1. Recent results on multiplicity from ZEUS
Michele Rosin
University of Wisconsin, Madison
on behalf of the ZEUS Collaboration
Hadron Structure 2004
September 1, 2004

2. HERA description & DIS kinematics
920 GeV p+ (820 GeV before 1998)
27.5 GeV e- or e+
318 GeV cms (300 GeV)
Equivalent to a 50 TeV Fixed Target
DIS Kinematics:
DESY Hamburg, Germany
ZEUS H1
remnant
e(k)
e’(k’)
p(P)
  (q) q’
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
Inelasticity 0 ≤ y ≤ 1
Virtuality of photon
Fraction of p momentum carried by struck parton

3. e+e- & ep : Breit Frame DIS event
Breit Frame definition:
“Brick wall frame” incoming quark scatters off photon and returns along same axis.
Current region of Breit Frame is analogous to e+e-.
Lab Frame
Breit Frame PT
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)
Breit Frame PL

4. 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

5. Local Parton-Hadron Duality
Local Parton Hadron Duality (LPHD): cut off parton shower at mass of pion, distribution of final partons is same as final hadrons.
Successful concept for most inclusive observables (e+e-, ave. multiplicities, single particle inclusive spectra)
Attempt to check LPHD using Normalized Factorial Moments: (NFM)
The idea is to reduce the cut off of the parton shower to the pion mass, and this model predicts that the distribution of final partons is the same as final hadrons. The model has been successful in describing most inclusive observables. So an attempt was made to compare the predictions of the LPHD using NFM. Where particle multiplcities are studies in terms of NFMs for a specified phase space region Omega. More information on NFMs can be found in this article.
So we compare the data to ARIADNE MC with large parton shower cut off and hadronization and ARIADNE MC with low parton shower cut off and no hadronization.
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.
Particle multiplicities are studied in terms of NFMs for a specified phase space region of size Ω.
Compare data to MC with and without hadronization
Phys. Lett B 510 (2001) 36-54

6. Factorial Moments vs. pT
Multiplicity moments of order q=2,…,5 in current region of Breit frame
LHPD doesn’t describe our data in soft part of the spectrum
Understanding hadronization is essential
Here it is found that if you use quantities that are also fully inclusive but done at low momentum, then some descrepencies are observed.
Here you see NFM distributions vs. pt. Here is the FM of 2nd order vs. pt of final partons. This line is Ariadne with hadronization and this like is the parton level mc. One can see a disagreement between the data and the paron level model that is pronounced in soft part of spectrum at low pt. One expects this momentum close to 1 if distribution is poisson-like, and the LPHD approach predicts that this FM goes to 1 at low pt and this is not supported by the behavior of the data. Another interesting multiplicity study was an attempt to study difference between the current and targer regions of the Breit frame
Pt cut restricts the transverse momentum to pt< ptcut. (The omega of the previous formula) The maximal transverse mom. And the pt values are
Defined with respect to the direction of this quark.
Parton level mc (ari without hadronization) consistant with analytical qcd predictions.
data, 38 pb-1
Q2>1000 GeV2

7. Multiplicity in Current and Target regions of Breit Frame
Measurement of multiplicities in Breit Frame vs. Q2
Ratio of mean multiplicities in current and target regions vs. Q2 show higher multiplicity in target region.
Is Q2 the proper scale for target region?
Behavior described by MC
Plotted here is ratio of multiplicity in target region to multiplicity in current region vs. q2. It is obvious that the multiplicity in target region is around 4 times larger than in the current region and the ratio is decreasing with Q2, but we don’t know if q2 is proper scale to describe the target region. nevertheless this behavior is described by Monte Carlo. Comparing this measurement for the current region of the Breit frame with e+e- we get an interesting result…
data, 38 pb-1
Q2>10 GeV2

8. European Physics Journal C11 (1999) 251-270
Measurement vs. Q
Consistent with e+e- data for high Q2
Disagreement at low Q2 may be attributed to gluon radiation
Idea of current analysis: Understand current and target multiplicity and compare to e+e-
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. Currently studies of multiplicity at ZEUS are underway and just presented in ICHEP which 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)

9. Multiplicity: ep vs. e+e- (1)
e+e-: boson with virtuality √s produces 2 quarks & hadronization is between 2 colored objects q and q
ep: boson with virtuality Q produces 1 quark: the 2nd quark comes from the interaction between the photon and the proton
current region of Breit frame for ep similar to one hemisphere of e+e-
If we use Q as scale to compare to e+e-, multiply hadrons by 2
Here you see the diagram that we use to describe the current region of BF to see correspondence btween e+e- and ep. What happens after e+e- annihilation is that a virtual boson is produced with virtuality sqrt s that produces, in LO, 2 quarks and the hadronization takes place between 2 colored objects, q and qbar, to produce the final state. In ep have a virtual boson with vituality Q, that produces 1 quark, because the 2nd q is coming from the interaction between photon and proton. The current region of the Breit frame for ep is similar to one hemisphere if e+e-, so if we are using Q as a scale for comparing to e+e- we multiply the multiplicity by 2

10. Multiplicity: ep vs. e+e- (2)
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

11. Gluon radiation, Q, and 2*EBreit
Soft Contribution
Hard Contribution
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 and 2*Nch 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:

12. Multiplicity vs. 2*Ebreit
Measure multiplicity dependence on 2*EBreit and compare to previous ZEUS measurement vs. Q, and to e+e-
Points agree with the e+e- points
This approximation of invariant mass partially takes into account the real distribution of the particles.
Current region understood, would like to use some energy scale to compare target region for ep to e+e-..
Now we see that our points agree with e+e- points. This approx is much better than used previously in ‘99 publication where they used q, because it partially takes into account the real distribution of the particles. Now that we have understood the current region of ep collision and have good agreement with e+e-, we would like to use some energy scale to compare target region for ep to e+e-. Let me remind you that previously it was observed that the multiplicity in e+e- and PP collision exhibit the same energy behavior if measured using proper energy scale.

