Investigating the Most Vortical Fluid in Nuclear Collisions with Beam Energy Scan

In a non-central nucleus-nucleus collision, the colliding system carries large orbital angular momentum, part of which remains within the hot dense matter created by the collision. This angular momentum turns into complex fluid vorticity structures in the bulk fluid, and eventually manifests itself through the global spin polarization of produced particles (e.g. hyperons). The STAR Collaboration reported the experimental discovery of this novel phenomenon in 2017. A crucial feature in establishing the intepretation is the predicted beam energy dependence, specifically a strong increase of fluid vorticity (and thus the polarization) when the collision beam energy is decresed from O(100) GeV to O(10) GeV range. There remains the interesting question: at which beam energy the truly most vortical fluid will be located. Here we perform a systematic study on the beam energy dependence of hyperon global polarization phenomenon, especially in the interesting Ô(1∼10) GeV region. We find a non-monotonic trend, with the global polarization to first increase and then decrease when beam energy is lowered from 27 GeV down to 3 GeV. The maximum polarization signal has been identified around 7.7 GeV beam energy, where the heavy ion collisions presumably create the most vortical fluid. On the theoretical side, one needs to develop a hydrodynamic theory including the angular momentum conservation in addition to the usual hydrodynamics based on energy-momentum and charge conservation. Recently there has been significant interest in constructing such a new hydrodynamic theory. In this talk, we examine the key conceptual issues for such a theory in the relativistic regime where the orbital and spin components get entangled. We derive the equations for relativistic viscous hydrodynamics with angular momentum through Navier-Stokes type of gradient expansion analysis. (arXiv:2105.13481 & 2105.04060.)