Stochastic background of a KNO scaling function given by the Peřina-McGill formula and the gamma distribution utilized by Carruthers and Shih —their interrelation and phenomenological applications

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It is found that a KNO scaling function given by the Peřina-McGill formula (i.e., the generalized Glauber-Lachs formula) satisfies the Fokker-Planck equation and moreover, the gamma distribution utilized in Carruthers and Shih's recent study is a stationary solution. Numerically these two KNO scaling functions are almost the same despite their different approaches. Comparisons of two KNO scaling functions with data at the CERN ISR and SPS collider show that charged pions with a pseudorapidity cutoff (| η | ⩽ 1.5) are dominantly incoherent. This fact is also confirmed through analyses of a negative pion interferometry as well as charge-charge correlation at the ISR region.