Quantum kinetic theory of spin polarization of massive quarks in perturbative QCD: Leading log

Abstract

We present the quantum kinetic equation for spin polarization of massive quarks in leading log order of perturbative QCD, which describes time evolution of the spin density matrix in momentum space of a massive quark interacting with a background QCD plasma. We find that the time evolution operator of the spin density matrix, or the quantum kinetic collision terms, are universally of order α 2 s log(1/α s ) in terms of the QCD coupling constant α s = g 2 /(4π). Our quantum kinetic equation is valid for an arbitrary quark mass m m D ∼ gT , where m D is the Debye mass, and can be used to study relaxation dynamics of spin polarization of massive quarks in perturbative QCD

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

“…Recently, a related study for spin diffusion has been presented in ref. [54] with a different approach. We will mostly follow the theoretical setup therein.…”

“…[69] and the same approximation in ref. [54]). Note that the O(f 2 A ) terms are not dropped a priori in the calculations, whereas shall see that only the terms linear to f A remain in the final result, which thus agrees with our power-counting scheme.…”

“…leading-logarithmic result in weakly coupled QCD as in the derivation shown in ref. [54] from a distinct approach. Recall that p µ = (q − q ) µ and g c denotes the coupling constant for strong interaction.…”

“…Such a diffusion term in collisions of the AKE has also been constructed in ref. [54] from a distinct approach, in which different parameterization of the spin vector is applied. Nonetheless, it may be more practical to adopt our parameterization for the spin vector, which has a direct connection to the axial-charge current equivalent to the spin polarization through the Wigner functions and the combination with the free-steaming part of the AKE.…”

“…On the other hand, in ref. [54], the spin-diffusion term at O( 0 ) in collisions was computed in perturbative QCD (see also refs. [55,56] for other studies of collisions).…”