Quantum Kinetic Theory for Quantum Chromodynamics

Abstract

We develop a quantum kinetic theory for QCD, which incorporates all leading order collision terms. At lowest order in gradient expansion, it reproduces the spin-averaged Boltzmann equation with both elastic and inelastic collisions. At next order in gradient expansion, the solution to the quantum kinetic equations give spin polarization of on-shell quarks and gluons in quark-gluon plasma when the gradients are of hydrodynamic ones. A power counting in the coupling shows the spin polarization behaves differently in vortical and non-vortical gradients: the former is free of collisional contribution to leading order, while the latter contains a collisional contribution at parametrically the same order as the free theory counterpart. We also find the inelastic collision in a spin basis provides a possible mechanism for conversion between spin and orbital angular momentum.

Figures (18)

• Figure 1: Retarded quark self-energy ${\Sigma}_{ar}$ diagrams in $ra$-basis.
• Figure 2: Retarded gluon self-energy ${\Pi}_{ar}^{{\mu}{\nu}}$ diagrams in $ra$-basis. For the first two diagrams, an inequivalent diagram can be obtained by swaping the $ra$ labelings of the upper and lower propagators in the loop. Color indices have been suppressed for clarity.
• Figure 3: Effective one-loop diagrams contributing to thermal width of quark and gluon. The heavy dotted gluon propagator corresponds to HTL resummed one. For the second diagram, an inequivalent diagram can be obtained by swaping the $ra$ labelings of the upper and lower propagators in the loop.
• Figure 4: QCD specific quark self-energy diagram of propagator correction type. $1$ and $2$ label position of vertices on the Schwinger-Keldysh contour. Arrows indicate momentum flow, see text for more details (same below).
• Figure 5: QCD specific quark self-energy diagram of vertex correction type. There are two possible contour labelings. The dummy momentum variables have been relabeled for convenience.