Study of strange quark density fluctuations in Au+Au Collisions at $\sqrt{s_{NN}}$ = 7.7-200 GeV from AMPT Model

The strangeness production is an important observable to study the QCD phase diagram. The yield ratios of strange quark can be helpful to search for the QCD critical end point (CEP) and/or first-order phase transition. In this work, we studied the production of $K^{\pm}$, $\Xi^-(\bar{\Xi}^{+})$, $\phi$ and $\Lambda (\bar \Lambda)$ in {\auau} collisions at {\sqrtsNN} = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV from A Multi-Phase Transport model with string melting version (AMPT-SM). We calculated the invariant yield of these strange hadrons using a different set of parameters compared to those reported in earlier studies and also by varying the hadronic cascade time ($t_{max}$) in the AMPT-SM model. We also calculated the yield ratios, $\mathcal{O}_{K^{\pm}-\Xi^{-}(\bar \Xi^{+})-\phi-\Lambda (\bar \Lambda)}$ which are reported as sensitive to the strange quark density fluctuations and found that the AMPT-SM model fails to describe the non-monotonic trend observed by the experimental data. The negative particle ratio are found to be higher than the ratio of positive particles which is consistent with the experimental data. A significant effect is also seen on these ratios by varying the $t_{max}$. For a crossover transition between the Quark-Gluon Plasma (QGP) and hadronic matter, the double yield ratios considered in the present study based on AMPT-SM model do not show any non-monotonic behaviors and thus providing a baseline for the search of CEP, because there is no first-order or second-order phase transition in the AMPT model. The more realistic equation of state based dynamical modeling is still required for the heavy-ion collisions in order to extract the definite physics conclusion about the non-monotonic energy dependence behavior.