1. Energy Dependence of the Mean Charged Multiplicity in Deep Inelastic Scattering with ZEUS at HERA
Michele Rosin
University of Wisconsin, Madison
Thesis Defense, Madison WI
Jan. 27th, 2006

2. Standard Model Fermions Matter made of fermions: quarks or leptons
Quarks (colored)
Flavor
Mass (GeV/c2)
Charge (Q/e) u
0.003
+2/3 d
0.006
-1/3 c
1.3 s
0.1 t
175 b
4.3
Matter made of fermions:
quarks or leptons
Each particle has anti-particle with opposite quantum numbers
Quarks carry color “charge”
Four fundamental forces
Electromagentic (EM) force
Weak force
Strong force
Gravity
Leptons (not colored)
Flavor
Mass (GeV/c2)
Charge (Q/e) νe
< 1x 10-8 e
5.11 x 10-3 -1 νμ
< μ
0.106 ντ
<0.02 τ
1.7771
Quantum number: any one of a set of numbers used to specify the full quantum state of any system in Quantum Mechanics.
Quarks and leptons electrically charged (pos neg)
Quarks colored: not visible light but analogy to color mixing. Color + anti color = colorless (3 colors or anti col too)

3. Standard Model (II) Bosons
Force
Types
Mass(GeV)
Charge (Q/e)
Color
γ (photon)
Electromagnetic 1 No W±
Weak 2
80.4 ±1 Z0
91.187
g (gluon)
Strong 8
Yes
Strength of forces determined by coupling constant (αEM and αs)
forces mediated by exchange of bosons: γ, W±, Z0,g
Gravity described at macroscopic scale by general relativity.
very weak, neglected in high energy particle physics
Quantum Electrodynamics (QED): theory of EM, combined with weak  Electro-weak theory
Quantum Chromodynamics (QCD): theory of strong interaction
Combined theories  Standard Model
Strength of the forces determined by coupling constant.
In QFT, forces mediated by bosons (read table)
EM  massless photon
Weak  Z and W, superscripts denote elec charge
Strong (binds quarks together into colorless hadrons) gluons 8 types
Gluons: no mass, or charge, carry color charge  self interaction

4. Particle Scattering Study structure of proton Scattering via probe
Wavelength
Deep Inelastic Scattering (DIS) – Q2 large
High energy lepton transfers momentum to a nucleon via probe
h : Plank’s Constant
Q2: related to momentum of probe
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

5. 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

6. History of DIS, QPM

7. 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

8. 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

9. pQCD

10. 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

11. 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
Universality of the hadronization process can be tested by comparison with data from e+e- and hadron colliders.

12. Hadronic center of mass (HCM) frame
Hadronic center of mass energy is W
Definition of HCM frame
Ecms
Nphoton region =W E
Ecms/2
Nproton region p g*
Nphoton region vs W
Forward moving particles: photon hemisphere
Backward moving particles: proton hemisphere
Incoming photon and proton E= W/2
Final state: both hemispheres E=W/2
This is the hcm frame this is collision if gam and p you have th epho and pro hemis and here we can measure the pho hemi multiplic vs w
Since we’ve explored the Breit frame, we move to the HCM frame, you see in hcm frame you have gamma p interaction as shown, and the energy of the system is w. What is important is after the interaction the particles go in 2 directions: one is proton region and is photon region, the energy of the system will be divided equally into 2 portions, similar to an e+e- collision. So now we would like to plot the number of particles in the photon region vs the hadronic center of mass energy, w.

13. Breit Frame
“Brickwall” frame: incoming quark scatters off photon and returns along same axis
Breit Frame definition:
pZ<0: current region, pZ>0: target region
Current region of Breit Frame is analogous to single hemisphere e+e-: diagrams are similar above dashed line
In e+e- pair of quarks produced back to back with E=√s/2 each of them equiv. to the struck quark of E=Q/2 in DIS.
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)
Mean charged multiplicity has been measured for various initial state interactions, e+e-, pp, ep DIS, and fixed target DIS, in both Breit and HCM frames

14. Previous Measurements: Multiplicity in e+e- and pp
pp vs. √q2had
pp vs. √spp pp
Il Nuovo Cimento 65A N3 (1981) 404
Start with mean multiplicity for e+e- and pp. Here is e+e- annhilation, and a plot of multiplicity for ee vs. the scale is sqrt s, (inv. Mass of ee collisions). In pp tried sqrt of s using whole energy of incoming protons, plotted number charged particles vs this scale, for three different values of sqrt s. Points are below ee data. So, tried to correct for leading effects: A certain amt of energy doesn’t contribute, and it is taken out by leading protons. Q2 had as shown here corresponds to inv. Mass of system that was created within the detector, (one should keep in mind the sqrt s for e+e- is also inv. Mass). And when multiplicity for pp is plotted against q2had, the data lie on top pf the e+e- points So based on this study it was suggested that hadronization has universal behvior for the inv. Mass (energy). To check: is it still true in ep collision.
Energy available for particle production
Agreement between e+e- and pp plotted vs.

