Simple 3-3-1 model and implication for dark matter

We propose a new and realistic 3-3-1 model with the minimal lepton and scalar contents, named the simple 3-3-1 model. The scalar sector contains two new heavy Higgs bosons—one neutral $H$ and another singly charged $H^{\pm }$—besides the standard-model Higgs boson. There is a mixing between the $Z$ boson and the new neutral gauge boson ($Z^{\prime }$). The $\rho$ parameter constrains the 3-3-1 breaking scale ($w$) to be $w>460\mathrm{GeV}$. The quarks get consistent masses via five-dimensional effective interactions, while the leptons do so via interactions up to six dimensions. Particularly, the neutrino small masses are generated as a consequence of the approximate lepton-number symmetry of the model. The proton is stabilized due to the lepton parity conservation $(-1{)}^L$. The hadronic flavor-changing neutral currents are calculated, giving a bound $w>3.6\mathrm{TeV}$, and yield that the third quark generation is different from the first two. The correct mass generation for the top quark implies that the minimal scalar sector as proposed is unique. By the simple 3-3-1 model, the other scalars besides the minimal ones can behave as inert fields responsible for dark matter. A triplet, doublet, and singlet dark matter are respectively recognized. Our proposals provide the solutions for the long-standing dark matter issue in the minimal 3-3-1 model.

Figure 1

Contributions to $H_{\sigma }$ and/or $H_1^{\pm }$ annihilation via the Higgs portal when they are lighter than the new particles of the simple 3-3-1 model. There are additionally two $u$ channels that can be derived from the corresponding $t$ channels above.

Figure 2

Contributions to $H_{\sigma }$ and/or $H_1^{\pm }$ annihilation via the gauge portal when they are lighter than the new particles of the simple 3-3-1 model. There remain the $u$-channel contributions for $H_1^{+}{H}_1^{-}\to A_3{A}_3$ and $H_{\sigma }{H}_{\sigma }\to W^{+}{W}^{-}$, respectively, which can be extracted from the corresponding t-channel diagrams above.

Figure 3

Dominant contributions to $H_{\sigma }$ quark scattering.