Effective quantum kinetic theory for spin transport of fermions with collsional effects

Abstract

We systematically derive the collision term for the axial kinetic theory, a quantum kinetic theory delineating the coupled dynamics of the vector/axial charges and spin transport carried by the massive spin-1/2 fermions traversing a medium. We employ the Wigner-function approach and propose a consistent power-counting scheme where the axial-charge distribution function, a non-conserved quantity for massive particles, is accounted as the first-order quantity in the expansion, while the vector-charge distribution function the zeroth-order quantity. This specific power-counting scheme allows us to organize a reduced expansion for the collision term and to formally identity the spindiffusion effect and the spin-polarization effect at the same order. We confirm that the obtained collisional axial kinetic theory smoothly reduces to the chiral kinetic theory in the massless limit, serving as a consistency check. In the absence of electromagnetic fields, we further present the simplified axial kinetic equations suitable for tracking dynamical spin polarization of heavy and light fermions, respectively. As an application to the weakly coupled quark-gluon plasma at high temperature, we compute the spin-diffusion term for massive quarks within the leading-log approximation. The formal expression for the firstorder terms provides a path toward evaluation of the spin polarization effect in quantum chromodynamics.

Wigner functions and quantum kinetic theory of polarized photons

“…Analogous to the power-counting scheme proposed in ref. [60] for fermions, we assume that f γ V = O( 0 ) and f γ A = O( 1 ). We confirm, a posteriori, that these assumptions are satisfied when a nonzero f γ A is induced by a vorticity in local thermal equilibrium (see below).…”

“…The primary goal is to derive the generic form of collision term with quantum correction at O( 1 ) in terms of lesser/greater self-energies. In such a formalism as recently constructed for fermions [21,60], given the information of classical collision term at O( 0 ) from, e.g., diagrammatic calculations, one can systematically obtain the corresponding quantum correction in collisions. 4…”

“…By using the real-time formalism and adopting a specific power counting scheme, we further construct the general form of the effective QKT for polarized photons with the collision term characterized by self-energies, similar to the fermionic case in ref. [60].…”

“…This would pave the way to future study of entangled spin transport of quarks and gluons in QGP. Motivated by recent experimental observations of global polarization of Λ hyperons in heavy ion collisions [61][62][63], this direction should be important to understand how the dynamical evolution of the quark spin will be converted to the local spin polarization of hadrons [60,[64][65][66][67][68][69][70] along the direction of the strong vorticity generated in peripheral collisions; see other theoretical works on developments of hydrodynamics with spin [71][72][73][74][75] and statistical quantum field theory [76][77][78], which also aim at exploring underlying mechanisms and reconciling the existing tension between theoretical predictions and experimental observations for local spin polarization in heavy ion collisions (see ref. [79] for a recent review and more references therein).…”

Kinetic theory with spin: From massive to massless fermions

“…Therefore, a kinetic theory for massive fermions with spin, also called the spin kinetic theory, is required to describe the spin evolution of massive quarks in phase space. Such a theory was constructed many years ago for nonrelativistic dilute spinful gases [58,59] and has recently been formulated for relativistic Dirac fermions using the covariant Wigner functions [60][61][62][63][64] and equal-time Wigner functions [65]. It can also be constructed in the worldline formalism [66,67].…”