A Qcd Space-time Analysis of Quarkonium Formation and Evolution in Hadronic Collisions

The production of heavy quarkonium as QQ̄ 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 QQ̄, directly or via gluon fragmentation and including both color-singlet and color-octet contributions, is calculated from the PQCD cross-sections. The subsequent development of the QQ̄ system is described within a space-time generalization of the DGLAP parton-evolution formalism in positionand momentumspace. The actual formation of the bound-states is accomplished through overlap of the QQ̄ pair and a spectrum of quarkonium wave-functions. This coalescence can only occur after sufficent gluon radiation reduces the QQ̄ relative velocity to a value commensurate with the non-relativistic 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 pp (pp̄) collisions from √ s = 30 GeV 14 TeV reveals very decent agreement with available data from ISR and Tevatron without the necessity of introducing fit parameters. Moreover, production probabilities are calculated for a complete spectrum of charmonium and bottonium 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 correponding experimental investigation.