Studying re-scattering effect in heavy-ion collision through $K^*$ Production

We have studied the $K^*$ production within A Multi-Phase Transport model (AMPT) for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV to understand the hadronic re-scattering effect on the measured yields of the resonance. The hadronic re-scattering of the $K^*$ decay daughter particles ($\pi$ and K) will alter their momentum distribution thereby making it difficult to reconstruct the $K^*$ signal through the invariant mass method. An increased hadronic re-scattering effect thus leads to a decrease in the reconstructed yield of $K^*$ in heavy-ion collisions. Through this simulation study we argue that a decrease in $K^*$/K ratio with increase in collision centrality necessarily reflects the hadronic re-scattering effect. Since the re-scattering occurs in the hadronic phase and $K^*$ has a lifetime of 4 fm/c, we present a toy model based discussion on using measured $K^*$/K to put a lower limit on the hadronic phase lifetime in high energy nuclear collisions.