Hydrodynamics near the QCD Phase Transition: Looking for the Longest-Lived Fireball

Abstract

We propose a new strategy for the experimental search of the QCD phase transition in heavy ion collisions: One may tune collision energy to the point where the lifetime of the fireball is the longest. Using hydrodynamical description of space-time evolution and assuming Landau-like initial conditions, we show that this longest lifetime corresponds to the initial energy density being at the "softest point" (where the pressure to energy density ratio reaches its minimum), ${\ensuremath{\epsilon}}_{i}\ensuremath{\approx}1.5$ GeV/${\mathrm{fm}}^{3}$ for our choice of equation of state. The plasma lifetime is effectively increased by about a factor of 3. We suggest distinct changes in various observables which may help to locate the softest point.