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A lattice based equation of state and $ϕ$ meson production in $\sqrt{s}$=6-200 GeV Pb+Pb and Au+Au collisions

In a boost-invariant hydrodynamic model, we have analyzed $ϕ$ meson production in Pb+Pb and Au+Au collisions, in the centre of mass energy range $\sqrt{s}$= 6-200 GeV. Hydrodynamic evolution is governed by a lattice based equation of state with a confinement-deconfinement {\em cross over} at $T_{co}$=196 MeV. We also look for the threshold energy above which the confined matter undergoes a deconfinement transition. Analysis indicate that above a threshold energy, ${\sqrt{s}}_{th}$=$13.65 \pm 3.06$ GeV, the fluid medium crosses over from a confined phase to a deconfined phase.