The scaling property of inelastic electron scattering with a fixed final hadron multiplicity is analysed. The relation between the structure functions and the average multiplicity at infinite energy is discussed. A possibility exists that, if one excludes all soft mesons, the remaining hadron multiplicity at infinite energy may stay finite and not too high, in which case some insight may be gained as to why the observed structure functions appear to scale at a relatively low energy.
By using the tree diagrams of the usual SU, phenomenological Lagrangian, explicit calculations of the structure functions W, and VW, are made for all two-body final channels, such asp@, npf, etc.; it is found that, in this simple model, the scaling property is satisfied for these particular channels. Possible experimental consequences are discussed.
Recently, there have been extensive discussions [l] in the literature concerning the high energy behavior of the electromagnetic structure functions IV, and v W, in elastic ep scattering e+p+e+c,
(1)
where c refers to some final hadron channel which is usually summed over. In this note, we call attention to some relatively simple aspects of the same problem, but for a given channel c. For definiteness, a channel c is specified only by the kind of particles present and the multiplicity of these particles; for example, c can be either pro, or nr+pO, etc. It is easy to see that for each given channel c, one can define two similar structure functions W,(c, X, S) and v W,(c, x, s); the usual structure functions for the so-called "deep inelastic" reactions are simply their sums W&, 8) = c Wl(C, x, 4 c and (2) vWz(x, s) = c VW&, x, 4, c * This research was supported in part by the U. S. Atomic Energy Commission.