Flavor Changing Neutral Current processes and family discrimination in 3-3-1 models

In 3-3-1 models anomaly cancellation requires that one of the three families of quarks transforms as triplet by $\text{SU}(3)_\text{L}$ with the other two transforming necessarily as anti-triplet. This is an important feature of the model because with it we explain family replication. Thus it is mandatory to discriminate which of the families will transform as triplet by $\text{SU}(3)_\text{L}$ because the main consequence of anomaly cancellation in 3-3-1 models is the arising of processes violating flavor at tree level by means of neutral currents mediated by gauge and scalar fields and each case leads to different results. In this work we consider the 3-3-1 model with right-handed neutrinos. Among the spectrum of 3-3-1 particles that contributes to the flavor changing neutral processes, there is a pseudoscalar that may be the lightest of the 3-3-1 particles and then should give the main contribution to such processes. We then calculate its contribution to the $K^0 -\bar K^0$ mixing transition and confront it with the current experimental results. We do this for the three cases in which one of the family of quarks transforms as a triplet by $\text{SU}(3)_\text{L}$. According to our findings each case leads to different constraints on the mass of the pseudoscalar and the case in which the third family of quarks transforms as triplet seems to be the favoured one. We also obtain the most stringent bounds on the mass of the pseudoscalar of the model.