Heavy quark polarization anisotropy as a novel probe of fireball geometry

TL;DR

This work introduces heavy-flavor polarization harmonics as a novel probe of the initial fireball geometry in relativistic heavy-ion collisions. It develops a rotational Brownian motion framework to connect spin depolarization, path length, and geometric eccentricities, yielding the relation $p_n(p_T,y) = (\alpha m_Q L_0 \epsilon_n) / [2 (n+2) |p| \tau_s]$ for the polarization harmonics and showing how these signals encode early-time geometry. A concrete application with ALICE inputs estimates the second harmonic $p_2$, corresponding to the $D^*+$ spin alignment, yielding $\langle p_2 \rangle \approx 0.17$ after spectral convolution, demonstrating phenomenological relevance. The paper outlines future work to embed the spin dynamics in realistic hydrodynamics and to determine the spin relaxation time $\tau_s$ from first principles, aiming for a quantitative extraction of polarization harmonics from heavy-ion data.

Abstract

We propose a new approach to probe the initial fireball geometry in relativistic heavy-ion collisions using spin polarization. Specifically, we introduce polarization harmonics of open heavy hadrons as a novel observable sensitive to geometric anisotropies. Heavy quarks are produced in early hard scatterings and can acquire spin polarization from the strong, transient electromagnetic fields present at early times. As they propagate through the anisotropic quark-gluon plasma, medium-induced interactions lead to path-length dependent depolarization, imprinting an azimuthally anisotropic polarization pattern. Within the framework of rotational Brownian motion, we show that the resulting polarization harmonics are directly related to the initial spatial eccentricities, thereby establishing heavy-flavor polarization anisotropies as a sensitive and complementary probe of the early-time collision geometry. We present quantitative estimates of the second polarization harmonic associated with the recently observed $D^{*+}$ spin alignment reported by the ALICE Collaboration.

Figures (1)

• Figure 1: The second polarization harmonic, $p_2$, as a function of transverse momentum $p_T$. The parameter values used in the plot are obtained from fits to ALICE measurements of the spin alignment of the $D^{*+}$ meson ALICE:2025cdfDey:2025ail.