We present measurements of $Omega$ and $phi$ production at mid-rapidity from Au+Au collisions at nucleon-nucleon center-of-mass energies $sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27 and 39 GeV by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). Motivated by the coalescence formation mechanism for these strange hadrons, we study the ratios of $N(Omega^{-}+Omega^{+})/(2N(phi))$. These ratios as a function of transverse momentum ($p_T$) fall on a consistent trend at high collision energies, but start to show deviations in peripheral collisions at $sqrt{s_{NN}}$ = 19.6, 27 and 39 GeV, and in central collisions at 11.5 GeV in the intermediate $p_T$ region of 2.4-3.6 GeV/c. We further evaluate empirically the strange quark $p_T$ distributions at hadronization by studying the $Omega/phi$ ratios scaled by the number of constituent quarks. The NCQ-scaled $Omega/phi$ ratios show a suppression of strange quark production in central collisions at 11.5 GeV compared to $sqrt{s_{NN}} >= 19.6$ GeV. The shapes of the presumably thermal strange quark distributions in 0-60% most central collisions at 7.7 GeV show significant deviations from those in 0-10% most central collisions at higher energies. These features suggest that there is likely a change of the underlying strange quark dynamics in the transition from quark-matter to hadronic matter at collision energies below 19.6 GeV.
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