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

TL;DR

This paper develops a quantum spin-density-matrix framework to study heavy-quark spin dynamics in relativistic heavy-ion collisions, connecting theoretical evolution equations to experimental observables and recent measurements.

Contribution

It introduces a novel quantum spin-density-matrix approach for heavy-quark polarization evolution and applies it to interpret recent experimental data.

Findings

Extracted an effective depolarization strength from ALICE data.

Provided estimates for $\Lambda_c^+$ and $ar{\Lambda}_c^-$ polarization.

Estimated elliptic polarization harmonic due to path-length-dependent depolarization.

Abstract

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 $D^{*+}$ spin alignment in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~{\rm TeV}$ and extract an effective depolarization strength that determines the spin-relaxation time scale. Using this fitted parameter, we provide benchmark estimates for $\Lambda_c^+$ and $\bar{\Lambda}_c^-$ 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.