Analysis of radial scaling in single-particle inclusive reactions

An analysis of an extensive sample of the world's data has been performed to test the hypothesis of radial scaling. We have studied the inclusive reactions p+p→(π^±,0 or K^± or p or p̄)+anything to determine the behavior of the invariant cross section as a function of p_⊥, xR=E*E*ₘₐₓ, the radial scaling variable, and s. The data cover a range in p_⊥ from 0.25 to {~}6.0 GeV/c and a range in s from 3.0 to 63 GeV. For small xR and all available p_⊥ the single-particle inclusive cross sections for the reactions studied scale to a good approximation for all s, even down to the kinematic threshold. For large xR, the single-particle inclusive cross sections for increasing s show a rapid approach to the scaling limit from above. In these cases the scaling limit is always approached by s≈10 GeV. Thus, data for all particles to a good approximation exhibit radial scaling at all available p_⊥ and xR over the CERN ISR energy range. A comparison of radial scaling with Feynman scaling is given. It is shown that in the Feynman case the cross sections for small x_∥ (x_∥=p*_∥p*ₘₐₓ) approach their scaling limit from below, and that the approach to the scaling limit is slower than is exhibited for the case of small xR. The systematic differences among the inclusive cross sections of various particles are discussed in the range of s where radial scaling has been shown to be valid. In particular, the p_⊥ and xR distributions of Edσdp³ are examined.