New Analysis of Cumulant Moments in e+e− Collisions by SLD Collaboration by Truncated Multiplicity Distributions

Newly reported normalized cumulant moments of charged particles in ee collisions by the SLD collaboration are analyzed by the truncated modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Calculated result by the MNBD describes the oscillatory behavior of the data much better than that by the NBD. PACS number(s): 13.65.+i, 34.10.+x Normalized cumulant moments of negatively charged particles and charged particles obtained from the data in ee collisions were analyzed by the truncated modified negative binomial distribution (MNBD) in [1]. Those moments show oscillatory behaviors as the rank of the moment increases, and are well described by the MNBD. The preliminary data of cumulant moments normalized by factorial moments, Hj (j = 1, 2, · · ·) of charged particles reported by the SLD Collaboration at √ s = 91 GeV were also analyzed in [1]. The SLD did not explicitly show us the multiplicity distribution. Therefore, we calculated Hj moments using the observed values of the average charged multiplicity, C2 moment, and the maximum of the negatively charged particles nmax = 27. The data were only qualitatively explained by our calculation. Recently, the new data for the Hj moments are reported by the SLD [2] and [3]. In this brief report, they are re-analyzed by the MNBD. The MNBD is given by P (0) = (1 + r1) N (1 + r2) N , P (n) = 1 n! ( r1 r2 )N N ∑ j=1 NCj Γ(n+ j) Γ(j) ( r2 − r1 r1 )j r 2 (1 + r2) n+j , n = 1, 2, · · · , (1)