Relativistic Nucleus-Nucleus Collisions: A Connection between the Strangeness-Maximum at $\sqrt{s} \approx$ 7 GeV and the QCD Critical Endpoint from Lattice Studies

Abstract

A steep maximum occurs in the Wroblewski ratio between strange and non-strange quarks created in central nucleus-nucleus collisions, of about A=200, at the lower SPS energy $\sqrt{s} \approx$ 7 GeV. By analyzing hadronic multiplicities within the grand canonical statistical hadronization model this maximum is shown to occur at a baryochemical potential of about 450 MeV. In comparison, recent QCD lattice calculations at finite baryochemical potential suggest a steep maximum of the light quark susceptibility, to occur at similar $\mu_B$, indicative of "critical fluctuation" expected to occur at or near the QCD critical endpoint. This endpoint hat not been firmly pinned down but should occur in the 300 MeV $ < \mu_B^c<700$ MeV interval. It is argued that central collisions within the low SPS energy range should exhibit a turning point between compression/heating, and expansion/cooling at energy density, temperature and $\mu_B$ close to the suspected critical point. Whereas from top SPS to RHIC energy the primordial dynamics create a turning point far above in $\epsilon$ and T, and far below in $\mu_B$. And at lower AGS energies the dynamical trajectory stays below the phase boundary. Thus, the observed sharp strangeness maximum might coincide with the critical $\sqrt{s}$ at which the dynamics settles at, or near the QCD endpoint.