15. Previous Measurements: Multiplicity vs. Q in Breit frame ep DIS
Current region Breit frame multiplicity vs. Q2 (hemisphere) shown along with e+e- data (whole sphere divided by 2)
Consistent with e+e- data for high Q2  disagreement at Q2< 80 GeV2
ep has gluon radiation whereas e+e- does not– possible source of disagreement at low Q2 ??
Here we show the results of a previous ZEUS measurement of the multiplicity measured in the CRBF vs. Q2 shown as solid spheres, and multiplicity vs. sqrt s for various e+e- experiments.
You can see that
If you plot all e+e- data together as multiplicity vs cm energy(e+e-) then they nicely lie on top of each other. And assuming that current region of the BF is half of e+e-, ZEUS points can be plotted as twice the multiplicity vs. Q (thou in this plot vice-vesra). The main feature is the following; it looks as though ep multiplicity agrees with e+e- for middle region of Q but disagrees at lower values. The current studies of multiplicity at ZEUS are devoted to studies of the current and target regions and the comparisons between them. The first strp toward that end is thinking if the q2 is the proper scale to compare ep and e+e- data.
European Physics Journal C11 (1999)

16. Measurement vs. W in HCM frame
Zeitschrift für Physik C72 (1996) 573
ep DIS vs. W compared to fixed target DIS experiments and e+e- prediction similar rate of increase with W for ep and e+e-

17. Present Analysis Study energy dependence of <nch> in
photon region of HCM frame
compared to e+e-, pp and previous DIS
Breit Frame: current and target regions
expected to behave similarly to one hemisphere of e+e-: previous results show disagreement at low energies: we use total energy in current region of Breit frame as a scale for comparison with e+e-
Laboratory frame: in bins of X and Q2
Propose an alternative energy scale, the effective mass of hadronic system, Meff
compared <nch> in different regions of Breit and HCM frames for ep DIS

18. 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

19. 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

20. 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)

21. 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

22. 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)
Region of good acceptance: < η < 1.75
R= p/qB
R=mv/qB relativistic
Filled with Ar(84.3%)
CO2(8.4%)
ethane(6.8%)
ethanol(0.5%)

23. 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

24. 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

25. Modeling DIS with Monte Carlo
Hadronization Models
String Fragmentation (Lund)
Cluster Model
Event generators use algorithms based on QCD and phenomenological models to simulate DIS events
Hard subprocess: pQCD
Parton Cascade
Hadronization
Detector Simulation
correct for detector effects: finite efficiency, resolutions & acceptances
Next slide
Parton Level
Hadron Level
Detector Simulation
Factorization scale, where hadronization begins
Parton Cascades
LO Matrix Element + Parton Showers (MEPS)
Color Dipole Model (CDM)
Next slide
PDFs

26. Monte Carlo models: parton cascades and hadronization
Models for parton cascades:
Color Dipole Model:
Parton Shower Model:
Gluons are emitted from the color field between quark-antiquark pairs, supplemented with BGF processes.
cascade of partons with decreasing virtuality continuing until a cut-off
LEPTO
HERWIG
ARIADNE
Hadronization models:
Lund String Model:
Cluster Fragmentation Model:
color "string" stretched between q and q moving apart,
string breaks to form 2 color singlet strings, and so on until only on-mass-shell hadrons.
Since we are measuring the multiplicity the fragmentation and hadronization are playing an important role, therefore I would like to introduce the MC models that we are using for comparing to our data. The MC use different models for describing parton cascades and hadronization. The different parton shower models, shown here, are the Parton shower model used by LEPTO and HERWIG and the CDM used by ARIADNE. In the PS model we have cascades of partons with descreasing virtuality continuing until a cut off of around 1GeV. In the CDM gluons are emitted from the color field between quark-antiquark pairs and we have a chain of independently radiating color dipoles with the 1st dipole between the struck quark and the proton remnant. After the parton shower we have hadronization, where there is the LSM used by LEPTO and ARIADNE and CFM used by HERWIG. In the LSM hadrons are created from a color sting that is stretched between 2 quarks moving apart and in the CFM color singlet clusters of neighboring partons are formed and these then decay into hadrons. Using LEPTO, ARIADNE and HERWIG together we can check these different approaches for parton showers and hadronization.
It is interesting to remind you that the Local Hadron Parton Duality approach that doesn’t require hadronization all.
color-singlet clusters of neighboring partons formed
Clusters decay into hadrons
LEPTO
HERWIG
ARIADNE

27. 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

28. 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

29. 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.

