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. 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)

5. 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-
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

6. 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

7. 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:

8. <nch> vs. 2*Ecurrent
Measurement of multiplicity dependence on 2*Ecurrent compared to previous ZEUS measurement vs. Q
2*E gives better description of multiplicity at lower energy
This approximation of invariant mass partially takes into account the real distribution of the particles.
Lepto prediction slightly above Ariadne
Current region understood, would like to use some energy scale to compare target region for ep to e+e-..

9. Visible multiplicity in Breit and hadronic center of mass (HCM) frames
Visible Part
Breit Frame: 90% of hadrons in current region visible in detector, only 30% of target region hadrons are visible
Need some other way to investigate these particles
All Hadrons
Current Region Breit Frame
Proton remnant

10. Hadronic center of mass frame
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

11. Visible multiplicity in Breit and hadronic center of mass (HCM) frames
HCM Frame: We see a bigger number of particle in the detector than in the current region of the Breit frame
Photon region dominated by contribution from target region of Breit frame (~80% of visible hadrons)
Proton region unseen in detector
Using HCM is intuitive because all interactions in e+e- and pp happen in center of mass frame
Visible Part
All Hadrons
Current Region Breit Frame
Proton remnant
Visible Part
All Hadrons
Photon Region HCM Frame
Proton Region HCM Frame

12. Multiplicity vs. W in HCM
Measurement of Multiplicity in photon region of HCM frame vs. W.
Lepto prediction slightly above that for Ariadne.
Interesting to multiply the multiplicity measured in both the current region of the Breit frame and the photon region of the HCM frame by 2 (there are 2 hemispheres) and compare to e+e-

13. 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. a scale that takes into account the leading particles.
Would also like to make a measurement vs. invariant mass, where we measure visible multiplicity and plot it vs. visible energyless model dependence.

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. Lab frame: <nch> vs. Meff in x bins
Lab frame multiplicity vs. Meff, shown in 4 xbins, with Ariadne predictions.
x range split into similar bins as in previous multiplicity paper.
weak x dependence in both data and MC observed.
Q2 dependence? => next page

16. Lab frame: x and Q2 bins Data described by ARIADNE
LEPTO slightly above data
No Q2 dependence observed

17. Summary
The mean charged multiplicity has been investigated in DIS ep scattering
Measurement in current region of the Breit frame show similar dependence to e+e- if 2*Ecurrent is used as the scale, the same dependence is obs for the pho reg of hcm fra vs W.
The mean ch multi in the lab frame has been also meas vs. inv mass of resp hadronic system. There is a weak x depen, and almost no Q dep were observed.