Bounds on quark mixing, $M_{Z^{\mathrm{\prime }}}$ and $Z-Z^{\mathrm{\prime }}$ mixing angle from flavor changing neutral processes in a 3-3-1 model

Meson and anti-meson mixing processes constitute an important source of constraints on models that give tree level contributions to flavor violating neutral processes. In electroweak $\text{SU}(3{)}_{\text{L}}\times \text{U}(1{)}_N$ models, where anomaly cancellation requires that one family of quarks transforms differently from the other ones, processes involving flavor changing neutral currents gain tree level contributions mediated by gauge and scalar fields. Here, we firstly investigate the contributions of the neutral scalar that mimics the standard Higgs to the $K^0-{\bar{K}}^0$, $B^0-{\bar{B}}^0$, and $D^0-{\bar{D}}^0$ mixing processes and confront our predictions with experiments. The results will determine the quark mixing matrices $V_L^{u,d}$. In possession of this information we, next, evaluate the contributions of the neutral gauge bosons $Z^{\mathrm{\prime }}$ and $Z$ to the $K^0-{\bar{K}}^0$, $B^0-{\bar{B}}^0$, and $D^0-{\bar{D}}^0$ processes. This realistic approach to meson transitions will provide severe bounds on $M_{Z^{\mathrm{\prime }}}$ and $Z-Z^{\mathrm{\prime }}$ mixing angle.