Analysis on Neutrino Masses and Leptogenesis in the CP-Violating Standard Model

This article extends the CP-violating Standard Model (CPVSM) from the quark sector to the lepton sector to investigate leptogenesis and neutrino masses. Using the identity $\Delta_{hm} + \Delta_{ml} = \Delta_{hl}$, where $\Delta_{ij} = (m^2_i - m^2_j)$ denoting the mass-squared difference (MSD) between fermions $i$ and $j$, and $h$, $m$, and $l$ labeling the heaviest, middle, and lightest fermions of a given type, respectively, we predict the third neutrino MSD from two experimental inputs: $\Delta_a = 2.51 \times 10^{-3}$ eV$^2$ and $\Delta_b = 7.42 \times 10^{-5}$ eV$^2$. Of six possible assignments of these values to the three $\Delta_{hm}, \Delta_{ml}$, and $\Delta_{hl}$, four consistent cases remain and are grouped into two classes. All four predict similar heaviest and lightest neutrino masses ($m_h = 5.01 \times 10^{-2}$ eV and $m_l = 6.09098 \times 10^{-3}$ eV), but differ in the middle mass: $m_m = 4.97283 \times 10^{-2}$ eV in Class 1, and $m_m = 1.05499 \times 10^{-2}$ eV in Class 2. In a complementary analysis, treating the mass ratio $g = m_h / m_m$ as a variable, we examine how $m_h$, $m_m$, $m_l$, and $g'$ evolve with $g$. Of particular interest are the ranges of $g$ bounded by MSD-based values derived in Subsection III-A (blue points) and values derived from a previously predicted $m_l = 8.61 \times 10^{-3}$ eV (green points). Finally, using the leptonic Jarlskog measure of CPV $\Delta_{CP(l)} = J_{(l)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\ell)} (\Delta_{ij} \Delta_{jk} \Delta_{ki})_{(\nu)}$, we find that leptogenesis is at least 71 orders of magnitude weaker than baryogenesis in the CPVSM. This striking discrepancy suggests that new physics beyond the Standard Model is required for leptogenesis to account for the observed BAU.