Particle abundance in a thermal plasma: Quantum kinetics versus Boltzmann equation

Abstract

We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the non-equilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation emerges naturally. We consider a particle species that is stable in the vacuum and interacts with heavier particles that constitute a thermal bath in equilibrium. Asymptotic theory suggests a definition of a fully renormalized single particle distribution function. Its real time dynamics is completely determined by the non-equilibrium effective action which furnishes a Dyson-like resummation of the perturbative expansion. The distribution function reaches thermal equilibrium on a time scale ∼ 1/2 Γ k (T ) with Γ k (T ) being the quasiparticle relaxation rate. The equilibrium distribution function depends on the full spectral density as a consequence the fluctuation-dissipation relation. Such dependence leads to off-shell contributions to the particle abundance. A specific model of a bosonic field Φ in interaction with two heavier bosonic fields χ1,2 is studied. The decay of the heaviest particle and its recombination lead to a width of the spectral function for the particle Φ and to off-shell corrections to the abundance. We find substantial departures from the Bose-Einstein result both in the high temperature and the low temperature but high momentum region. In the latter the abundance is exponentially suppressed but larger than the Bose-Einstein result. We obtain the Boltzmann equation in renormalized perturbation theory and highlight the origin of the differences. Cosmological consequences are discussed: we argue that the corrections to the abundance of cold dark matter candidates are observationally negligible and that recombination erases any possible spectral distortions of the CMB. However we expect that the enhancement at high temperature may be important for baryogenesis.

Thermal noise and stochastic strings in AdS/CFT

“…In the recent literature we have found refs. [41,42] instructive. For a heavy particle coupled to an equilibrated bath of forces the real time partition function is…”

Production of a sterile species: Quantum kinetics

“…The reduced density matrix can be represented by a path integral in terms of the non-equilibrium effective action that includes the influence functional. This method has been used extensively to study quantum brownian motion [52,53], and quantum kinetics [54,55] and more recently in the study of the non-equilibrium dynamics of thermalization in a similar model [48]. The time evolution of the initial density matrix is given by…”

Quantum mechanics of leptogenesis

“…In both cases the imaginary part of the self-energy is known analytically [84], the calculation can be seen in Appendix B.1. For m ≫ m 1 , m 2 , the decay width of Φ at zero temperature is given by…”

“…In order to illustrate the results of the previous sections, we now consider a toy model (cf. [84,108]), where the quanta of two massive scalar fields represent the thermal bath. The full Lagrangian is given by…”

“…The full treatment of non-equilibrium processes in quantum field theory is usually based either on Kadanoff-Baym equations [74] and the Schwinger-Keldysh formalism [75][76][77][78][79][80] or on stochastic Langevin equations [81][82][83][84]. The Kadanoff-Baym equations are the thermal analogs to the Schwinger-Dyson equations [85], and its first order solution in an expansion around its center of mass coordinate after a Wigner transformation gives back the normal Boltzmann equations.…”