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The production of heavy quarkonium as QQbar bound-states in hadron-hadroncollisions is considered within the framework of a space-time description,combining parton-cascade evolution with a coalescence model for bound-stateformation. The `hard' production of the initial QQbar, directly or via gluonfragmentation and including both color-singlet and color-octet contributions,is calculated from the PQCD cross-sections. The subsequent development of theQQbar system is described within a space-time generalization of the DGLAPparton-evolution formalism in position- and momentum-space. The actualformation of the bound-states is accomplished through overlap of the QQbar pairand a spectrum of quarkonium wave-functions. This coalescence can only occurafter sufficent gluon radiation reduces the QQbar relative velocity to a valuecommensurate with the non-relativistic kinematics of these bound systems. Thepresence of gluon participants in the cascade then is both necessary and leadsto the natural inclusion of both color-singlet and color-octet mechanisms. Theapplication of this approach to pp (ppbar) collisions from sqrt(s)= 30 GeV - 14TeV reveals very decent agreement with available data from ISR and Tevatron -without the necessity of introducing fit parameters. Moreover, productionprobabilities are calculated for a complete spectrum of charmonium andbottonium states, with the relative significance compared to open charm(bottom) production. An analysis of the space-time development is carriedthrough which sheds light on the relevance of gluon radiation andcolor-structure, suggesting a correponding experimental investigation.Comment: 37 pages including 16 postscript figure

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