  Invariant inclusive single particle/jet cross sections in p-p collisions can
be factorized in terms of two separable pT dependences, a [pT - sqrt(s)] sector
and an [xR - pT - sqrt(s)] sector, where xR = E/Emax is the radial scaling
variable. Here, we extend our earlier work by analyzing more extensive data to
explore various s-dependent attributes and other systematics of inclusive jet,
photon and single particle inclusive reactions. Approximate power laws in
sqrt(s), pT and xR are found. Physical arguments are given which relate
observations to the underlying physics of parton - parton hard scattering and
the parton distribution functions in the proton. We show that the A(sqrt(s),
pT)-function, introduced in our earlier publication to describe the
pT-dependence of the inclusive cross section, is directly related to the
underlying hard parton-parton scattering for jet production with little
influence from soft physics. In addition to the A-function, we introduce
another function, the F(sqrt(s), xR)-function, which obeys radial scaling for
inclusive jets that offers another test of the underlying parton physics. An
application to heavy ion physics is given where we use our variables to
determine the transparency of cold nuclear matter to penetrating heavy mesons
through the lead nucleus.
