Initial-state control of vorticity--shear competition in longitudinal $\Lambda$ polarization in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.36\mathrm{TeV}$

Abstract

We investigate how the transverse initial energy-density distribution controls the second sine harmonic of longitudinal $\Lambda$ polarization in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.36\mathrm{TeV}$. We use (3+1)-dimensional Particle-In-Cell Relativistic ideal hydrodynamics and the Becattini--Buzzegoli--Palermo isothermal local-equilibrium prescription. Across the twelve selected initial states, the kinematic-vorticity contribution $P_{z,s2}^{\omega }$ is negative, whereas the kinematic-shear contribution $P_{z,s2}^{\Xi }$ is positive. Changing the initial energy-density normalization $e_{\mathrm{peak}}$, transverse smoothing width ${\sigma }_{\perp }$, or reduced impact parameter $b_0$ modifies the relative magnitudes of the two contributions rather than merely rescaling their sum. Reducing the transverse smoothing width ${\sigma }_{\perp }$ generally strengthens both contributions, whereas increasing the initial energy-density normalization $e_{\mathrm{peak}}$ can preferentially weaken $P_{z,s2}^{\Xi }$ and reverse the total harmonic. At fixed $e_{\mathrm{peak}}$, the impact-parameter dependence is mainly shear driven for narrower transverse smoothing and mainly vorticity driven for broader transverse smoothing. Applying the Liu--Yin prescription to the two tested hydrodynamic backgrounds reverses the total sign, showing that the sign depends on the polarization formula as well as on the fluid fields. Our results obtained with ideal hydrodynamics and the ILE prescription have the same sign and order of magnitude as the ALICE measurements for peripheral Pb--Pb collisions in the $50$--$70\%$ centrality interval, showing that such a positive harmonic can arise from an initial-state-controlled, shear-dominated balance at decoupling.