Process dependence of perturbative quantum-chromodynamic jet structures

We examine the structure of elementary 2→3 processes involving leptons, quarks, and gluons, as calculated to lowest nontrivial order in the perturbation series for quantum chromodynamics. Particular attention is devoted to the canonical mass-singularity structure of these perturbative expressions along the borders of phase space, since it is precisely the residues of these poles which yield the asymptotic ratio $\frac{C_2\mathrm{}\left(G\right)\mathrm{}}{C_2\mathrm{}\left(R\right)\mathrm{}}$ for the widths of gluon/quark jets. We find, however, that the extent to which this simple pole behavior can be applied in regions of phase space corresponding to observable jet structures is extremely limited. In fact, the perturbative widths for quark jets need not always be narrower than those for gluon jets. Distributions in various jet variables are presented. We find that the three-jet signal in hadronic processes is typically 2 to 4 times larger than in $e^{+}{e}^{-}$ annihilation.