The Time-Delay Signature of Quark-Gluon-Plasma Formation in Relativistic Nuclear Collisions

The hydrodynamic expansion of quark-gluon plasmas with spherical and longitudinally boost-invariant geometries is studied as a function of the initial energy density. The sensitivity of the collective flow pattern to uncertainties in the nuclear matter equation of state is explored. We concentrate on the effect of a possible finite width, $\Delta T \sim 0.1 T_c$, of the transition region between quark-gluon plasma and hadronic phase. Although slow deflagration solutions that act to stall the expansion do not exist for $\Delta T > 0.08 T_c$, we find, nevertheless, that the equation of state remains sufficiently soft in the transition region to delay the propagation of ordinary rarefaction waves for a considerable time. We compute the dependence of the pion-interferometry correlation function on $\Delta T$, since this is the most promising observable for time-delayed expansion. The signature of time delay, proposed by Pratt and Bertsch, is an enhancement of the ratio of the inverse width of the pion correlation function in out-direction to that in side-direction. One of our main results is that this generic signature of quark-gluon plasma formation is rather robust to the uncertainties in the width of the transition region. Furthermore, for longitudinal boost-invariant geometries, the signal is likely to be maximized around RHIC energies, $\sqrt{s} \sim 200$ AGeV.