Realizing flavored leptogenesis: a reappraisal through special kinds of orthogonal matrices

The parameterisation proposed by Casas and Ibarra in the year 2001 have shown promising role in the extraction of neutrino Yukawa coupling which is a basic ingredient of the seesaw mechanism generating neutrino mass. We pay special attention in establishing the crucial role of the Casas-Ibarra (CI) parameterisation in presence of two different orthogonal matrices, $R= \textbf{O} \,\rm e^{i {\bf A}}$ and $R= \textbf{O} \,\rm e^{\bf A}$ in order to investigate flavored leptogenesis. In the light of these two choices of the orthogonal matrix we examine the connection between the low energy and high energy CP violations along with certain interesting predictions on the low energy parameters namely, the lightest neutrino mass and the Dirac CP phase ($\delta$). Considering the right handed neutrino (RHN) mass window to be $10^8$ GeV, we show that Dirac phase leptogenesis is possible with the choices of these two orthogonal matrices. We choose a nearly degenerate spectrum for the RHN masses for having a successful leptogenesis. We also emphasize on presenting a range of the matrix elements of the skew symmetric matrix $ \textbf{A}$. The results obtained in the present analysis underline the importance of understanding the status of CP violation in the low energy sector. We also discuss the phenomenological implications of these two case studies in the context of LFV considering the $\mu \rightarrow e\gamma$ decay process.