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

2 Contents Introduction Data and MC for Z 0 decays Moments for restricted PS bins Moments for hadrons and jets Conclusions and outlook

3 Introduction Factorial and cumulant moments: F q  [n!/(n-q)!]P(n), K q  F q -  {(q-1)!/[(i-1)!(q-i)!]}K q-i F i, investigated usually for q<5 only. Pavia group (I.D.Dremin et al., PLB336): H q  K q /F q meaningful even for q>10; negative minimum at q=5, oscillations? Relation to NNLO pQCD?

4 Data and MC for Z 0 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. H q vs q: L3 data and JETSET, a) full, b) truncated

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

7 Fig.3. H q 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. H q vs q: PYTHIA, jets a) from 1.1  1.5 charged, b) 1.3  2 stable hadrons

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

13 Conclusions and outlook Analysis of PYTHIA events for Z 0 decays in terms of H q 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.