Impact parameter representation of the leading proton spectrum in the diffractive region

Recent experiment indicates that there is no limiting value for the pion invariant inclusive cross section at x=0 at the highest energies reached by the CERN intersecting storage rings. The author first notes that a recently proposed integral representation of the leading proton spectrum is physically equivalent to representing this spectrum in terms of very narrow multiplicity distributions from each initial impact parameter, with a single factorizable function for the average multiplicity at any impact parameter b, (n(s, b/R(s)))=N(s)n(b/R(s)). He then observes that, in this approach, the explicit form for the scaled part of the spectrum for mod x mod <0.97 and p/sub T/ approximately 0 depends essentially upon the assumed asymptotic form for the growth of average multiplicity with energy s. The data do not exclude the empirical possibility of N(s varies as s/sup epsilon /, epsilon <1/4. (19 refs).