30. 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

31. 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

32. 1996-97 Data sample Event Selection
Scattered positron found with E > 12 GeV
A reconstructed vertex with |Zvtx| < 50 cm
Scattered positron position cut: radius > 25cm
40 GeV < E-pz < 60 GeV
Diffractive contribution excluded by requiring ηmax> 3.2
Track Selection
Tracks associated with primary vertex
|| < 1.75
pT > 150 MeV
Physics and Kinematic Requirement
Q2 da > 25 GeV2
y el < 0.95
y JB > 0.04
70 GeV < W < 225 GeV ( W2 = (q + p)2 )
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)
E-pz calculated from cells
Q2da calculated from cells
Yjb calculated from cells

33. Analysis Method
This analysis: Look at final state mean charged multiplicity, <nch>, and compare to other experiments to study similarities in particle production from different initial state particles.

34. Analysis Methods: Breit Frame
Investigate cause of disagreement between ep vs. Q and e+e- at low energies look more closely at comparison of one hemisphere e+e- and current region Breit frame
ep: Split into Current and Target Region – one string two segments.
In ep we have a color field between 2 colored objects the struck quark and the proton remnant
When we use Q2 as a scale we are assuming the configuration is as symmetric as it is in e+e-, but it isn’t
This asymmetric configuration leads to migration of particles from the current region to the target region
Here you see FD with the gluon ladder, this is the current region in ep and this is the target region in ep. In other words, we have a color field between 2 colored objects, the struck quark and the proton remnant that is shown here. When we use q2 as a scale we assume the configuration is as symmetric as in e+e-, but we can see that that is not true. This assumption doesn’t work because the assymetric configuration leads to migration of particles from current region into target region. The simple example if such migration can be demonstrated here.
Breit Frame diagram

35. Current region Breit Frame Q and 2*EBreit
Soft Contribution
Hard Contribution
e+e-: whole sphere
ep: shaded region: current region of Breit frame
QCD Compton
In hard and soft processes gluon radiation occurs
These gluons can migrate to target region
Total energy in the current region of Breit frame and multiplicity are decreased due to these migrations (Q2 is not)
Effect is more pronounced for low Q2 : more low energy gluons
Must use 2*EBreit instead of Q for comparing with e+e-
We can imagine 2 major contribution of migration of particles out of the CR as comp to e+e-. 1st soft contribution because of the parton shower mechanism where the gluons in the shower are produced with certain pt, because of this pt dependence on energy of the initial quark, some partons can escape the current region, as you can see in the figure it is not a problem for e+e- where we measure the whole sphere and the total number of particles will be the same but it is certainly a problem for ep because the number of particles will decrease while the scale, q, stays the same. Another type of migration is because of hard scattering in ep cascade (the typical diagram for this is QCD compton) where we have a gluon with energy comparable to the energy of the initial quark and this is shown here, so we can here also have migrations of particles out of CR. So it means that instead of scale q we need to use a scale that describes, not the expected, but the real energy on the current region of the Breit frame. So we can use the energy of all the particles that were found in the current region, and use it as a scale to investigate our multiplicity. So if there would be no migrations E=q over 2, but in case of migrations the energy will always be smaller than that. So to make comparisons between ep and e+e- we would need to plot 2*number of particles (again because ep is only ½ hemispere) vs. 2* E in the current region of the Breit frame. It is also important to note that 2*E is Lawerence invariant, exactly as sqrt s, or q.
N < N expected
No migrations:
With migrations:

36. Monte Carlo study of
2*E/Q as a function of Q.
Lower energies: Q doesn’t accurately reflect actual energy in hemisphere.
Use 2*E as a scale for comparing to e+e-

37. Analysis Methods: photon hemishpere HCM frame
2*E/W as function of W
Difference is negligable
Want to measure dependence of <nch> on Minv as was done in Breit frame,
Migrations here are small, so
2*Ephoton = W so use
Minv = W as scale

