Towards a realistic model of quarks and leptons, leptonic CP violation, and neutrinoless ββ -decay

To explain the fermion masses and mixings naturally, we introduce a specific flavor symmetry and mass suppression pattern that constrain the flavor structure of the fermion Yukawa couplings. Our model describes why the hierarchy of neutrino masses is milder than the hierarchy of charged fermion masses in terms of successive powers of flavon fields. We investigate $CP$ violation and neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay and show how they can be predicted and constrained in our model by present and upcoming experimental data. Our model predicts that the atmospheric neutrino mixing angle ${\ensuremath{\theta}}_{23}$ should be within $\ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}$ of 45\ifmmode^\circ\else\textdegree\fi{} for the normal neutrino mass ordering and between $\ensuremath{\sim}4\ifmmode^\circ\else\textdegree\fi{}$ and $\ensuremath{\sim}8\ifmmode^\circ\else\textdegree\fi{}$ degrees away from 45\ifmmode^\circ\else\textdegree\fi{} (in either direction) for the inverted neutrino mass ordering. For both neutrino mass ordering and inverted neutrino mass ordering, our model predicts that a $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ Majorana mass in the limited range $0.035\text{ }\text{ }\mathrm{eV}<|{m}_{ee}|\ensuremath{\lesssim}0.15\text{ }\text{ }\mathrm{eV}$, which can be tested in current experiments. Moreover, our model can successfully accommodate flavorless leptogenesis as the mechanism to generate the baryon asymmetry in the Universe, provided the neutrino mass ordering is normal, $|{m}_{ee}|\ensuremath{\simeq}0.072\ifmmode\pm\else\textpm\fi{}0.012\text{ }\text{ }\mathrm{eV}$, and either ${\ensuremath{\theta}}_{23}\ensuremath{\simeq}44\ifmmode^\circ\else\textdegree\fi{}$ and the Dirac $CP$-violating phase ${\ensuremath{\delta}}_{CP}\ensuremath{\simeq}20\ifmmode^\circ\else\textdegree\fi{}$ or 60\ifmmode^\circ\else\textdegree\fi{} or ${\ensuremath{\theta}}_{23}\ensuremath{\simeq}46\ifmmode^\circ\else\textdegree\fi{}$ and ${\ensuremath{\delta}}_{CP}\ensuremath{\simeq}205\ifmmode^\circ\else\textdegree\fi{}$ or 245\ifmmode^\circ\else\textdegree\fi{}.