Polarization of massive fermions in a vortical fluid

Abstract

Fermions become polarized in a vortical 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-toleading 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 ω. 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 ω/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..

Pseudoscalar condensation induced by chiral anomaly and vorticity for massive fermions

“…We use the following form for the axial vector component for massive fermions by generalizing the solution for massless fermions [13,[44][45][46],…”

“…Quantum kinetic theory in terms of Wigner function [40][41][42][43] is a useful tool to study the CME, CVE and other related effects [13,[44][45][46]. The axial vector component of the Wigner function for massless fermions can be generalized to massive fermions and gives their phase-space density of the spin vector.…”

“…The spin vector arises from nonzero fermion mass [47]. Therefore one can calculate the polarization of massive fermions from the axial vector component [46]. The polarization density is found to be proportional to the local vorticity ω as well as the magnetic field.…”

Covariant chiral kinetic equation in the Wigner function approach

“…The spin vector arises from nonzero fermion mass [60]. Therefore one can calculate the polarization of massive fermions from the axial vector component, and the polarization density is found to be proportional to the local vorticity ω as well as the magnetic field [59].…”

“…Therefore people use quantum kinetic theory in terms of Wigner function [51][52][53][54], which turns out to be a useful tool to describe the CME, CVE, and other related effects [55][56][57][58]. The axial vector component of the Wigner function for massless fermions can be generalized to massive fermions and gives their phase-space density of the spin vector [59]. The spin vector arises from nonzero fermion mass [60].…”