1. Study of Multiplicity and Event Shapes using ZEUS detector at HERA
Michele Rosin
University of Wisconsin, Madison
on behalf of the ZEUS Collaboration
QFTHEP 2004
June 17th

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
Virtuality of photon
Fraction of p momentum carried by struck parton
Inelasticity 0 ≤ y ≤ 1

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. Hard and soft processes
In any reaction we have contribution from hard process that is well described by perturbative QCD. And big contribution from the soft process that should be described by non preturbative effects like hadronizaton. In this sence the multiplicity and event shape studies give us a good tool to study non perturbative effects, in first case we study no. of charged particles and 2nd case study energy flow.
Hard processes: perturbative QCD
Soft processes: (hadronization) non-perturbative QCD

5. Multiplicity e+e- and pp
pp vs. √q2had
pp vs. √spp pp
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.
Invariant mass of pp
Agreement between e+e- and pp plotted vs. pp invariant mass

6. Motivation for the use of Meff as energy scale
Analogous to the pp study: want to measure the dependence of <nch> of on the invariant mass of the system
Boost in proton direction => proton remnant & fraction of string escape down the beam pipe
Can measure only a fraction of string: assume <nch> vs. invariant mass is universal, can compare to pp data
Use Meff as a scale
Meff
Lab Frame
-Then it would be natural to repeat this measurement for ep using the ZEUS detector.
-Analagous to the pp study, we would want to measure the dependence of the mean charged multiplicity on the invariant mass of the system.
-Because of the high boost in the proton direction, the proton remnant and a fraction of the string escape down the beam pipe. We measure the energy available for hadronization in our detector only where tracking efficiency is maximized using this formula and refer to it as the Effective Mass.
-So If you assume that mean charged multiplicity vs. the energy available for hadronization is universal then we can use the Effective Mass as a scale for comparing to pp and e+e- data.
Meff: HFS measured in the detector where the tracking efficiency is maximized

7. Comparison of multiplicity for ep, with e+e- & pp
mean charged multiplicity, <nch>, for different energy scales: e+e- (√s), pp (√q2) and ep (Meff)
Excess in <nch> observed for ep data
Possible explanations: Different contributions from gluons (HERA can reach smaller x than pp)

8. Compare to LEP data
LEP data at higher energy: should have contribution from gluons
Can’t conclude from this plot, it seems both ep and pp data could meet LEP points
<nch> vs. Q for ep in current region of Breit frame agrees with e+e- and pp data, for high Q
Working on improving this measurement using more statistics, and spitting data into x and Q2 bins, in current and target region aiming for new results for ICHEP 2004.
With present errors of measurement, one can’t easily conclude that our ep measurement will meet the LEP data
On the other hand, there is a set of point measured in the BF vs. Q, these points lie on top of pp and ee .

9. Study Hadronization using Event Shapes
Event shape variables measure aspects of the topology of the hadronic final state
Event shapes in DIS should allow investigation of QCD over a wide range of energy scales, though hadronization corrections are large for these variables
Power Correction: analytical calculation suggested by Dokshitzer & Webber to describe the effect of hadronization for these variables
Event shape analysis is done in current region of the Breit frame

10. Power corrections: an analytical approach
Power correction is used to calculate hadronization corrections for any infrared safe event shape variable, F
Mean event shape variables are sum of perturbative and non-perturbative (power correction) parts
The power correction depends on two parameters, α0 and αs
Used to determine the hadronization corrections
Try to develop non-perturbative QCD model
“non-perturbative parameter”
-(Dokshitzer, Webber Phys. Lett. B 352(1995)451)

11. Event Shape Variables Thrust Thrust: longitudinal momentum sum
n for TT axis
Photon axis n : T
Thrust: longitudinal momentum sum
Broadening: transverse momentum sum
Measured with n set to the thrust axis, and photon axis
Jet Mass and C parameter: correlations of pairs of particles
Sum over all momenta in current region of Breit frame.
Now I will introduce the event shape variables used in this analysis. Start with thrust. In the BF, the thrust maximizes the longitudinal momentum sum of all the hadrons and will define a thrust axis as shown in the figure. Together with thrust with respect to thrust axis, TT, we also define Tg w.r.t the photon axis. Same as for the broadening, which should maximize transverse momentum sum, and is measured w,r,t to the thrust and photon axis. And also have M2 and C parameter that are axis independent, and describe correlation between pair of particles.

12. Mean event shape variables
NLO + Power correction fits to means measured in bins of X and Q2
High x points (open circles) not fitted
All variables fitted with a good χ2
Photon axis variables (1-Tγ) show large x-dependence
1-Tγ correction very small and negative
Model describes data well
Fit each variable seperately, all points simultaneously.
The effect of the PC is quite significant except for gamma variables., So you are able to extract parameters ao and as from the fits

13. Extraction of α0 and αs from NLO + PC fits to means
Not all variables give same αs and αo.
1 – Tγ fit poorly defined -large systematic errors
Extracted parameters: αo≈ 0.45, αs≈0.12
The data are consistent with previous pub based on data. Can possibly improve this measurment by measuring diff distrib.

14. Differential distributions
NLO+PC Fits to Differential Distributions
NLO doesn’t predict the shape and because of this can’t use the whole range to fit to NLO+PC. So fit only the range where the description is good.
Try to improve our understanding using differential distributions
Power correction is interpreted as a
‘shift’ in the NLO distribution

15. Extraction of α0 and αs from fits to differential distributions
Photon axis variables fit with high αs, but other variables consistent with each other in αs and αo
Fits αo somewhat high compared to that from means
Extracted parameters: αo≈ 0.65, αs≈ 0.12
Method a little unstable, try adding NNLO effects- resummations
Method is unstable because the data is not well described by the NLO, one way to improve the desc, is to include the NNLO contrib, using resummaton technique.

16. Differential distributions: with resummation
NNLO+NLO+PC Fits to Differential Distributions
Calculation describes data better; able to enlarge range of fit

17. Extraction of α0 and αs from fits to differential distributions
C is consistent in αs but low in αo. C result very sensitive to fitted range: under investigation
α0 consistent with results from fit to means. Extracted parameters: αo≈ 0.118, αs≈ 0.5
For C parameter we have problems with NLO (doesn’t describe data and also shows non-physical behaviours.)

18. Summary Showed results for two methods of investigating hadronization:
Multiplicity:
Mean charged multiplicity vs. effective mass was measured for ep and compared to e+e- and pp. Multiplicity shows excess in data for ep.
Current study aiming for higher precision using new data
Event Shapes:
NLO + power correction has been fitted to the mean event shape data, αs ≈ 0.12, α0 ≈ Consistent with published results. Photon axis variables poorly determined
NNLO Resummed calculations give better results than NLO + power correction only, with αs ≈ , α0≈0.5. Resummation gives consistent αs,αo for all event shape variables, but C fit dependant on range
Current investigation of new event shape variables & new methods. (Kout for events with 2 or more jets, 2 jets can fix the NLO predictions better)