Non-universal flipped trinification models with arbitrary β

We explore the recently proposed gauge symmetry SU(3)C ⊗ SU(3)L ⊗ SU(3)R ⊗ U(1)X S U ( 3 ) C ⊗ S U ( 3 ) L ⊗ S U ( 3 ) R ⊗ U ( 1 ) X , which naturally embeds both the Left-Right symmetric model and the 3-3-1 model as subgroups. Within this unified framework, we propose four families of leptons and quarks. A detailed analysis of their contributions to gauge anomaly cancellation is carried out for a general value of the parameter β β . From this analysis, eight non-universal anomaly-free three-family models and four non-universal two-family anomaly free sets were identified. The three-family models offer realistic extensions of the Standard Model, retaining several appealing features of the 3-3-1 models, while the two-family sets provide flexibility for constructing models with even numbers of families. We also report LHC bounds on the $$Z'$$ Z ′ mass for the particular case β = -1/√3 β = - 1 / 3 , considering all possible combinations of lepton and quark families. These limits exhibit a strong dependence on the mixing parameter θ θ , which enters the couplings of Standard Model fermions to the $$Z'$$ Z ′ boson.