Spin Polarization Formula for Dirac Fermions at Local Equilibrium

Abstract

We derive a Cooper-Frye type spin polarization formula for Dirac fermions at local thermal equilibrium described by a grand canonical ensemble specified by temperature, fluid velocity, chemical potential, and spin potential. We discuss the physical meaning of different contributions to spin polarization and compare them with previous works. The present formula provides machinery to convert the spin potential computed in, e.g., relativistic spin hydrodynamics to the spin polarization observable in, e.g., heavy-ion collisions.

V3: 9 pages, no figure

References in corpus (14)

• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Global $\Lambda$ Polarization in high energy collisions
• Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation
• Global polarization of $\Xi$ and $\Omega$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Mass Correction to Chiral Kinetic Equations
• A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions
• Ideal spin hydrodynamics from Wigner function approach
• Different space-time freeze-out picture -- an explanation of different $\Lambda$ and $\bar{\Lambda }$ polarization?
• Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
• $\Lambda$ polarization in peripheral collisions at moderate relativistic energies
• Kinetic theory with spin: From massive to massless fermions
• Massless Limit of Transport Theory for Massive Fermions
• Helicity polarization in relativistic heavy ion collisions

Cited by in corpus (22)

• Foundations and Applications of Quantum Kinetic Theory
• Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term
• Local and global polarization of $\Lambda$ hyperons across RHIC-BES energies: the roles of spin hall effect, initial condition and baryon diffusion
• Hydrodynamics, spin currents and torsion
• $\Lambda /\bar{\Lambda }$ Polarization and Splitting Induced by Rotation and Magnetic Field
• Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
• Electromagnetic fields in ultra-peripheral relativistic heavy-ion collisions
• Quantum kinetic theory for spin transport of quarks with background chromo-electromagnetic fields
• Lorentz-covariant kinetic theory for massive spin-1/2 particles
• An introduction to relativistic spin hydrodynamics
• Collisional corrections to spin polarization from quantum kinetic theory using Chapman-Enskog expansion
• Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD
• Effects of the $\alpha$-cluster structure and the intrinsic momentum component of nuclei on the longitudinal asymmetry in relativistic heavy-ion collisions
• Vector and Tensor Spin Polarization for Vector Bosons at Local Equilibrium
• Generalized Chiral Kinetic Equations
• Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
• Polarization in heavy ion collisions: a theoretical review
• Hadron productions and jet substructures associated with $Z^0/\gamma$ in Pb+Pb collisions at the LHC
• Dynamical induced quark spin polarization by magnetic field at the early stage of heavy-ion collisions
• An improved formula for Wigner function and spin polarization in a decoupling relativistic fluid at local thermodynamic equilibrium
• The Static Heavy Quark-Antiquark Potential within String Theory in Arbitrary Stationary Backgrounds
• Tensor spin polarization induced by curved freeze-out hypersurface