the energy available for hadron production, but in order to campare to e+e-, I need to remove the proton remnant. The variable I need is Meff.
It is calculated form the square of the energy of the hadrons minus the square of their momentum.
It measures the hadronic final state within some eta region,
Charged Tracks are counted in CTD while effective mass of this part is determined within the same opening angle in the calorimeter

37. Mean Charged Multiplicity vs. Meff
Average number of charged particles vs. effective mass
Reasonable agreement for first look at partial data sample, statistics limited at high Meff
Uncorrected ZEUS ’96 data compared to Ariadne
proportional to ln (Meff)
Here is my first measurement of mean charged multiplicity with Meff:

38. ZEUS Measurement
Investigation of degree of universality in particle production
<nch> consistent with linear dependence vs. Meff
<nch> 15% above corresponding e+e-
Understand color dynamics at the pre- hadronization stage at HERA
Now we look at a previous ZEUS investigation of the degree…,
A possible explanation is initial gluon radiation at HERA .
Further study in this area could lead to better understanding…
NOTES:
The obtained results can be considered as possible evidence that in the inclusive production about 85% of final state hadrons are produced by non-perturbative mechanism (confinement) while about 15% of the mean charged multiplicity is contributed by the hard perturbative mechanism of color charge radiation

39. Summary
First look at Multiplicity Distributions in DIS at HERA   using 1996 data
DIS data sample compared to pQCD + parton showers + hadronization models predictions
Event kinematics and tracking well understood and simulated
Plan
Increase statistics of data and simulation events
include all 96 and 97 data
Investigate diffractive effects
Measure multiplicities vs. Q^2 in the current and target region of the Breit frame
Measure momentum spectra
Compare different models for parton showers and hadronization to data
Evaluate systematic uncertainties
Including all 96 Data will increase my statistics an order of magnitude
Total luminosity for my study 0.06 pb-1; total for 1996 ~12pb-1
Diffraction:
Events with low momentum transferred to the hadron.

40. Diffractive events expected at large angles (low max)
Diffraction & max
Diagram
Event Display
DIS
Diffraction
5-10% of events
Not modeled by
Ariadne
Dynamics different for these events
Will distribution be same?
Eta max, eta of most forward energy in the calorimeter
Diffractive events expected at large angles (low max)

41. Look for Diffractive Events
Only max>3.2 is described by Ariadne
~500 events out of total data sample (4798 events)
These are diffractive events that are not simulated by the Ariadne Monte Carlo
Note: Log Scale
Solutions:
(fast) Cut out diffractive events
(better) Use mixture of diffractive & non-diffractive monte carlo.
will do both
Move this to later, say I didn’t put the cut, add it to Plans
Describe what is eta max, eta of most forward hadron
Normalized above max = 3.2

42. Mix Diffractive & Non-Diffractive Models
RapGap contains diffraction; Ariadne does not
A fit to a superposition of RapGap and Ariadne max distributions, determines relative contribution of each
Data & fitted MC mixture
16% RAPGAP+ 84% Ariadne
# of events
RapGap + Ariadne 10<Q2<1200
Plans
70<W<260
Correct for detector effects
Understand purities/efficiencies
To give the best description of the inclusive events, a superposition of the corresponding distributions from non-diffractive and DIS diffractive MC event samples should be used. The relative contribution of each to be determined by fitting the measured inclusive etamax distributions to the combination of the etamax distributions from the diffractive & non-diffractive MC event samples

43. pQCD series Perturbative QCD (pQCD) series: A = A0 + A1aS + A2aS2 +...
photon
quark
lepton
gluon
QCD studies strong interactions
Coupling : leads to two regimes of QCD
What does expand with alpha_s mean?
A = A0 + A1aS + A2aS2 +...
Leading Order (LO)
Next to Leading Order (NLO)