Factorization of Deep Inelastic Final State Interactions in Quarkonium Models

Abstract

We consider the deep inelastic process for a nonrelativistic quark confined by the po­ tential, allowing emissions of mesons for transitions from one level to the others of the quark bound states. We study the mechanisms by which the meson emission process (quark materialization) can be factorized out, and clarify it for some examples of the potential. These mechanisms are useful in understanding the similar problem in relativistic field theories. § I. Introduction Although the free parton model has succeeded in predicting many phenomeno­ logical features of deep inelastic processes, it contains the difficult problem that the basic assumption of the model, that the struck quark is essentially free, seem­ ingly contradicts the quark confinement. It is conventionally asserted that the effect of the final-state interactions by confinements can be factorized out from the whole amplitude and can reduce to the term representing unit probability. However, the previous investigations]) on the simple field theoretical model [ ¢ 3-multiperipheral model] do not lead to the above assertions; every diagram with final state interactions gives the vanishing contribution for Q--.oo. It is also ar­ gued in the covariant parton modeJ2l that softened field theories, producing the transverse momentum cutoff, give vanishing amplitudes for final state interactions. In this paper, we shall discuss the deep inelastic processes in a simple quantum mechanical system where a quark is confined inside the potential [Quarkonium] and the struck quark yet confined as an excited state can fall back into lower levels by meson emissions. We are not going to assert that the model is phenomenologically workable in the analyses of existing data of deep inelastic processes. Our aim is to get, through this simple solvable model, a c1 ue to the proper treatment of final state interactions. In our model, two types of the final state interactions exist: The one is clue to the potential and the other the quark materialization through the emissions of mesons. There have already been many investigations 31 ' 41 on the deep process in the quarkonium model. In all these, however, no consideration was put on the quark materialization. The latter is important in the field theoretical