Power spectrum of hadronic multiparticle rapidity distributions

We discuss issues that arise in studying the power spectrum of rapidity histograms. These questions exist because the correlation functions are typically nontranslation invariant and confined to a finite kinematical interval. It is noted that the event density ρ referred and normalized to the average single-particle density ρ1, leads to (normalized) factorial cumulant bin moments dependent only on the k parameter appearing in the special case of the negative-binomial distribution. An averaged two-particle correlation function is proposed to implement the purpose of the usual Wiener-Khinchin theorem. We then generalize the bin-averaged factorial-moment technique and strip-domain moment approaches to encompass power-spectra methods. The latter connect naturally to the correlation dimensions of fractal sets and evade the problems of nonstationarity at the price of increased computational complexity. Numerical examples of chaotic time series are used to generate data. Their power spectra possess distinct properties in Gaussian and intermittent dynamics. Event averaging smooths out the power spectrum of the Gaussian dynamics, whereas the nontrivial dynamical fluctuations survive the same averaging. We argue that statistically independent events can be generated by uniformly reshuffling the rapidity histograms only if fluctuations themselves are dominantly statistical. In the presence of strongly intermittent dynamical fluctuations, correlations may exist between different events when the event points are generated by a deterministic map. In the Appendix we give the recipe for generalizing the Wiener-Khinchin theorem to calculate the power spectrum of higher-order correlations