By analyzing the available data on strange hadrons in central Pb+Pb collisions from the NA49 Collaboration at the Super Proton Synchrotron (SPS) and in central Au+Au collisions from the STAR Collaboration at the Relativistic Heavy-Ion Collider (RHIC) in a wide collision energy range from $sqrt{s_{rm NN}}$ = 6.3 GeV to 200 GeV, we find a possible non-monotonic behavior in the ratio $mathcal{O}_text{K-$Xi$-$phi$-$Lambda$}$= $frac{N(K^+)N(Xi^-)}{N(phi)N(Lambda)}$ of $K^+$, $Xi^-$, $phi$, and $Lambda$ yields as a function of $sqrt{s_{rm NN}}$. Based on the quark coalescence model, which can take into account the effect of quark density fluctuations on hadron production, a possible non-monotonic behavior in the dependence of the strange quark density fluctuation on $sqrt{s_{NN}}$ is obtained. This is in contrast to the coalescence model that does not include quark density fluctuations and also to the statistical hadronization model as both fail to describe even qualitatively the collision energy dependence of the ratio $mathcal{O}_text{K-$Xi$-$phi$-$Lambda$}$. Our findings thus suggest that the signal and location of a possible critical endpoint in the QCD phase diagram, which is expected to result in large quark density fluctuations, can be found in the on-going Bean Energy Scan program at RHIC.
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