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

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

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

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

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

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

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)

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 .

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

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)

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.

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

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 96-07 data. Can possibly improve this measurment by measuring diff distrib.

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

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.

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

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.)

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 ≈ 0.45. Consistent with published results. Photon axis variables poorly determined NNLO Resummed calculations give better results than NLO + power correction only, with αs ≈ 0. 118, 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)