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 $Λ$ hyperon polarization in isobaric $^{96}{40}$Zr+$^{96}{40}$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 $η$ dependences) and the azimuthal modulation coefficients $P_{y,\mathrm{c0}}$ and $P_{y,\mathrm{c2}}$. 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, $P_{y,\mathrm{c2}}$ 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.