A Statistical Measure of Clustering in Multiparticle Final States

A quantitative measure of clustering effects in many-particle final states is defined and its significance discussed. The results consist of a single curve and a number, $〈{{\omega }_n}^2〉$, which may be extracted from inclusive or exclusive data where the longitudinal momenta (or some other variable) have been measured for $n$ particles in each event. The curve is a measure of the average fluctuation of each event away from the over-all distribution, and is defined strictly in terms of experimental quantities. The results appear to provide a sensitive test for models of hadron production. Comparison with Monte Carlo calculations, or with a statistical reference model which is described, allow one to interpret the results in a fairly model-independent manner. The analysis is then applied to some 13-GeV/c $K^{-}p$ data.