Formation time and the suppression ofJ/?'s in relativistic ion collisions

Abstract

Recent discussions of the suppression ofJ/ψ's in relativistic ion collisions make use of the concept of resonance formation time. We investigate the use of this concept in classical and quantum mechanics and find striking differences in the two cases. It is argued that the conditions of formation of quarkantiquark pairs which become constituents of aJ/ψ are such that the quantum mechanical nature of the problem is an essential element. As a first step towards implementation of a complete calculation we assume initial production of aJ/ψ and present a quantummechanical model of the suppression. The basic idea of the model is that during the lifetime of the plasma the confining region of the charm-anticharm pair is considerably enlarged while afterwards it returns to its normal size. The model is thus characterized by an expansion followed by a contraction. Confinement is simulated by introducing a one-dimensional infinite square-well potential. The creation of a quark-gluon plasma is simulated by allowing this infinite square well to expand suddenly. The subsequent cooling and the return to the hadronic phase is represented by letting the square well shrink again to its original size. The probability is calculated for the system to remain in the ground state after the sudden expansion and contraction are completed. One of the interesting features is that this probability becomes an oscillating function of time, with the period of oscillation determined by the size of the quark-gluon plasma region and the quark mass. Assuming that this feature will survive in a full three-dimensional calculation, one should expect correlations of the suppression factor with plasma lifetimes and volumes on an event by event basis, as well as a modification of the simple transverse momentum dependence predicted by the classical calculations.