Quantum spin dynamics of heavy quarks and polarization observables in relativistic heavy-ion collisions

We develop a quantum spin-density-matrix framework for heavy-quark spin dynamics in relativistic heavy-ion collisions. Starting from an initial polarization induced along the magnetic-field direction, we derive the evolution equation for spin polarization within this framework and obtain analytic solutions. The evolved polarization is connected to open heavy-flavor observables via a fragmentation-based hadronization prescription. For vector mesons, the spin-alignment parameter ${\rho }_{00}$ is constructed by coupling the heavy-quark spin to that of the light antiquark produced during fragmentation. We confront our results with recent ALICE measurements of prompt $D^{\ast +}$ spin alignment in Pb–Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02\mathrm{T}\mathrm{e}\mathrm{V}$ and extract an effective depolarization strength that determines the spin-relaxation time scale. Using this fitted parameter, we provide benchmark estimates for ${\mathrm{\Lambda }}_c^{+}$ and ${\bar{\mathrm{\Lambda }}}_c^{-}$ polarization, up to an overall spin-transfer normalization. We further estimate the recently proposed elliptic polarization harmonic arising from path-length-dependent depolarization in an anisotropic fireball.