On multiplicity, pionization and the hypothesis of limiting fragmentation in high-energy collisions

Recently, an elegant hypothesis of l imiting fragmentat ion in extra-high-energy collisions was propossed by B E N E C K E , CHOU, YANG and Y ~ (1). The naive picture of fragmentation in extra-high-energy collisions is that two hadrons, viewed as extended objects with many internal degrees of freedom, pass through each other and break up into fragments. The fragments of the target (the projectile) are assumed to have finite energies and to approach limiting distributions in the target system (the projeeti!e system) as the incoming energy Ein¢-> oo. These authors argue, par t ly on the basis of the naive picture of fragmentation, that there is no pionization process (2) although it is not inconsistent with their hypothesis. They further assume that an electron as a projectile would not break up into fragments in colliding with hadrons, and believe that the average multiplicity will be divergent as Eino--> oo. I t has been shown (3), by using general kinematic constraints, tha t the average multiplici ty must be strictly Jinite, which contradicts their belief. This inconsistency can also be viewed in the following way. The ratio aei/ato t for any hadron-hadron or lepton-hadron collision process will become negative if the average multiplicity in the BCYY framework of limiting fragmentation diverges, however slowly, as Ei .o~ oo. We whall al~o show that, in contrast with their assumption, the electron is very likely to break up into fragments in colliding with hadrons at high energies. These considerations suggest the possible existence of pionization at extra-high-energy collisions in the BCYY framework. Let us begin with a general and exact un i ta r i ty sum rule expressed in terms of the quantities in the e.m. system: