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 Δhm+Δml=Δhl, where Δij≡(mi2−mj2) 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: Δa=2.51×10−3 eV2 and Δb=7.42×10−5 eV2. Of six possible assignments of these values to the three MSDs Δhm, Δml, and Δhl, four consistent cases remain and are grouped into two classes under a phenomenological point-like approach. All four predict similar heaviest and lightest neutrino masses (mh∼ 5.01 ×10−2 eV and ml∼ 6.09098 ×10−3 eV), but differ in the middle mass: mm∼ 4.97283 ×10−2 eV in Class 1, and mm∼ 1.05499 ×10−2 eV in Class 2. In a complementary analysis, treating the mass ratio g ≡ mh/mm as a variable, we examine how mh, mm, ml, and g’ ≡ mm/ml 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 ml∼ 8.61 ×10−3 eV (green points). Finally, using the leptonic Jarlskog measure of CP violation (CPV) ΔCP(l) ≡ J(l)·(Δij·Δjk·Δki)(ℓ)·(Δij·Δjk·Δki)(ν), 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 (BSM) is required for leptogenesis to account for the observed Baryon Asymmetry of the Universe (BAU).
Chilong Lin (Thu,) studied this question.