General Connections Between Inclusive and Exclusive Processes and Cluster Decomposition

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Abstract
General connections between exclusive and inclusive cross sections are studied by the generating-functional technique. Exclusive cross sections, inclusive cross sections, and correlation functions appear as coefficients of different Taylor series expansions of the same generating functional. Also studied are the connections between semi-inclusive processes where all charged particles in an event are observed and genuine inclusive processes with only some of the charged particles observed. No information on neutral particles enter in these connections for semi-inclusive processes. In special cases our results reproduce several seemingly unrelated aspects of inclusive processes treated by Mueller, Predazzi, and Veneziano and by Campbell and Chang. Our approach yields additional constraints and sum rules for inclusive cross sections. It is established that an infinite number of correlation functions are needed; and correlation in the pionization region necessarily exists if the multiplicity increases with energy and the transverse momenta of the final particles are limited. A brief comparison between exclusive and inclusive cluster decomposition is given. The question of diffraction dissociation is also very briefly discussed.