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Exploring Spin Polarization of Heavy Quarks in Magnetic Fields and Hot Medium

Zhiwei Liu, Yunfan Bai, Shiqi Zheng, Anping Huang, Baoyi Chen

TL;DR

This work examines heavy-quark spin polarization in a hot QCD medium under external magnetic fields produced in relativistic heavy-ion collisions. It couples the Landau–Lifshitz–Gilbert equation for spin dynamics with a Langevin framework for momentum evolution, incorporating realistic temperature and magnetic-field histories from RHIC and LHC environments. The results show that polarization is limited by the short magnetic-field lifetime and the high medium temperature, with strange quarks displaying a larger polarization than charm due to mass dependence. The findings imply that, in typical central collisions, polarization effects are small, while peripheral collisions could yield a few-percent level polarization, and that observed heavy-flavor spin signals may be significantly influenced by other mechanisms such as vortical fields. The approach provides non-equilibrium spin and momentum distributions useful for interpreting heavy-flavor spin observables, including potential implications for $J/\psi$ spin polarization.

Abstract

Relativistic heavy-ion collisions give rise to the formation of both deconfined QCD matter and a strong magnetic field. The spin of heavy quarks is influenced by interactions with the external magnetic field as well as by random scatterings with thermal light partons. The presence of QCD matter comprising charged quarks can extend the lifetime and strength of the magnetic field, thereby enhancing the degree of heavy quark polarization. However, the random scatterings with QCD matter tend to diminish heavy quark polarization. In this study, we utilize the Landau-Lifshitz-Gilbert (LLG) equation to investigate both these contributions. Taking into account the realistic evolutions of medium temperatures and the in-medium magnetic fields at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC), we observe that heavy quark polarization is limited by the short lifetime of the magnetic field and the high temperatures of the medium. Furthermore, we explore the mass dependence of quark polarization, revealing that the polarization degree of strange quarks is much larger than that of charm quarks.

Exploring Spin Polarization of Heavy Quarks in Magnetic Fields and Hot Medium

TL;DR

This work examines heavy-quark spin polarization in a hot QCD medium under external magnetic fields produced in relativistic heavy-ion collisions. It couples the Landau–Lifshitz–Gilbert equation for spin dynamics with a Langevin framework for momentum evolution, incorporating realistic temperature and magnetic-field histories from RHIC and LHC environments. The results show that polarization is limited by the short magnetic-field lifetime and the high medium temperature, with strange quarks displaying a larger polarization than charm due to mass dependence. The findings imply that, in typical central collisions, polarization effects are small, while peripheral collisions could yield a few-percent level polarization, and that observed heavy-flavor spin signals may be significantly influenced by other mechanisms such as vortical fields. The approach provides non-equilibrium spin and momentum distributions useful for interpreting heavy-flavor spin observables, including potential implications for spin polarization.

Abstract

Relativistic heavy-ion collisions give rise to the formation of both deconfined QCD matter and a strong magnetic field. The spin of heavy quarks is influenced by interactions with the external magnetic field as well as by random scatterings with thermal light partons. The presence of QCD matter comprising charged quarks can extend the lifetime and strength of the magnetic field, thereby enhancing the degree of heavy quark polarization. However, the random scatterings with QCD matter tend to diminish heavy quark polarization. In this study, we utilize the Landau-Lifshitz-Gilbert (LLG) equation to investigate both these contributions. Taking into account the realistic evolutions of medium temperatures and the in-medium magnetic fields at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC), we observe that heavy quark polarization is limited by the short lifetime of the magnetic field and the high temperatures of the medium. Furthermore, we explore the mass dependence of quark polarization, revealing that the polarization degree of strange quarks is much larger than that of charm quarks.
Paper Structure (7 sections, 5 equations, 6 figures)

This paper contains 7 sections, 5 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Landau–Lifshitz–Gilbert equation
  3. Langevin equation for momentum evolution
  4. Spin polarization in magnetic field
  5. Polarization in constant magnetic field
  6. Polarization in heavy-ion collisions
  7. Summary

Figures (6)

  • Figure 1: Fermion spin evolution: (a) in the presence of a magnetic field and (b) when the polarization process is simulated considering the combined effects of spin-magnetic field interaction and spin-spin interactions.
  • Figure 2: (Upper panel) Time evolution of the realistic in-medium magnetic field in RHIC 200 GeV Au-Au collisions in centrality 30-40%. Solid and dashed lines are for $eB_1(t)$ and $eB_2(t,x,y)$ respectively with $(x=0, y=0)$. The value of $eB_0$ is determined based on the formula in Deng:2012pc by taking the corresponding value of the impact parameter in cent.30-40%. $t_B$ is taken as 0.4 fm/c. (Lower panel) The spatial transverse distribution of the magnetic field $eB_2(t,x,y)$ at the initial time $t=0$.
  • Figure 3: Left subplot: The spin polarization of heavy quarks over time is examined under the conditions of a constant temperature $T=0.2$ GeV and a constant magnetic field strength of $eB=20 m_\pi^2$. Various values of the damping factor $\alpha=(0.1, 0.2, 1.0)$ are utilized to investigate the rate of quark spin polarization. Right subplot: Different masses m=(0.1, 1.5, 4.5) GeV which characterize the cases of strange, charm, and bottom quarks, are employed to analyze the extent of quark spin polarization. The damping factor in the LLG equation is taken as $\alpha=0.1$. The electric charge of the quark is taken as $q=(2/3)e$.
  • Figure 4: The average polarization of quark spins over time for centrality 30-40% in the central rapidity of 5.02 TeV Pb-Pb collisions. Three distinct lines represent varying levels of in-medium magnetic fields with the form $eB_1(t)$ by taking different values of $t_B$. The initial maximum magnetic field strength is set at $eB_0=128m_\pi^2$ at $t=0$.
  • Figure 5: The final spin polarization of charm and strange quarks plotted against transverse momentum in 5.02 TeV Pb-Pb collisions in the centrality 30-40% (left subplot) and 60-70% (right subplot). The damping factor is taken as $\alpha=1.0$. A uniformly distributed magnetic field $eB_1(t)$ is taken, where the value of $eB_0$ is determined to be $128\ m_\pi^2$ and $145\ m_\pi^2$ respectively in two centralities.
  • ...and 1 more figures