Polarization of massive fermions in a vortical fluid

TL;DR

This paper derives the Wigner function for massive fermions in a vortical fluid, revealing how their polarization depends on vorticity, energy, and chemical potential, with implications for understanding spin polarization in relativistic fluids.

Contribution

It extends the quantum kinetic approach to massive fermions, deriving the Wigner function up to next-to-leading order and analyzing polarization dependence on physical parameters.

Findings

Polarization proportional to local vorticity $oldsymbol{ abla} imes oldsymbol{v}$.

Polarization per particle approaches $rac{oldsymbol{ abla} imes oldsymbol{v}}{4}$ at high energy or mass.

Anti-fermions exhibit higher polarization than fermions, with ratios decreasing as chemical potential increases.

Abstract

Fermions become polarized in a vorticular fluid due to spin-vorticity coupling. Such a polarization can be calculated from the Wigner function in a quantum kinetic approach. Extending previous results for chiral fermions, we derive the Wigner function for massive fermions up to the next-to-leading order in spatial gradient expansion. The polarization density of fermions can be calculated from the axial vector component of the Wigner function and is found to be proportional to the local vorticity $\omega$. The polarizations per particle for fermions and anti-fermions decrease with the chemical potential and increase with energy (mass). Both quantities approach the asymptotic value $\hbar\omega/4$ in the large energy (mass) limit. The polarization per particle for fermions is always smaller than that for anti-fermions, whose ratio of fermions to anti-fermions also decreases with the chemical potential. The polarization per particle on the Cooper-Frye freeze-out hyper-surface can also be formulated and is consistent with the previous result of Becattini et al..