Abstract
We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos propagating in a constant but otherwise generic CPT-violating axial time-like background (motivated by string theory). At temperatures much higher than the temperature of the electroweak phase transition, we solve approximately, but analytically (using Padé approximants), the corresponding Boltzmann equations, which describe the generation of lepton asymmetry from the tree-level decays of heavy neutrinos into Standard Model leptons. At such temperatures these leptons are effectively massless. The current work completes in a rigorous way a preliminary treatment of the same system, by some of the present authors. In this earlier work, lepton asymmetry was crudely estimated considering the decay of a right-handed neutrino at rest. Our present analysis includes thermal momentum modes for the heavy neutrino and this leads to a total lepton asymmetry which is bigger by a factor of two as compared to the previous estimate. Nevertheless, our current and preliminary results for the freezeout are found to be in agreement (within a sim 12.5% uncertainty). Our analysis depends on a novel use of Padé approximants to solve the Boltzmann equations and may be more widely useful in cosmology.
Highlights
Introduction and motivationA plethora of cosmological measurements, especially those associated with observations of the cosmic microwave background radiation (CMB) in the universe [1,2], lead to an estimate of the observed asymmetry between matter and antimatter of order: n(T ∼ 1 GeV) = nB nB − nB + nB ∼ nB − nB s (1) (2)nγ where nγ is the density of photons in the universe
In a previous work [43] we presented a phenomenological model for generating a lepton asymmetry via CPT violation (CPTV) in the early universe
As the Boltzmann equations associated with the leptogenesis scenario advocated here and in [43] involve appropriately averaged thermal rates of the decays (9), we develop in Appendix 7.D the relevant formalism; the formalism will be used in the Sect. 3 to set up the pertinent system of Boltzmann equations
Summary
A plethora of cosmological measurements, especially those associated with observations of the cosmic microwave background radiation (CMB) in the universe [1,2], lead to an estimate of the observed asymmetry between matter (mostly baryons) and antimatter of order: n(T. 2 we review the model of [43] and an earlier estimate of the CPTV-background induced lepton asymmetry, which shall be compared with the much more accurate result of the present article, obtained by solving the appropriate Boltzmann equations analytically. 4, we solve the Boltzmann equations using Padé approximants [54], which is an approximation popular in several fields of physics, ranging from statistical mechanics to particle physics and quantum field theory [55,56,57,58,59,60] In this way, we manage to compute the induced lepton asymmetry at RHN decoupling analytically, avoiding numerical treatment. A review of the formalism and derivations of the corresponding decay amplitudes and thermally averaged rates used in the Boltzmann equations, are presented in several Appendices
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