New scaling variable and early scaling in single-particle inclusive distributions for hadron-hadron collisions

Abstract

We suggest that the invariant cross section for $a+b\ensuremath{\rightarrow}c+X$ should be plotted in terms of ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}}$), where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x}=\frac{2{E}^{*}}{\sqrt{s}}$ and ${E}^{*}$ is the energy of particle $c$ in the center-of-mass system. We have shown for processes with exotic $\mathrm{ab}\overline{c}$ [such as $p+p\ensuremath{\rightarrow}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},{K}^{\ifmmode\pm\else\textpm\fi{}},\overline{p})+X$] that the invariant cross sections $\frac{E{d}^{3}\ensuremath{\sigma}}{{d}^{3}p}\ensuremath{\rightarrow}f(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}})$ at ${P}_{\ensuremath{\perp}}=0.2, 0.4, \mathrm{and} 0.8$ GeV/c over an energy range of ${P}_{\mathrm{inc}}=12\ensuremath{-}1500$ GeV/c. Furthermore, scaling in terms of ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}}$) provides a natural connection between the small-${P}_{\ensuremath{\perp}}$ and large-${P}_{\ensuremath{\perp}}$ regions. Predictions on the single-particle distribution when both ${P}_{\ensuremath{\parallel}}^{*}$ and ${P}_{\ensuremath{\perp}}^{*}$ are large are also presented.