Transverse momenta of hadronically produced heavy-quark systems: 2→3 processes in quantum chromodynamics

Transverse-momentum spectra are calculated for heavy quarkonium states $Q\overline{Q}$ ($\frac{J}{\psi }$,$\Upsilon$) produced in $\mathrm{pp}$ and $\overline{p}p$ collisions. These transverse momenta result from the hard quark ($q$) and gluon ($g$) subprocesses $q\overline{q}\to Q\overline{Q}g$, $\mathrm{gq}\to Q\overline{Q}q$, and $\mathrm{gg}\to Q\overline{Q}g$. The $p_T$ distributions for $\frac{J}{\psi }$ production are expected to be significantly steeper than for the ${\mu }^{+}{\mu }^{-}$ continuum, whereas the two distributions become similar in the $\Upsilon$ mass region. These effects are partly confirmed by recent CERN ISR measurements. Predictions for $\overline{p}p$ collisions at $\sqrt{s}=540\mathrm{}$ GeV are also given.