Study of the singly charged Higgs in the economic at 3-3-1 model at e^+e^ colliders

The $\mathrm {SU}(3)_C\otimes \mathrm {SU}(3)_L \otimes {\mathrm U}(1)_X$ gauge model with two Higgs triplets (the economical 3-3-1 model) are presented. This model predicts a new singly-charged Higgs bosons $H_2^\pm$, namely a scalar bilepton (a particle of lepton number 2) with mass proportional to the bilepton mass $M_Y$ through the coefficient $\la_4$. Pair production of $H_2^\pm$ at high energy $e^+ e^-$ colliders with polarization of $e^+$, $e^-$ beams was studied in detail. Numerical evaluation shows that if Higgs mass is not too heavy and at high degree of polarization then the reaction can give observable cross section in future colliders. The reaction $e^+ e^- \to H^{-}_2W^+$ is also examined. Based on the result, it shows that production cross sections of $H^{-}_2W^+$ are very small, much below pair production of $H^{\pm}_2$, so that the direct production of them is in general not expected to lead to easily observable signals in $e^+e^-$ annihilation.