38. Invariant Mass of Hadronic System
Measure hadronic final state within  for best acceptance in the central tracking detector (CTD)
Measure # charged tracks, reconstruct number of charged hadrons
Measure invariant mass of the system (Meff) in corresponding Δη region.
Energy is measured in the Calorimeter (CAL)
I’ll start by explaining the experimental method used for this check. We want to measure the HFS within delta eta which corresponds to region of best CTD acceptance. We measure the number of charged tracks in the CTD because we want to reconstruct the number of charged hadrons. We measure the invariant mass of the system, Meff . Meff is calculated like this, using Energy measured in the corresponding delta eta region of the calorimeter. So then we can study the dependence of the number of charged hadrons on Meff.
Used as a scale to compare: current and target regions of Breit frame current region Briet frame to photon region HCM
CAL within the CTD acceptance
Study: <nch> vs. Meff
CTD

39. Correction to hadron level: matrix
Step 1: Correction Matrix:
The matrix relates the observed to the generated distributions by:
Step 2: Correction for acceptance of event selection cuts in the bins
ρGEN :distribution with GEN level cuts
ρDET :distribution with GEN level cuts
Matrix corrects tracks to hadron level
ρ corrects phase space to hadron level

40. Correction to hadron level: matrix
Example: current region of Breit frame vs. 2*E
To illustrate average size of 1st part of correction:
Mean matrix correction factor:
range: average: ~1.2
Mean of C distributions:
range: average: ~1.02

41. Correction to hadron level: modified bin-by-bin
Part one: correct to hadron level using only hadrons generated with pT > 0.15 GeV (Detector Effects)
Part two: correct for hadrons with lower pT, using ratio of <gen> with pT cut to <gen> no pT cut in each bin.
number
distribution

42. Correction to hadron level: modified bin-by-bin
Example: lab frame vs. Meff
Average correction for detector effects: <C1,i>
range: average: ~1.1
Correction of hadrons of pT > 0.15 GeV to all hadrons
Invariant Mass correction: normal bin-by-bin method:
Average less than 2%
range: average: ~1.05

43. Acceptance correction: Current region of Breit frame:
Visible Part
Breit Frame: 95% of hadrons in current region visible in detector, only 30% of target region hadrons are visible
All Hadrons
Current Region Breit Frame
Proton remnant
Generated in visible part
Multiplied by <nch>
This plot shows the lab eta distribution of all the hadrons with the CRBF hadrons shown in blue. The vertical lines indicate the area that is visible in the detector. You can see that 90% of the CRBF hadrons are visible in the detector, where only 30% of all TRBF hadrons are visible. Can’t easily measure...

44. Acceptance correction: Photon region HCM
HCM Frame: 60-80% Photon region HCM frame contained in visible part of detector.  larger corrections.
Visible Part
All Hadrons
Photon Region HCM Frame
Proton Region HCM Frame
Correction factors for <nch> vs. W in photon region HCM frame: 1.78, 1.42, 1.26
Additional correction needed for Meff in HCM:calculated in bins of W, similar to hadron acceptance correction:
Correction factors: 2.38, 1.73, 1.45 Applied on an event by event basis
Here I show a similar plot as I showed for the Breit frame, here the total hadrons are divided into the photon and proton regions of the hadronic center of mass frame. The main advantage of the photon hemisphere is that it is well contained in our detector and our correction factors are not so big, and we can rely on our measurement.

45. Results
<nch>

46. Comparison to other <nch> measurements at HERA

47. Comparison of ep DIS <nch> to other experiments
Measurement of multiplicity dependence on 2*Ecurrent compared to previous ZEUS measurement vs. Q, and to e+e- and pp data (<nch> is multiplied by 2 for comparison)
2*E gives better description of multiplicity at lower energy
Current region understood, would also like to compare the target region of ep to e+e- but…
Explain the features of the plot…

48. bins

50. Correlated & Uncorrelated Systematics
Change
Ee’
± 1 GeV
Radius Cut
± 1cm Q2
± 2.25 GeV2
yJB
± .008
yel
± .05
Zvtx
± 15 cm
W (upper)
± 15 GeV
W (lower)
± 7 Gev
E - pz
± 2 GeV
CAL energy scale
± 3 %
Main systematics here |

51. Summary and Conclusions
HFS investigated in NC ep DIS in range 25<q2 and 70< W< 225 in terms of <nch> , the center of mass energy, and the invariant mass, Meff
1st time, lower energy data of cr Breit frame shown to agree with e+e- and pp by using 2*E as energy scale
<nch> in photon region HCM agree with e+e-
Total energy region of analysis from 2 to 200
New energy variable used for comparison between diff e regions of ep HFS
<nch> scales with Meff in the same way as 2*E in cr Breit frame, (and therefore also same as e+e-), <nch> in photon region HCM rises faster as a function of Meff than <nch> in current region BF.
<nch> in photon region HCM show no dep. On x or Q