Hadronicϒproduction, parton distributions, and quantum chromodynamics

Using the combined version of light-quark ($q\overline{q}\to b\overline{b}$) and gluon-gluon ($\mathrm{gg}\to b\overline{b}$) fusion mechanisms for hadronic $\Upsilon \mathrm{}\left(9.5\right)\mathrm{}$ production, we give predictions for $x_F$ distributions using pion and proton beams, and for various total-cross-section beam ratios. In addition, we make a detailed comparison of counting-rule-like nucleonic and pionic parton distributions with those predicted by dynamical quantum-chromodynamics (QCD) calculations, and give analytic parametrizations of their QCD $x$ and $Q^2$ dependence.