1. Recent results on multiplicity from ZEUS
Michele Rosin
on behalf of the ZEUS Collaboration
University of Wisconsin, Madison
DIS 2005, Madison WI
April 29, 2005

2. e+e- & ep : Breit Frame DIS event
Use Breit frame to compare multiplicity for ep to e+e-
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
The aim of this study is to measure the dependence of the mean charged ep multiplicity and compare to other experiments including e+e-. In order to directly compare the two experiments one must move into the Breit frame, which has been described several times by other speakers. It is defined using this equation, and the main feature is that the current region of the BF is analogous to one hemisphere of an e+e- interaction.
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

3. Measurement vs. Q in Breit Frame
Current region Breit frame multiplicity vs. Q (hemisphere) shown along with e+e- data (whole sphere divided by 2)
Consistent with e+e- data for high Q2
ep has gluon radiation whereas e+e- does not– source of disagreement at low Q2 ??
Idea of current analysis: Understand current and target multiplicity and compare to e+e-
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)

4. 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: In the hard collision between the photon & quark only 1 final quark is produced, so the 2nd quark on the diagram is the incoming one
current region of Breit frame for ep similar to one hemisphere of e+e-
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

5. 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

6. Gluon radiation, 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:

7. <nch> vs. 2*Ecurrent
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…

8. Visible multiplicity in Breit frame
Visible Part
…comparing the target region is not possible:
Breit Frame: 90% of hadrons in current region visible in detector, only 30% of target region hadrons are visible
Can’t easily measure target hadrons, but these are a huge portion of the produced hadrons which we would still like to study
Need some other way to investigate these particles
All Hadrons
Current Region Breit Frame
Proton remnant
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...

9. Hadronic center of mass frame
Hadronic center of mass energy is W
Ecms
Nphoton region =W E
Ecms/2
Nproton region p g*
Nphoton region vs W
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.

10. Visible multiplicity in HCM frame
Visible Part
HCM Frame: Photon region dominated by contribution from target region of Breit frame (~80% of visible hadrons)
Photon region HCM frame well contained in visible part of detector
Photon Region HCM Frame
All Hadrons
Proton Region HCM Frame
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.

11. Multiplicity vs. W in HCM
Measurement of Multiplicity in photon region of HCM frame vs. W.
Both Lepto and Ariadne describe the data: last bin slightly above
Like to compare current region Breit frame and photon region HCM frame to e+e-
Must multiply <nch> by 2 because both measurements are for hemispheres and e+e- is total sphere

12. Multiplicity in current region of Breit and HCM frames compared to e+e- and pp
Measurements in current region of Breit frame and photon region of HCM frame multiplied by 2.
There is agreement with e+e- at low and high energy and with the pp results which are plotted vs. √q2had (the scale with the leading particles removed)
the HCM prediction has been extended to lower energies where a measurement isn’t possible (region is outside detector acceptance) and it agrees with all the points at low energy
One can also measure <nch> vs. the invariant mass of the corresponding hadronic system. Measure only what is visible in detector & minimize effect of acceptance correction
You see the mc pred for the W behovior can be prolongated to lower energies, where we can make a measuremtn bec it lies outside the acceptance of our det. And it will also agree with allthe points at low energy.

13. 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 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.
CAL within the CTD acceptance
Study: <nch> vs. Meff
CTD

14. Lab frame: <nch> vs. Meff in x bins
Plot shown previously at ICHEP 2004
Lab frame multiplicity vs. Meff, shown in 4 x bins, with Ariadne predictions.
x range split into similar bins as in previous multiplicity paper.
weak x dependence in both data and Monte Carlo observed.
Q2 dependence? => next slide
Here I show a plot that was previously shown at ICHEP 2004, of the dependence of the mean charged multiplicity on Meff in 4 bins of X, along with the Ariadne predictions

15. Lab frame: x and Q2 bins Data described by ARIADNE
LEPTO slightly above data
No Q2 dependence observed
Here we have further divided the phase space into 3 Q2 bins. So X is increasing as you move to the right, and q2 increases as you move up. Data for each bin is shown with predictions from both lepto and ariadne. Lepto is slightly above the data. No q2 dependence is observed

16. Summary
For the 1st time, the measurement of mean charged multiplicity had been extended to a higher energy scale than previously measured in ep collisions.
Measurement in current region of the Breit frame shows similar dependence to e+e- if 2*Ecurrent is used as the scale
The same dependence is observed for the photon region of the HCM frame vs. W.