Physics beyond the standard model using 3-3-1 models

Several problems in the SM of the Fundamental Particles, such as neutrino masses, dark matter, and the Muon Anomalous Magnetic Moment, require new physics. Therefore, the present work investigates the feasibility of these issues and possible collision signatures. This work focuses on models based on an extended gauge group, known as 3-3-1 models. Considering the result from the gµ − 2 experiment E989 at Fermilab laboratory, 3-3-1 models are examined to determine if they can explain this anomaly observed. This result favored a new physics interpretation with over 4σ of confidence level at the beginning of 2021. Later, it was discussed how these 3-3-1 models could be extended to successfully explain the MAMM while agreeing with current and future colliders. Further, we dive into the details of the 3-3-1 models and carry out a Monte Carlo Simulation of the LHC to obtain lower mass bounds for the masses of the new gauge bosons, namely the Z′ field. Moreover, we forecast the mass range of the Z′ gauge boson at the LHC at High Luminosity and High Energy. Given that DM is present in several models discussed in this thesis, we investigate the interaction between the DM in one of these models, known as 3-3-1 LHN, and collider searches. Thus, the results also compare the experimental relic density of DM with the DM candidates. Besides, numerous flavor anomalies have emerged recently. Then, we assume flavor-changing interactions mediated by a gauge boson Z′, at tree level, analyzing the SM deviations in the K0 − K0, D0 − D0, B0d − B0d and B0s − B0s meson systems. Here, we use updated data on the mass difference of the four meson systems. We derive lower mass bounds on Z′ at two different parameterizations of the quark mixing matrices between the mass eigenstate and flavor bases. By focusing on a model based on the SU(3) gauge group, we put our results in perspective with current and future hadron colliders to conclude that mass meson systems can give rise to much more stringent bounds than those at high-energy colliders ...