Hydrodynamics near the QCD phase transition: Looking for the longest-lived fireball

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), i1.5 GeV/fm3 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.