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The gauge model based on SU(3)C ⊗ SU(3)L ⊗ U(1)X group with arbitrarily electric charged exotic leptons is presented. The mass eigenvalues and eigenstates for neutral gauge bosons are presented in the general form. We show that in the 3-3-1 models, there always exists triple Higgs self-coupling. The lepton number operator is also presented. | Communications in Physics, Vol. 26, No. 3 (2016), pp. 221-228 DOI:10.15625/0868-3166/26/3/8053 THE 3-3-1 MODEL WITH ARBITRARILY CHARGED LEPTONS HOANG NGOC LONG† Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam DUONG VAN LOI, NGUYEN CHI THAO Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam THANH HUU HONG GIANG Graduate School, Department of Physics, Hanoi Pedagogical University 2, Phuc Yen, Vinh Phuc, Vietnam † E-mail: hnlong@iop.vast.ac.vn Received 27 December 2016 Accepted for publication 19 January 2017 Abstract. The gauge model based on SU(3)C ⊗ SU(3)L ⊗ U(1)X group with arbitrarily electric charged exotic leptons is presented. The mass eigenvalues and eigenstates for neutral gauge bosons are presented in the general form. We show that in the 3-3-1 models, there always exists triple Higgs self-coupling. The lepton number operator is also presented. Keywords: unified theories, models of strong, electroweak interactions. Classification numbers: 14.60.Pq, 12.60.Cn, 14.60.St, 14.70.Pw, 12.15.Ff. I. INTRODUCTION The current status of Particle Physics shows that the Standard Model (SM) must be extended. Among beyond the Standard Models, the models based on SU(3)C ⊗ SU(3)L ⊗ U(1)X (3-3-1) gauge group have some interesting properties due to the following reasons. The first reason concerns the generation number problem. In the SM, there exists the replica of the generations meaning the number of the latter is not constrained. However, in the 3-3-1 models [1, 2], one of quark generation behaves differently from the two other, and this fact leads to the consequence that the number of fermion generations is multiple of the quark color number (3), i.e., 3, 6, . Combining with the Quantum Chromodynamics (QCD) asymptotic freedom requiring the quark generations is less than five, we get the answer why number of fermion generations is .
