Effective Kinetic Theory for High Temperature Gauge Theories

TL;DR

This work constructs a leading-order effective kinetic theory for hot, weakly coupled gauge theories by formulating Boltzmann equations for ultrarelativistic quasiparticles that include both elastic $2\leftrightarrow2$ scatterings and near-collinear $1\leftrightarrow2$ splittings with Landau-Pomeranchuk-Migdal suppression. It develops medium-corrected amplitudes via HTL self-energies, treats soft screening and hard effective masses consistently, and provides a detailed treatment of formation times and interference effects essential for accurate rates. The paper surveys the domain of validity for near-equilibrium and non-equilibrium systems, addresses double-counting and soft gauge-field instabilities, and outlines challenges for extending the framework beyond leading order. Overall, it establishes a robust LO kinetic description for transport and equilibration in high-temperature gauge theories, guiding both theoretical analyses and future refinements.

Abstract

Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $2<->2$ particle scattering processes as well as effective ``$1<->2$'' collinear splitting processes in the Boltzmann equations. The latter account for nearly collinear bremsstrahlung and pair production/annihilation processes which take place in the presence of fluctuations in the background gauge field. Our effective kinetic theory is applicable not only to near-equilibrium systems (relevant for the calculation of transport coefficients), but also to highly non-equilibrium situations, provided some simple conditions on distribution functions are satisfied.

Figures (13)

• Figure 1: Scattering of hard particles by $t$-channel gauge boson exchange. The straight lines could represent any type of hard charged particle, including fermions, gauge bosons, or scalars.
• Figure 2: $t$-channel diagram for $q\bar{q}\to gg$.
• Figure 3: Simplest examples of near-collinear processes which contribute at leading order. The upper diagrams depict hard, nearly collinear gluon bremsstrahlung accompanying a soft gluon exchange between hard particles. The lower diagrams show the conversion of a hard gluon into a nearly collinear quark-antiquark pair when accompanied by a soft exchange with another excitation in the plasma.
• Figure 4: Examples of interference terms involving multiple scatterings that also contribute to hard-gluon bremsstrahlung at leading order.
• Figure 5: Lowest-order diagrams for all $2\leftrightarrow 2$ particle scattering processes in a gauge theory with fermions. Solid lines denote fermions and wiggly lines are gauge bosons. Time may be regarded as running horizontally, either way, so a diagram such as $(D)$ represents both $q \bar{q} \to gg$ and $gg \to q \bar{q}$.