Scaling and the approach to scaling at large transverse momentum

Large transverse-momentum scaling as Edσ/d³p=p_^_⁻⁸f(x_,x₎ is first discussed in terms of models of parton-parton scattering. We review explicitly the equivalence of this approach to the multiperipheral and field-theory approaches, and we find the parton distribution function that fits the recent CERN ISR and NAL data. Then the deviations from scaling at nonasymptotic energies due to internal and external masses are examined by an exact numerical calculation of the general peripheral structure for the single-particle spectrum, which includes the parton models. This provides good fits to the single-particle spectra at all pₐnd explains the observed deviations from scaling at small p_. The rise of the central plateau, secondary trajectories, and particle ratios at large pₐre also discussed.