We show that the mass matrix of electrically neutral gauge bosons in the recent proposed model based on SU(3)C ⊗ SU(3)L ⊗ U(1)X group with three neutrino singlets [9] has two exact eigenvalues and corresponding eigenvectors. Hence the neutral non-Hermitian gauge boson X0 µ is properly determined. With extra vacuum expectation values of the Higgs fields, there are mixings among charged gauge bosons W± and Y ± as well as among neutral gauge bosons Z,Z 0 and X0 . | Communications in Physics, Vol. 25, No. 3 (2015), pp. 227-237 DOI: GAUGE BOSONS IN THE 3-3-1 MODEL WITH THREE NEUTRINO SINGLETS HOANG NGOC LONG Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam LAM PHU AN HUY, TRAN THANH THUY, LY THI TU TRAN, VU THI HOANG YEN Graduate School, Can Tho University, Can Tho, Vietnam Received 12 April 2015 Accepted for publication 30 September 2015 E-mail: hnlong@ Abstract. We show that the mass matrix of electrically neutral gauge bosons in the recent proposed model based on SU(3)C ⊗ SU(3)L ⊗ U(1)X group with three neutrino singlets [9] has two exact eigenvalues and corresponding eigenvectors. Hence the neutral non-Hermitian gauge boson Xµ0 is properly determined. With extra vacuum expectation values of the Higgs fields, there are mixings among charged gauge bosons W ± and Y ± as well as among neutral gauge bosons Z, Z 0 and X 0 . Keywords: neutrino mass, beyond the standard model. I. INTRODUCTION At present, it is well known that neutrinos are massive that contradicts the Standard Model (SM). The experimental data [1] show that masses of neutrinos are tiny small and neutrinos mix with special pattern in approximately tribimaximal form [2]. The neutrino masses, dark matter and the baryon asymmetry of Universe (BAU) are the facts requiring extension of the SM. Among the extensions beyond the SM, the models based on SU(3)C ⊗ SU(3)L ⊗ U(1)X gauge group (called 3-3-1 for short) [3, 4] have some interesting features including the ability to explain the generation problem [3, 4] and the electric charge quantization [5]. Concerning the content in lepton triplet, the exist two main versions of 3-3-1 models: the minimal version [3] without extra lepton and the model with right-handed neutrinos [4] without exotic charged particles. Due to the fact that particles with different lepton numbers lie in the same triplet, the lepton number is violated and .
