Fermion masses and mixings in an extended SM based on A4 flavor symmetry with the linear seesaw for majorana neutrino

Abstract: We propose a $U(1)L$ model with $A_4$ symmetry in light of the linear seesaw for majorana neutrino that capable of generating the current lepton and quark mass and mixing patterns. The smallness of Majorana neutrino mass is reproduced through the linear seesaw mechanism. The model can accommodate the current observed patterns of lepton and quark mixing in which the solar neutrino mixing angle and the Dirac CP violating phase are in $2\sigma$ range for both NO and IO, the Majorana violating phases are predicted to be $\eta{1} \in (2.29, 10.31)^\circ$ and $\eta_{2} \in (57.30, 302.70)^\circ $ for NO while $\eta_1\in (3.44, 10.31)^\circ$ and $\eta_{2} \in(79.07, 87.09)^\circ$ for IO. The obtained sum of neutrino mass and the effective Majorana neutrino mass are in good consistent with the recent upper limits. For quark sector, all the quark masses can get the best-fit values and all the elements of the quark mixing matrix are in agreement with the experimental constraints except one element, $(V_{\mathrm{CKM}})_{21}$, with a deviation about $0.25\,\%$ deviation.