The Distribution Functions and the Underlying String Structure of Hadronic Reactions*

On the basis of the topological l/Nc expansion, various types of the distribution function for the soft and the hard processes are obtained, which contain the freedoms pertaining to the underlying string structure of hadronic reactions. It is stressed that the distribution functions for the soft process refer to the energy fractions of jets and are distinct from those for the hard process in their physical meanings. In order to test the present model the average multiplicities are studied by using the distribution functions. For multi-string processes the freedom of partitioning the energy among jets causes the effective energy for each extended string to be largely reduced compared with the total energy. In deep inelastic leptonhadron scattering, owing to the peculiar double-string structure of the singlet component the average multiplicity is predicted to increase with decreasing Q2 at fixed W higher than -20 GeV. Submitted to Physical Review D 'Work supported in part by the Department of Energy, contract DE-AC03-76SF00515 and by the Yamada Science Foundation. +On leave of absence from Department of Physics, Nagoya University, Nagoya 464, Japan.