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. Outline
Introduction and motivation

3. HERA description & DIS kinematics
920 GeV p+ (820 GeV before 1999)
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 of photon
Fraction of p momentum carried by struck parton
Inelasticity 0 ≤ y ≤ 1

4. e+e- & ep : Breit Frame DIS event
Breit Frame definition:
“Brickwall frame” incoming quark scatters off photon and returns along same axis.
The hadronization products are in the current region
Current region of Breit Frame is analogous to e+e-.
Lab Frame
Breit Frame
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)
Breit Frame

5. Hard and soft processes
??? Maybe don’t need. Don’t have only hard production havea good device to investigate features of soft prod. Like frag & hadroniz canactuall study by analyzing the energy flow in the det multiplicity & e.s.
Investigating QCD using Multiplicity and Event shapes

6. Mean multiplicity: e+e- and pp
To be done in ee and pp one observed this universal behavior of multiplicity explain how did they go, in ee 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. Points are below ee data. So, tried to correct for leading effects: certain amt of energy doesn’t contribute to hadronizatation, taken out by leading protons. Q2 hard = sqrt e init – e out,^2. 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). so based on ee study it was suggested that hadronization has universal behvior for their inv. Mass (energy) was inport. To check: is it still true in ep collision.

7. Motivation for the use of Meff as energy scale
Analogous to the pp study: want to measure the dependence of <nch> of on the total 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. energy available for hadronization is universal, can compare to pp data
Use Meff as scale for comparing to pp (and e+e-)
Meff
Lab Frame
Then it would be natural to repeat this measurement. in zeus det., one should keep in mind because of the high boost in the proton direction, the proton remnant and some part of the string will escape down the beam pipe undetected. We can determine only a fraction of the string, but assuming that nch vs. energy allowed for hadronization should be universal, we can be allowed to compare to pp data . Method has advantage:. We are working with visible part of the string, and if something happens not immedialtley near the proton it should be universal.
-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 it’s total invariant mass.
-Because of the high boost in the proton direction, the proton remnant and a fraction of the string escape down the beam pipe. So we can’t measure the TOTAL invariant mass of the ep system, We can measure the energy available for hadronization, (which for pp collisions is the tot. inv. Mass) We measure the energy available for hadronization in our detector 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

8. Comparison of multiplicity for ep, with e+e- & pp
mean charged multiplicity, <nch>, vs. energy available for hadronization for 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)
<nch> vs. Q for ep in current region of Breit frame agrees with e+e- and pp data, for high Q
Show 1995 measurement, now it is observed that number of charged hadrons for same amount of energy is higher than for ee and pp, there might be few explanations for excess: for example, diff contribution from gluons, HERA can reach a smaller x than pp. So then it would be interesting to compare to LEP data (high energy) which should have contribution from gluons.

9. Compare to LEP data
LEP data at higher energy: should have contribution form gluons
Can’t conclude from this plot, it seems both ep and pp data could meet LEP points
Working on improving this measurement using more statistics, and spitting data into x and Q2 bins
New results should be ready for ICHEP 2004; might lead to a better conclusion
Lep points are added, and based on this data can’t say exactlly, seems both could meet lep data, other hand, zeus did meas in cr bf. Think that the ene that goes into the cr is prop to the q , nch prod in cf plotted a fun of q lies on top of ee and pp. same meas showed that in temrs of q, for the same events higher multiplicity in the target region then in the cr.conc, that s why it is imp to continue study with higher stat and to show new results at ichep, aiming to show here, but too early.

10. Study Hadronization using Event Shapes
Event shape variables measure aspects of the topology an event’s hadronic final state
Event shapes in DIS should allow investigation of QCD over a wide range of energy scales, but hadronization corrections are large for these variables
Power Correction model seeks to describe the effect of hadronization on these variables
Event shape analysis is done in Breit Frame
Measure event shapes in the Breit frame, where you have the larges possible separation between proton and scattered quark.

11. Power corrections: an analytical approach
Power correction reduces hadronization corrections for any infrared safe event shape variable, F
Mean event shape variables are sum of perturbative and non-perturbative parts
The non-perturbative power corrrection is based on two parameters, α0 and αs
Used to determine the hadronization corrections
Idea behind pc mean shape varibales is sum of mean es variables at lev of pertab (parton level) + hadronization caclculated analytically with this for. 2 parameters inthis model, ao as, where ao is non pert free papameter
“non perturbative parameter”
-(Dokshitzer, Weber Phys. Lett. B 352(1995)451)

12. Event Shape Variables Thrust Thrust: longitudinal momentum sum
n for TT axis
Photon axis = n : T
Thrust
Thrust: longitudinal momentum sum
Broadening: transverse momentum sum
Both measured with set to the Thrust axis and Photon axis
Another way es studies, dis of energy, introduce variables, thrust, broadening, cparam, and jet mass.
Thrust: Linear columnation of hadronic system along a specific(“thrust”) axis. 4 thrusts in DIS Tz, TM, Tm, and Tc depending on the axis.
Broadening: Broadening of particles in transverse momentum w.r.t. thrust axis. Can range from 0<B<0.5, where for columnated events values of B tend toward min, and for isotropic events B tends toward max. Two types of broadening: Bw, Bt
Jet Mass and C parameter are correlations of pairs of particles, and are indepandant of the axis. C parameter varies between 0 and 1 and like broadening tends toward 0 for colimated events and towards the max for isotropic events.
Jet Mass and C parameter: correlations of pairs of particles
Sum over all momenta in Current Region of Breit Frame

13. Mean event shape variables
NLO + Power correction fits to means plotted 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
Take a plot in bins of x and q2, to get eff & pur of method at certain level, in each bin the pred was fittted..kink: artificial, two lines, two x regions, other ways overload the plot, because there you have two points that differ, not a fit, every point was corrected simultan. Now fitting all points simul for diff variable sget a0 and as, show data presented to dis04,

14. Extraction of αs and α0 from NLO + PC fits to means
Not all variables give same αs and αo.
1 – Tγ fit poorly defined -large systematic errors
Show as famous plot, ask adam for title, concl. Not all variab give same as and a0 have some vars not well described.

15. Differential distributions
NLO+PC Fits to Differential Distributions
Try to improv our unders using dv. Show sh slide 7, and explain in words,
Fit differential distributions over a limited range
Usable range increases with Q2,
Try to improve our understanding using differential distributions
Power correction is interpreted as a
‘shift’ in the NLO distribution

16. Extraction of αs and α0 from fits to differential distributions
Photon axis variables fit with high αs, but other variables consistent in αs and αo
Fits αo somewhat high compared to that from means
Method a little unstable, try adding NNLO effects- resummations
As and ao once more, exracted usng diff dist, page 10 od stevens talk, makes a big diff, a0 went down by fact of somehow this methof isnt stable, need to add nnlo effects, resummations, so we tried to fit dd+nnlo+resummat+pc

17. Differential distributions: with resummation
NNLO+NLO+PC Fits to Differential Distributions
Page 12 of sh, helps describe beter the behavior of nlo, make the hope that the fitting procedure is better, enlarged range of fit,
Behavior of NLO better described, possible fitting procedure is better
Enlarged range of fit

18. Extraction of αs and α0 from fits to differential distributions
C is consistent in αs but low in αo. C result very sensitive to fitted range: under investigation
Results consistent with αs = and suggest α0 ≈ 0.5.
Sh slide 15, as and ao again, now ao comes backto where it was, as is unique, some pron with c param under investigation,

19. 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