Fermion masses in the economical 3-3-1 model

Abstract

We show that, in frameworks of the economical 3-3-1 model, all fermions get masses. At the tree level, one up-quark and two down-quarks are massless, but the one-loop corrections give all quarks the consistent masses. This conclusion is in contradiction to the previous analysis in which, the third scalar triplet has been introduced. This result is based on the key properties of the model: First, there are three quite different scales of vacuum expectation values: $\om \sim {\cal O}(1) \mathrm{TeV}, v \approx 246 \mathrm{GeV}$ and $ u \sim {\cal O}(1) \mathrm{GeV}$. Second, there exist two types of Yukawa couplings with different strengths: the lepton-number conserving couplings $h$'s and the lepton-number violating ones $s$'s satisfying the condition in which the second are much smaller than the first ones: $ s \ll h$. With the acceptable set of parameters, numerical evaluation shows that in this model, masses of the exotic quarks also have different scales, namely, the $U$ exotic quark ($q_U = 2/3$) gains mass $m_U \approx 700 $ GeV, while the $D_\al$ exotic quarks ($q_{D_\al} = -1/3$) have masses in the TeV scale: $m_{D_\al} \in 10 ÷80$ TeV.