QCD space-time analysis of quarkonium formation and evolution in hadronic collisions

Abstract

The production of heavy quarkonium as $Q\overline{Q}$ bound states in hadron-hadron collisions is considered within the framework of a space-time description, combining parton-cascade evolution with a coalescence model for bound-state formation. The ``hard'' production of the initial $Q\overline{Q}$, directly or via gluon fragmentation and including both color-singlet and color-octet contributions, is calculated from the perturbative QCD cross sections. The subsequent development of the $Q\overline{Q}$ system is described within a space-time generalization of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi parton-evolution formalism in position and momentum space. The actual formation of the bound states is accomplished through overlap of the $Q\overline{Q}$ pair and a spectrum of quarkonium wave functions. This coalescence can only occur after sufficient gluon radiation reduces the $Q\overline{Q}$ relative velocity to a value commensurate with the nonrelativistic kinematics of these bound systems. The presence of gluon participants in the cascade then is both necessary and leads to the natural inclusion of both color-singlet and color-octet mechanisms. The application of this approach to $\mathrm{pp}$ $(p\overline{p})$ collisions from $\sqrt{s}=$ 30 GeV--14 TeV reveals very decent agreement with available data from the CERN Intersecting Storage Rings and Fermilab Tevatron---without the necessity of introducing fit parameters. Moreover, production probabilities are calculated for a complete spectrum of charmonium and bottomonium states, with the relative significance compared to open charm (bottom) production. An analysis of the space-time development is carried through which sheds light on the relevance of gluon radiation and color structure, suggesting a corresponding experimental investigation.