The horn in the kaon to pion ratio

A microscopic approach has been employed to study the kaon productions in heavy ion collisions. The momentum integrated Boltzmann equation has been used to study the evolution of strangeness in the system formed in heavy ion collision at relativistic energies. The kaon productions have been calculated for different centre of mass energies ($\sqrt{s_{\mathrm {NN}}}$) ranging from AGS to RHIC. The results have been compared with available experimental data. We obtain a non-monotonic horn like structure for $K^+/\pi^+$ when plotted with $\sqrt{s_{\mathrm {NN}}}$ with the assumption of an initial partonic phase beyond a certain threshold in $\sqrt{s_{NN}}$. However, a monotonic rise of $K^+/\pi^+$ is observed when a hadronic initial state is assumed for all $\sqrt{s_{\mathrm {NN}}}$. Experimental values of $K^-/\pi^-$ are also reproduced within the ambit of the same formalism. Results from scenarios where the strange quarks and hadrons are formed in equilibrium and evolves with and without secondary productions have also been presented.