Inclusive Processes at High Transverse Momentum

Abstract

We calculate the distribution of secondary particles $C$ in processes $A+B\ensuremath{\rightarrow}C+\mathrm{anything}$ at very high energies when (1) particle $C$ has transverse momentum ${p}_{T}$ far in excess of 1 GeV/c, (2) the basic reaction mechanism is presumed to be a deep-inelastic electromagnetic process, and (3) particles $A$, $B$, and $C$ are either leptons ($l$), photons ($\ensuremath{\gamma}$), or hadrons ($h$). We find that such distribution functions possess a scaling behavior, as governed by dimensional analysis. Furthermore, the typical behavior even for $A$, $B$, and $C$ all hadrons, is a power-law decrease in yield with increasing ${p}_{T}$, implying measurable yields at NAL of hadrons, leptons, and photons produced in 400- GeV $\mathrm{pp}$ collisions even when the observed secondary-particle ${p}_{T}$ exceeds 8 GeV/c. There are similar implications for particle yields from ${e}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}{e}^{\ensuremath{-}}$ colliding-beam experiments and for hadron yields in deep-inelastic electro-production (or neutrino processes). Among the processes discussed in some detail are $\mathrm{ll}\ensuremath{\rightarrow}h$, $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}h$, $\mathrm{lh}\ensuremath{\rightarrow}h$, $\ensuremath{\gamma}h\ensuremath{\rightarrow}h$, $\ensuremath{\gamma}h\ensuremath{\rightarrow}l$, as well as $\mathrm{hh}\ensuremath{\rightarrow}l$, $\mathrm{hh}\ensuremath{\rightarrow}\ensuremath{\gamma}$, $\mathrm{hh}\ensuremath{\rightarrow}W$, and $W\ensuremath{\rightarrow}h$, where $W$ is the conjectured weak-interaction intermediate boson. The basis of the calculation is an extension of the parton model. The new ingredient necessary to calculate the processes of interest is the inclusive probability for finding a hadron emerging from a parton struck in a deep-inelastic collision. This probability is taken to have a form similar to that generally presumed for finding a parton in an energetic hadron. We study the dependence of our conclusions on the validity of the parton model, and conclude that they follow mainly from kinematics, duality arguments $\stackrel{`}{a}\mathrm{la}$ Bloom and Gilman, and the crucial assumption that multiplicities in such reactions grow slowly with energy. The picture we obtain generalizes the concept of deep-inelastic process, and predicts the existence of "multiple cores" in such reactions. We speculate on the possibility of strong, nonelectromagnetic deep-inelastic processes. If such processes exist, our predictions of particle yields for $\mathrm{hh}\ensuremath{\rightarrow}h$ could be up to 4 orders of magnitude too low, and for $\ensuremath{\gamma}h\ensuremath{\rightarrow}h$ and $\mathrm{hh}\ensuremath{\rightarrow}\ensuremath{\gamma}$ up to 2 orders of magnitude too low.