KNO scaling 30 years later

KNO scaling, i.e. the collapse of multiplicity distributions P_n onto a universal scaling curve manifests when P_n is expressed as the distribution of the standardized multiplicity (n-c)/lambda with c and lambda being location and scale parameters governed by leading particle effects and the growth of average multiplicity. At very high energies, strong violation of KNO scaling behavior is observed (p-pbar) and expected to occur (e+e-). This challenges one to introduce novel, physically well motivated and preferably simple scaling rules obeyed by high-energy data. One possibility what I find useful and which satisfies the above requirements is the repetition of the original scaling prescription (shifting and rescaling) in Mellin space, that is, for the multiplicity moments' rank. This scaling principle is discussed here, illustrating its capabilities both on model predictions and on real data.Comment: 8 pages LaTeX, 9th Int. Workshop on Multiparticle Production, Torino, Ital

Scaling Laws in Hierarchical Clustering Models with Poisson Superposition

Properties of cumulant- and combinant ratios are studied for multihadron final states composed of Poisson distributed clusters. The application of these quantities to ``detect'' clusters is discussed. For the scaling laws which hold in hierarchical clustering models (void scaling, combinant scaling) a generalization is provided. It is shown that testing hierarchical models is meaningful only for phase-space volumes not larger than the characteristic correlation length introduced by Poisson superposition. Violation of the scaling laws due to QCD effects is predicted.Comment: 14 pages, Plain TeX, no figure

A Bose-Einstein Model of Particle Multiplicity Distributions

A model of particle production is developed based on a parallel with a theory of Bose-Einstein condensation and similarities with other critical phenomena such as critical opalescence. The role of a power law critical exponent tau and Levy index alpha are studied. Various features of this model are developed and compared with other commonly used models of particle production which are shown to differ by having different values for tau, alpha. While void scaling is a feature of this model, hierarchical structure is not a general property of it. The value of the exponent tau=2 is a transition point associated with void and hierarchical scaling features. An exponent gamma is introduced to describe enhanced fluctuations near a critical point. Experimentally determined properties of the void scaling function can be used to determine tau.Comment: Accepted for publication in Nucl. Phys.

Stable Bose-Einstein correlations

The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation function is shown to have a {\it stretched exponential} shape, characterized by the L\'evy index of stability $0 < \alpha \le 2$ and the scale parameter $R$. The normal, Gaussian shape corresponds to a particular case, when $\alpha = 2$ is selected. The asymmetry parameter of the stable source, $\beta$ is shown to be proportional to the angle, measured by the normalized three-particle cumulant correlations.Comment: 7 pages, no figures, invited talk of T. Csorgo at the 2nd Warsaw Meeting on Particle Correlations and Resonances in HIC, see http://hirg.if.pw.edu.pl/en/meeting/oct2003/talks/csorgo/Csorgo.pp

Description of local multiplicity fluctuations and genuine multiparticle correlations

Various parametrizations of the multiplicity distribution are studied using the recently published large statistics OPAL results on multidimensional local fluctuations and genuine correlations in e+e- -> Z -> hadrons. The measured normalized factorial and cumulant moments are compared to the predictions of the negative binomial distribution, the modified and generalized versions of it, the log-normal distribution and the model of the generalized birth process with immigration. This is the first study which uses the multiplicity distribution parametrizations to describe high-order genuine correlations. Although the parametrizations fit well the measured fluctuations and correlations for low orders, they do show certain deviations at high orders. We have shown that it is necessary to incorporate the multiparticle character of the correlations along with the property of self-similarity to attain a good description of the measurements.Comment: 15 pages, 2 ps figure

Depigmented wing patch size is a condition-dependent indicator of viability in male collared flycatchers

Honesty of sexual advertisement is thought to be the result of signalling costs. Because production costs of depigmented plumage patches are probably very low, their role as honest signals of individual quality has been questioned. Costs of bearing these traits, however, should also be taken into account. Studies on proximate determination and possible information content of white badges are very rare. We investigated repeatability, sensu lato heritability, and condition- and age-dependence of white wing patch size, a male display trait in a population of collared flycatchers (Ficedula albicollis), based on 4 years of data. By comparing relationships between age and wing patch size (1) within individuals among years versus (2) among individuals within years, we could address the viability indicator value of the trait. Wing patch size approximately doubled at the transition from subadult to adult plumage, and its change was significantly related to body condition the previous season. Repeatability and heritability values suggest that the trait is informative already in subadult plumage, and that genetic and early environmental effects are important in its determination, the latter only during the first year of life. Thus, wing patch size can act as a condition-dependent signal of genetic quality. Indeed, discrepancy between results from the horizontal and vertical age-dependence approaches shows that the trait was positively related to expected lifespan. After examining several alternative explanations, we conclude that wing patch size indicates genetically based viability. This is the first study to demonstrate a good genes viability benefit conferred by a depigmented plumage patch