Solutions of the Differential-Difference Equation of the Perina and McGill Formula and Their Interrelations: Role of Coherent Component in Hadronic Collisions

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Abstract
Stochastico-physical structures of the Peřina-McGill formula are investigated. We find two new analytic solutions with the Planck-Polya type, and a condition defined in the Fock state as initial conditions. Moreover, we investigate physical connections between the probability distributions with discrete and continuous variables in the Fock state and those in the coherent state. It is found that there is another procedure in addition to the randomization for hadronization from the QCD-world to the meson-world, provided that the Peřina-McGill formula describes correctly meson production mechanism. The role of coherent in KNO scaling distributions and pion interferometry is elucidated.

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