The $\mathrm{SU}(3{)}_C\otimes \mathrm{SU}(3{)}_L\otimes \mathrm{U}(1{)}_X$ gauge model with the minimal scalar sector (two Higgs triplets) is studied in detail. One of the vacuum expectation values $u$ is a source of lepton-number violations and a reason for the mixing among the charged gauge bosons—the standard model $W$ and the bilepton (with $L=2$) gauge bosons as well as among neutral non-Hermitian $X^0$ and neutral gauge bosons: the photon, the $Z$, and the new $Z^{\prime }$. Because of these mixings, the lepton-number violating interactions exist in both charged and neutral gauge boson sectors. An exact diagonalization of the neutral gauge boson sector is derived and bilepton mass splitting is also given. The lepton-number violation happens only in the neutrino but not in the charged lepton sector. In this model, lepton-number changing ($\Delta L=\pm 2$) processes exist but only in the neutrino sector. Constraints on vacuum expectation values of the model are estimated and $u\simeq O(1)\mathrm{GeV}$, $v\simeq v_{\mathrm{weak}}=246\mathrm{GeV}$, and $\omega \simeq O(1)\mathrm{TeV}$.

• Received 9 January 2006

DOI:https://doi.org/10.1103/PhysRevD.73.035004