The 3-3-1 Model with Exotic Electric Charges, Right-Handed Neutrinos with Type-I+II Seesaw Mechanism and Their Effects on LFV

In this research, we propose a modified version of the 3-3-1 model, incorporating a type-I+II seesaw mechanism and \(Z_{4}\) discrete symmetry, as a framework for investigating lepton flavor-violating (LFV) decays. This model successfully yields the left-handed neutrino’s mass square differences in the eV scale, with specific values \(\Delta m_{21}^{2}=7.12\times 10^{-5}~eV^{2},\) \(\Delta m_{31}^{2}=2.55\times 10^{-3}~eV^{2}\), and generates mixing angles \(\sin ^{2}\theta _{12}=0.304,~\sin ^{2}\theta _{23}=0.595~\)and \(\sin ^{2} \theta _{13}=2.15\times 10^{-2}\) that align with experimental data. Furthermore, we develop SARAH and SPheno (Comput. Phy. Commun. 185, 1773, 2014) algorithms tailored for our modified model, enabling us to estimate the magnitude of LFV observables. Our calculations indicate favorable results for various LFV branching ratios, including \(Br(\mu \rightarrow e\gamma )=7.82\times 10^{-20},\) \(Br(\tau \rightarrow e\gamma )=3.66\times 10^{-22},\) \(Br(\tau \rightarrow \mu \gamma )=1.03\times 10^{-19},\) \(Br(\tau \rightarrow eee)=3.97\times 10^{-12},\) \(Br(\tau \rightarrow \mu \mu \mu )=1.33\times 10^{-12},\) \(Br(\tau \rightarrow \mu ee)=8.89\times 10^{-13}\). These findings demonstrate improved agreement with experimental measurements compared to previously reported results, which typically fall within the range of \(10^{-2}\) to \(10^{-6}\).