Energy Sum Rule and the Approach to Scaling: An Inclusive and Exclusive View

The approach to Feynman-Yang scaling of single-particle inclusive spectra is discussed in terms of the average fraction of c.m. energy per event carried off by each type of constituent. Experimental values for energy fractions in $\mathrm{pp}$ collisions are presented and compared with the results of a Mueller-Regge expansion for the invariant cross sections in the fragmentation region. By examining the behavior of energy fractions in an independent-emission model, it is shown that known dynamic properties of the exclusive components of an inclusive process provide a natural scale by which the energy fractions approach their asymptotic values. The existence of such a scale is shown to explain the rapid approach to asymptotic behavior of the inclusive $\mathrm{pp}\to \pi$ spectra while the $\mathrm{pp}\to \overline{p}$ spectrum rises to an order of magnitude between Brookhaven Alternating Gradient Synchrotron and CERN Intersecting Storage Rings energies.