13. Multiplicity e+e- and pp
pp vs. √q2had
pp vs. √spp pp
For example, here is e+e- annhilation, and on 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.
Invariant mass of pp
Agreement between e+e- and pp plotted vs. pp invariant mass

14. Charged Hadrons & Effective Mass: experimental method
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 delta eta 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.
CAL within the CTD acceptance
Study: <nch> vs. Meff
CTD

15. The use of Meff as energy scale
Previously shown in e+e- and pp that the number of charged particles vs. invariant mass of the system is universal
For ep in lab frame, measure visible part of <nch> vs. visible part of energy available for hadronization: Meff
Whad
Meff
Lab Frame
Visible part
So for the ep in the lab frame we want to try to repeat what was done in the pp measurement. The only difference between ep and pp being that ep is more asymmetrical. Here you see a schematic for ep scattering together with hadronization. We effectively cut out part of the final state, and measure number of charged particles there along with the corresponding invariant mass. It was previously shown in e+e- and pp that the num of particles vs. the inv mass of the system is universal, So for ep we will measure multiplicity vs. this effective mass in order to try to reproduce as closely as possible the method used in pp.
Meff: HFS measured in the detector where the tracking efficiency is maximized

16. Detector acceptances for current and target regions
The visible part of the multiplicity is very different for the current and target region of the Breit Frame.
Visible Part
Observed portion of hadrons from total number generated is 90% for current region & only 30% for target region.
When comparing visible part of the current and target regions we compare total current region with only the part of the target region that is far from the proton remnant
This visible part of the multi is very diff for the current and target regions of the Breit frame. The acceptance of the detector with all our cuts is more than 90% for current region, but we observe only 1/5 of the total multiplicity of the target.region So when we compare the visible part of the current and target regions we have to keep in mind that we compare the total current region with only the part of the target region that is quite far from the proton remnant. (since the proton remnant corresponds to very high pseudorapidity)
Proton remnant

17. Previous results in lab frame: <nch> vs. Meff
1995 preliminary results
<nch> plotted vs. Meff for ep, vs. qhad for pp and vs. √s for e+e-.
<nch> for ep is ~15% higher than that for e+e- and pp.
Investigate this difference: look at visible charged multiplicity vs. Meff for current and target regions of the Breit frame.
Keep in mind that I have just shown that the current region of the Breit frame for ep reproduces the e+e- multiplicity well. We are trying to understand what makes the difference in multiplicity between ep and e+e- & pp when we plot using Meff as a scale. So lets look at visible charged multiplicity vs. effective mass for current and target regions of the Breit frame.

18. Breit frame vs Meff
Similar dependence in multiplicity for visible parts of current and target regions of the Breit frame as a function of their respective effective mass
Target multiplicity is higher than current multiplicity and can reach higher values of Meff
combined current and target region show same behavior as target region
Multiplicity and Meff are Lorentz invariant so can move to the lab frame
See here is comparison between multiplicity of current and target regions of the Breit frame vs. effective mass.1st bullet. The target multiplicity go to higher values and it would go even farther if we would be able to see whole tr but this is only the part that we observe in our detector. Clearly, the combined cr and tr multiplicity (black points) behaves in the same way. And the combined multiplicity ismainly dominated by the target, shown here as black dots. Now we can use the fact that the number of charged hadrons and eff mass are both Larence invariant. to move to the lab frame because the number of hadrons vs eff mass should behave in same way, ( visible breit is equal visible lab) now we try to investigate the behavior of the multiplicity in the lab frame in terms of x and q2.

19. Current lab frame measurement
Agreement between data and ARIADNE
LEPTO also describes data but when including the soft color interactions LEPTO-SCI deviates from data
Say a few words about comparison to mc, agreemet to ari is better than lep, and lep w sci doesn’t desc data.then x and q2 beh from prev
SCI : additional contamination from diffractive exchange. Doesn’t ingeneral describe our multiplicity data people are trying to improve it.
data, 38 pb-1
Q2>20 GeV2

20. Lab frame: <nch> vs. Meff in x bins
Would also like to study x and Q2 dependence
x range split into similar bins as in previous multiplicity paper.
weak x dependence in both data and MC observed not sufficient to explain difference
Q2 dependence? => next page

21. Lab frame: x and Q2 bins Data described by ARIADNE LEPTO above data
No Q2 dependence observed
Dependence of the <nch> on Meff doesn’t change with x & Q2 enough to explain observed difference between ep and e+e-

22. Summary
The hadronic final state has been investigated in DIS ep scattering in terms of the mean charged multiplicity and respective invariant mass of the charged and neutral particles, Meff
Measurement in current region of the Breit frame show same dependence as e+e- if 2*Ecurrent is used as the scale
Similar dependence observed in multiplicity for visible part of the current and target regions of the Breit frame as a function of their respective effective mass
Lab frame measurements show no strong dependence on x or Q2
Full comparison of current and target region is still underway, the main problem being that visible part of the target region is only 30% of the total, and MC studies expect that the multiplicity behavior changes when we go closer to the proton remnant.