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ON THE HIGH ORDER MULTIPLICITY MOMENTS

K. Fiałkowski, R. Wit

Jagellonian University

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Contents

• Introduction

• Data and MC for Z0 decays

• Moments for restricted PS bins

• Moments for hadrons and jets

• Conclusions and outlook

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Introduction

• Factorial and cumulant moments: Fq[n!/(n-q)!]P(n), Kq Fq-{(q-1)!/[(i-1)!(q-i)!]}Kq-iFi,

investigated usually for q<5 only.

• Pavia group (I.D.Dremin et al., PLB336): Hq Kq /Fq meaningful even for q>10; negative minimum at q=5, oscillations? Relation to NNLO pQCD?

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Data and MC for Z0 decay

• LEP-1 data: sufficient statistics, accuracy. L3 analysis (PLB 577) confirms minimum at q=5 (Fig.1).

• JETSET OK.; oscillations seen only for truncated data (0.035% off).

• PYTHIA events: as above (Fig.2); stable results for statistics >2M events (no „natural” cut - Fig.3).

• Toy model with two NBD (2/3 ratio) OK.!

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Fig.1. Hq vs q: L3 data and JETSET, a) full, b) truncated

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Fig.2. Hq vs q: PYTHIA, a) default, b) L3 parameters, +-s full, x-s truncated

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Fig.3. Hq vs q: PYTHIA, + and x from two different 1M samples, * 2M, 4M

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Moments in restricted PS bins

• CERN collider data (UA5) suggested that MD for restricted PS change smoothly with bin size: good NBD fits, n/k scaling etc. What about high order moments? Test for PYTHIA events (Fig.4): dip at q=5 disappears even for very large bins, survives only for truncated distributions! Data?

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Fig.4. H vs q: PYTHIA, limited PS bins, a)full, b) truncated

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Moments for hadrons and for jets

• pQCD predictions for gluons, not hadrons. Are the data similar for hadrons and „small” jets defined e.g. by PYCLUS? Test for PYTHIA events (Fig.5) negative: minimum shifts to q=4 even for very small jets. Counting neutrals or positive only destroys or shifts the minimum (Fig.6). Extending LPHD unjustified?

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Fig.5. Hq vs q: PYTHIA, jets a) from 1.11.5 charged, b) 1.32 stable hadrons

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Fig.6. Hq vs q: PYTHIA, +-s charged, x-s all, *-s positive hadrons

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Conclusions and outlook

• Analysis of PYTHIA events for Z0 decays in terms of Hq moments for high q:

• confirms agreement with data for full PS,

• shows stability of results for >2M events,

• suggests interesting features for PS bins,

• questions validity of extended LPHD,

• shows importance of charge conservation.