Spectator Processes and Baryogenesis

Spectator processes which are in thermal equilibrium during the period of baryogenesis influence the final baryon asymmetry. We study this effect quantitatively for thermal leptogenesis where we find a suppression by a factor O(1). The cosmological baryon asymmetry is naturally explained by thermal leptogenesis, i.e. the out-of-equilibrium decays of heavy Majorana neutrinos [1]. This mechanism has been studied in detail by several groups [2], and it has been shown that the observed baryon asymmetry can be obtained over a wide range of parameters which are consistent with the observed properties of light neutrinos. In a complete analysis decays, inverse decays and various scattering processes in the primordial plasma have to be taken into account in order to get a reliable estimate of the generated baryon asymmetry [3, 4]. In all previous analyses only the chemical potential μL of the standard model (SM) leptons was treated as a dynamical variable during the process of leptogenesis. All other chemical potentials, and also the baryon asymmetry, were then obtained from μL assuming thermal equilibrium after the period of leptogenesis. However, this picture is incorrect. The duration τL of leptogenesis, which is driven by the out-of-equilibrium decays of heavy Majorana neutrinos, is larger than the Hubble time, τL > 1/H . On the other hand, many processes in the plasma, in particular the sphaleron processes, are in thermal equilibrium, i.e. τi = 1/Γi < 1/H . Hence, many spectator processes in the plasma are faster than leptogenesis. As a consequence the chemical potentials of particles in thermal equilibrium are changed already during the process of leptogenesis. In the following we study the effect of these spectator processes on the final baryon asymmetry in the framework of the SM with additional heavy Majorana neutrinos Nj . Boltzmann equations The most important processes that have to be considered are decays and inverse decays, whose reaction densities will be denoted by γD,j in the following, top-quark neutrino scatterings mediated by a SM Higgs in the sor t-channel, denoted by γ φ,s and γ j φ,t, and ∆L = 2 processes mediated by heavy right-handed neutrinos in the sor t-channel, denoted by γN and γN,t (cf. [2]). Hence, in addition to the lepton number YL we also have to consider the chemical potentials of the Higgs doublet φ, of the quark doublets Q and of the right-handed top quarks t. Since the Yukawa couplings of up and charm quarks are significantly smaller they do not have to be considered here. We will use the following notation for the particle number asymmetries: YH = nφ − nφ̄ s , YQ = nQ − nQ̄ s and YT = nt − nt̄ s , (1) where s denotes the entropy density of the universe and ni are the number densities of the corresponding particles. 2 Taking these chemical potentials into consideration one obtains after a straightforward calculation the following set of Boltzmann equations for the evolution of the number of heavy Majorana neutrinos YNj and the lepton asymmetry YL: dYNj dz = − z sH(M1) (