Hyperon polarization in isobaric Zr+Zr collisions at $\sqrt{s_{NN}}=200$ GeV: TRENRo3D + CLVisc with an initial longitudinal flow gradient

Abstract

We present a theoretical study of global and azimuthal-angle-dependent $\hat{I}›$ hyperon polarization in isobaric ${}_{40}^{96}$Zr+${}_{40}^{96}$Zr collisions at $\sqrt{s_{NN}}=200$~GeV using the TRENTo3D initial condition model coupled to the (3+1)-D viscous hydrodynamic model CLVisc. A longitudinal flow velocity gradient, controlled by $f_v$, is introduced into TRENTo3D for the first time, providing an essential source of initial vorticity in this symmetric isobaric system. Within the isothermal polarization framework, the model provides a simultaneous description of STAR measurements of the global polarization $-P^y$ (centrality, $p_T$, and $\hat{I}\cdot$ dependences) and the azimuthal modulation coefficients $P_{y,c0}$ and $P_{y,c2}$. The $p_T$ dependence reflects the competition between thermal vorticity and shear contributions: the thermal term decreases with $p_T$, while the shear term rises and increasingly shapes the curvature of the total polarization. In this decomposition, $P_{y,c2}$ is dominantly shear-driven and serves as a clean probe of shear-induced polarization. Scans of $f_v$, $k_T$, and nuclear structure provide complementary constraints on the initial state, while the bulk-viscosity dependence is also examined; the five nuclear structure configurations from the STAR isobar blind analysis yield nearly indistinguishable polarization. For $P_z$, the isothermal scenario captures the azimuthal modulation but overpredicts the high-$p_T$ modulation amplitude, and comparison with the standard thermal treatment shows that neither scenario achieves a unified description of all observables.

17 pages, 13 figures. We welcome any comments. If there are relevant references we may have overlooked, please don't hesitate to let us know and we'd be very grateful!