Abstract
We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of $\hbar$ from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a small chemical potential and ignorance of electromagnetic fields by adopting an equation of state different from those in other recent studies. Although the shear correction alone upon the local polarization results in a sign and azimuthal-angle dependence more consistent with experimental observations, as also discovered in other recent studies, it is mostly suppressed by the contributions from thermal vorticity and other terms that yield an opposite trend. It is found that the total local spin polarization can be very sensitive to the equation of states, the ratio of shear viscosity to entropy density, and the freeze-out temperature.
Highlights
In noncentral heavy ion collisions, large orbital angular momenta can be generated and transferred to the quark gluon plasma (QGP) in the form of vorticity fields
From the detailed balance of massless fermions with two-to-two scattering in chiral kinetic theory, it has been shown that the Wigner function pertinent to spin polarization contains several corrections besides the thermal vorticity at local equilibrium as derived by some of the authors of this paper [36] in 2017
II, we review the main results of our early work [36] and present all possible corrections at local equilibrium to polarization up to order hexplicitly
Summary
In noncentral heavy ion collisions, large orbital angular momenta can be generated and transferred to the quark gluon plasma (QGP) in the form of vorticity fields. From the detailed balance of massless fermions with two-to-two scattering in chiral kinetic theory, it has been shown that the Wigner function pertinent to spin polarization contains several corrections besides the thermal vorticity at local equilibrium as derived by some of the authors of this paper [36] in 2017. [88], the authors have simultaneously derived the shearinduced polarization through statistical models Based on their findings with the shear correction, the hydrodynamic simulations in Ref. We introduce the notations A(ρ Bσ ) ≡ (Aρ Bσ + Aσ Bρ )/2 and A[ρ Bσ ] ≡ (Aρ Bσ − Aσ Bρ )/2
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