Baryon asymmetry via leptogenesis in a neutrino mass model with complex scaling

Baryogenesis via leptogenesis is investigated in a specific model of light neutrino masses and mixing angles. The latter was proposed on the basis of an assumed complex-extended scaling property of the neutrino Majorana mass matrix $M_\nu$, derived with a type-1 seesaw from a Dirac mass matrix $m_D$ and a heavy singlet neutrino Majorana mass matrix $M_R$. One of its important features, highlighted here, is that there is a common source of the origin of a nonzero $\theta_{13}$ and the CP violating lepton asymmetry through the imaginary part of $m_D$. The model predicted CP violation to be maximal for the Dirac type and vanishing for the Majorana type. We assume strongly hierarchical mass eigenvalues for $M_R$. The leptonic CP asymmetry parameter $\varepsilon^\alpha_{1}\hspace{1mm}$ with lepton flavor $\alpha$, originating from the decays of the lightest of the heavy neutrinos $N_1$ (of mass $M_1$) at a temperature $T\sim M_1$, is what matters here with $\varepsilon^\alpha_{2,3}$, originating from the decays of $N_{2,3}$, being washed out. The light leptonic and heavy neutrino number densities (normalized to the entropy density) are evolved via Boltzmann equations down to electroweak temperatures to yield a baryon asymmetry through sphaleronic transitions. The effect of flavored vs. unflavored leptogenesis in the three mass regimes (1) $M_1<10^{9}$ GeV, (2) $10^9$ GeV $<M_1<$ $10^{12}$ GeV and (3) $M_1>10^{12}$ GeV are numerically worked out for both a normal and an inverted mass ordering of the light neutrinos. Corresponding results on the baryon asymmetry of the universe are obtained, displayed and discussed.