[Paper Review] Signatures of the spin Hall effect in hot and dense QCD matter

Baochi Fu, Long-Gang Pang+2 more|arXiv (Cornell University)|Jan 31, 2022

Physics of Superconductivity and Magnetism7 citations

TL;DR

This paper proposes that the spin Hall effect (SHE) in hot and dense QCD matter—driven by gradients in baryon chemical potential—produces measurable spin polarization in Lambda hyperons at RHIC Beam Energy Scan (BES) energies. Using a (3+1)D viscous hydrodynamic model with AMPT initial conditions, the authors predict that the second Fourier harmonics of net spin polarization, $P_{2,z}^{\text{net}}$ and $P_{2,y}^{\text{net}}$, serve as key observables that exhibit distinct sign and energy dependence in the presence versus absence of SHE, offering a unique experimental signature for its detection.

ABSTRACT

The spin Hall effect (SHE) is a generation of spin polarization for moving spin carriers in materials under an external electric field and has been observed in semiconductors, metals, and insulators at or below room temperature. Recent theoretical analyses show that spin Hall current can be induced by the baryon chemical potential gradient which plays the role of the analogous electric field and which becomes sizable in the fireballs created in heavy-ion collisions at beam energy of ${\cal O}(10)$~GeV. In this letter, we study this important mechanism for spin polarization generation that has not been systematically explored before and predict the signature of the SHE in those collisions using a (3+1)~D viscous hydrodynamic model MUSIC with AMPT initial condition. We propose to use the second Fourier coefficients of the net spin polarization of Lambda hyperon as sensitive probes to search for the SHE. Those SHE observables show a qualitative difference in both the sign and beam energy dependence for the situations with and without the SHE. Future experimental observation of these distinct qualitative features would provide strong evidence for the existence of the SHE in the hot and dense QCD matter at trillions of degrees.

Motivation & Objective

• To investigate the role of the spin Hall effect (SHE) in generating spin polarization in hot and dense QCD matter at RHIC-BES energies.
• To identify experimentally accessible observables that can distinguish SHE contributions from other spin polarization mechanisms such as vorticity and shear-induced polarization.
• To quantify the impact of baryon chemical potential gradients on differential spin polarization of Lambda and anti-Lambda hyperons.
• To demonstrate that the second Fourier harmonics of net spin polarization are sensitive probes for detecting the SHE in heavy-ion collisions.

Proposed method

• The study employs the (3+1)D viscous hydrodynamic model MUSIC with AMPT initial conditions to simulate the space-time evolution of QCD matter in heavy-ion collisions at $\sqrt{s_{NN}} = 7.7$ GeV.
• The spin polarization of Lambda and anti-Lambda hyperons is calculated using the Wigner function formalism and relativistic kinetic theory, incorporating the SHE response to gradients in baryon chemical potential.
• The SHE-induced spin polarization is modeled via the relation $\bm{P} \propto -\bm{p} \times (q_B \nabla \mu_B)$, where $q_B$ is the baryon charge and $\bm{p}$ is the momentum of the spin carrier.
• The second Fourier coefficients $P_{2,z}^{\text{net}}$ and $P_{2,y}^{\text{net}}$ of the net spin polarization are extracted as key observables to isolate SHE effects from competing mechanisms.
• The model includes contributions from vorticity, shear-induced polarization (SIP), and temperature gradients, with the SHE contribution isolated through comparative simulations with and without it.
• Sensitivity analysis is performed on initial conditions, shear and bulk viscosities, baryon diffusion, and equation of state to validate robustness of the SHE signal.

Experimental results

Research questions

• RQ1 Does the spin Hall effect induced by baryon chemical potential gradients produce a measurable signal in the differential spin polarization of Lambda hyperons at RHIC-BES energies?
• RQ2 How does the sign and energy dependence of the second Fourier harmonics of net spin polarization differ when the SHE is present versus absent?
• RQ3 To what extent is the SHE contribution comparable in magnitude to other known spin polarization mechanisms such as vorticity and shear-induced polarization at low beam energies?
• RQ4 Can the second harmonics of net spin polarization $P_{2,z}^{\text{net}}$ and $P_{2,y}^{\text{net}}$ serve as robust, isolatable probes for detecting the SHE in heavy-ion collisions?

Key findings

• The SHE contribution to the differential spin polarization of Lambda hyperons is comparable in magnitude to those from vorticity and shear-induced polarization at $\sqrt{s_{NN}} = 7.7$ GeV.
• The second Fourier harmonics of net spin polarization, $P_{2,z}^{\text{net}}$ and $P_{2,y}^{\text{net}}$, show a qualitative difference in both sign and beam energy dependence when the SHE is included versus excluded in simulations.
• The sign of the SHE contribution to $P_{y}^{\text{net}}$ is sensitive to the longitudinal profile of the baryon chemical potential and can reverse from negative to positive with decreasing beam energy.
• The net spin polarization is more sensitive to the SHE than individual components $P_{z,y}$ or $\overline{P}_{z,y}$ because it isolates the chemical potential gradient effect from other mechanisms.
• The SHE signal remains robust under variations in initial baryon density, flow profile, shear and bulk viscosities, baryon diffusion, and equation of state within realistic ranges.
• The model results show that the SHE contribution to $P_{z}^{\text{net}}$ is positive and comparable in magnitude to the SIP and T-gradient contributions, with the same sign as SIP at low energies.