Transition from constituent-interchange to quantum-chromodynamicpT−4dominance at high transverse momentum

We discuss the relationship, in quantum chromodynamics (QCD), between constituent-interchange-model (CIM) processes (e.g., $\mathrm{qM}\to \mathrm{qM}$) and the most elementary QCD processes, such as $\mathrm{qq}\to \mathrm{qq}$, as manifested in single-particle inclusive production at high transverse momentum, $p_T$. Based on the "subprocess expansion" the CIM contributions are seen to be the next-to-leading terms in an asymptotic expansion of the cross section, ${p_T}^{-8\mathrm{}}$ (or ${p_T}^{-12\mathrm{}}$) behavior vs ${p_T}^{-4\mathrm{}}$ for the elementary subprocesses. We explore the systematic features of the transition from CIM behavior to ${p_T}^{-4\mathrm{}}$ behavior with increasing $p_T$. Marked variations with trigger-particle type ($\pi$, $K^{-}$, $p$, or $\overline{p}$) and beam type ($\mathrm{pp}$, ${\pi }^{+}p$, and ${\pi }^{-}p$) emerge.