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ON THE HIGH ORDER MULTIPLICITY MOMENTS

ON THE HIGH ORDER MULTIPLICITY MOMENTS. K. Fiałkowski, R. Wit Jagellonian University. Contents. Introduction Data and MC for Z 0 decays Moments for restricted PS bins Moments for hadrons and jets Conclusions and outlook. Introduction.

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ON THE HIGH ORDER MULTIPLICITY MOMENTS

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  1. ON THE HIGH ORDER MULTIPLICITY MOMENTS K. Fiałkowski, R. Wit Jagellonian University

  2. Contents • Introduction • Data and MC for Z0 decays • Moments for restricted PS bins • Moments for hadrons and jets • Conclusions and outlook

  3. 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?

  4. 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.!

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

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

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

  8. 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?

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

  10. 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?

  11. Fig.5. Hq vs q: PYTHIA, jets a) from 1.11.5 charged, b) 1.32 stable hadrons

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

  13. Conclusions and outlook • Analysis of PYTHIA events for Z0 decays in terms of Hqmoments 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.

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