Dirac Leptogenesis via Scattering using CTP Formalism

We investigate the generation of the matter–antimatter asymmetry in the early universe, prior to the electroweak phase transition, by extending the Standard Model with three right-handed neutrinos that complete Dirac mass terms and two heavy scalar fields. This constitutes a minimal and well-motivated Beyond-the-Standard-Model framework, since the Standard Model alone cannot account for neutrino masses or produce the observed baryon asymmetry due to insufficient CP violation. Using the Closed Time Path (CTP) formalism, we analyze-2-by 2 scattering processes mediated by heavy off-shell scalars. Since these scalars remain off-shell throughout, the post-inflationary temperature of the universe does not need to be high enough to produce them on-shell.

In this setup, right-handed neutrinos depart from thermal equilibrium, generating a lepton asymmetry that is subsequently converted into the observed baryon asymmetry via sphaleron processes. We compute the resulting baryon-to-photon ratio and compare it with the observational value reported by the Planck mission. We also compare the predicted contribution of the right-handed neutrinos to the effective number of relativistic species N_{eff}​ with current cosmological bounds, confirming the model’s consistency with observations.

The use of the CTP formalism eliminates the need for Real Intermediate State (RIS) subtraction, leading to a more consistent and elegant treatment. Furthermore, by incorporating quantum statistical factors, we demonstrate that viable asymmetry generation is achievable even with only two right-handed neutrino flavours. Consequently, the mechanism is generic and does not rely on specific particle species such as leptoquarks or other particular Standard Model extensions.