Supersymmetric electroweak baryogenesis, non-equilibrium field theory and quantum Boltzmann equations

Abstract

The closed time-path (CTP) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CTP formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest "memory" effects which are typical of the quantum transport theory and are not present in the classical approach. The slowdown of the relaxation processes may keep the system out of equilibrium for longer times and therefore enhance the final baryon asymmetry. We also stress that the classical approximation is not adequate to describe the quantum interference nature of CP-violation and that a quantum approach should be adopted to compute the sources since they are most easily built up by the transmission of low momentum particles.

Flavor-dependentCPviolation and electroweak baryogenesis in supersymmetric theories

“…are the expectation values of the two Higgs doublets) [21,22], is absent, thus leading to a suppressed baryon asymmetry [23,24]. However, in a recent work [25] it is argued that such a suppression is in fact an artifact of the approximation used by the authors of Refs.…”

“…For instance, the results obtained in the MSSM framework for the chargino and squark sources by making use of the continuity equations and the relaxation time approximation [21,22] are different from those based on WKB-methods [23].…”

“…A considerable amount of work has been done concerning the implications of the new flavor-independent CP -violating phases on generating an acceptable value of the baryon asymmetry [20][21][22][23][24][25]. It has been shown that in the minimal supersymmetric extension of the SM (MSSM), if the relative phase φ µ between the gaugino soft mass and the µ term is not too small, φ µ 0.04, a considerable BAU can be generated through the scattering of the charginos with the bubble wall.…”

“…In this framework, the dominant sources of CP violation that are relevant to electroweak baryogenesis are in general associated with the lightest of the right-handed up-squarks [33]. In the usual MSSM scenario with complex µ and gaugino masses, this contribution would be always subdominant, and could even be neglected when compared to that of the charginos and neutralinos [21,22].…”

Thermalization in thick wall electroweak baryogenesis

“…[6], and in the choice of thermal equilibrium Green's functions while evaluating the source in the Closed Time Path formalism of Refs. [7,8,9,10,11]. The thermal assumption is justified by arguing that departures from kinetic equilibrium are small for v w ≪ 1 or Γl w /v w ≫ 1, where l w and v w are the wall width and velocity and Γ is the rate of interactions that maintain kinetic equilibrium.…”