Hidden symmetries and their implications for Particle Physics

In this thesis, we study the hidden symmetries in the SM and also use discrete gauge symmetries as model building tools to solve various problems in the SM as well as the MSSM, such as R-parity, mu-term, stabilizing the axion solutions, etc. The flavor independent non-supersymmetric SM at the renormalizable level has a discrete Z_3 gauge symmetry known as baryon parity. It is anomaly free at the discrete level as a result of the existence of three generations. The symmetry can effectively act as the Baryon number up to the \Delta B=3 mod 3 level which is also consistent with the prediction from non-perturbative processes corrections in the SM, such as electroweak instanton and sphaleron processes. This symmetry is not consistent with the simple GUTs since those theories explicitly break it. Thus this baryon parity provides a strong hint for new physics like GUTs. Quantum mechanically, we estimate the triple nucleon decay rate which is predicted by the existence of this symmetry. We find a simple U(1) realization with the presence of right-handed neutrinos, from which this baryon parity can naturally emerge. Gauged R-parity is studied in the following chapter. We also study various different approaches to the mu-term problem via a symmetry classification. One explicit example in terms of a Z_4 subgroup of the anomalous U(1) symmetry is given. Another solution arises from a SUSY version of QCD invisible axion. Discrete flavor gauge symmetries are discussed to explain the observed hierarchy fermion masses. D-term splitting problem can then be avoided. In the last part, we show how to use discrete gauge symmetries to stabilize the QCD invisible axion solutions, for both DFSZ and KSVZ invisible axion models