Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

Abstract

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant g. The spin relaxation rate Γ s in spin hydrodynamics is shown to be Γ s ∼ g 4 log(1/g)T (T /M ) 2 in the heavy-quark limit T /M 1, which is smaller than the relaxation rate of other non-hydrodynamic modes by additional powers of T /M . We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.

New Developments in Relativistic Magnetohydrodynamics

“…We thus use the symmetric energy-momentum tensor T µν = T νµ in the following discussion In the transient time scale, called the spin hydrodynamic regime in Refs. [122][123][124], the spin density of microscopic constituents may show its intrinsic dynamics, and the energy-momentum tensor has the anti-symmetric components. This is the main topic of relativistic spin hydrodynamics which we will briefly discuss in Section 8.…”

New developments in relativistic magnetohydrodynamics

“…However, when the spin-orbit coupling is weak (see Ref. [123] for a concrete analysis showing how the spin-orbit coupling can be parametrically weak), the spin relaxation time can be parametically large, making spin density a quasihydrodynamic mode [122]. The spin hydrodynamics is thus well formulated in this regime as a quasi-hydrodynamics [259] or Hydro+ [260].…”

“…In the transient time scale, called the spin hydrodynamic regime in Refs [122][123][124],. the spin density of microscopic constituents may show its intrinsic dynamics, and the energy-momentum tensor has the antisymmetric components.…”

Spin evolution of massive fermion in QED plasma

“…So as to self-consistently incorporate the two processes, we derive the collision terms to O( ) with all the first order hydrodynamic gradients included. In [36,37,67], only classical processes characterizing the diffusion processes are discussed; in [40] the polarization effect of vorticity is discussed while the contact interaction of NJL model is not enough to catch the dynamical process in QGP; in [42] the collision term is derived to O( ), while the probe fermion is massless. In this paper, we derive the collision term to the leading logarithmic order in coupling e, similar to the procedure in [36,37,42,67].…”

“…In [36,37,67], only classical processes characterizing the diffusion processes are discussed; in [40] the polarization effect of vorticity is discussed while the contact interaction of NJL model is not enough to catch the dynamical process in QGP; in [42] the collision term is derived to O( ), while the probe fermion is massless. In this paper, we derive the collision term to the leading logarithmic order in coupling e, similar to the procedure in [36,37,42,67]. For the massive fermion, the axial-vector component of Wigner function characterizing the spin distribution has three degrees of freedom.…”