Abstract:
Going beyond the Standard Model (BSM) becomes mandatory to explain many outstanding unsolved problems. Among of many theories beyond the Standard Model, we are interested in the extension of the SM SU(3)C SU(2)L U(1)Y gauge group to SU(3)C SU(4)L U(1)X the so called 341 models. The most attractive feature of those models is the explanation of the family replication coming from the triangle gauge anomaly cancellation which requires that the three quark generations belong to different SU(4)L representations: two with a left handed chirality QiL lie in the fundamental representation 4, whereas , the third one Q3L together with the three lepton generations `L have to transform under the conjugate fundamental representation 4 (or vice versa). In this thesis, we showed various versions of these models which are characterized by each lepton generation having a different representation under the gauge group. In the compact version, we studied the neutral scalar bosons decays through the study of the various modes of the neutral scalar bosons. where we have constrained the unknown scalar parameters using
the vacuum stability, minimization of the scalar potential, perturbative unitarity bounds and perturbativity of the scalar potential couplings. Moreover, we derived other conditions that come from the positivity of the scalar bosons masses with the stringent condition of the Landau pole. It turns out that this quarks and leptons replication is not the only way to have a model free from the SU(4)L U(1)X gauge anomalies, based on that we introduced a new unique gauge anomaly free model without exotic electric charges baptized the flipped 341 model as an extension of where the previous scheme of construction is reversed that is all the quarks generations transform under the same representation while leptons are not. Thus, a flavor changing neutral current (FCNC) is expected at the tree level in the lepton sector through the exchange of new neutral gauge bosons Z0 and Z00. Using the experimental bounds of the branching ratios of the two rare leptonic decays an upper limit on the lepton flavor violating matrix element jUe j as well as a stringent bound on the neutral gauge bosons masses are obtained.
