Textures, model building, and orbifold gauge anomalies: Research in three topics in physics beyond the Standard Model

We introduce the Standard Model, list a large sector of the low energy data, and present extensions to the Standard Model including grand unification, supersymmetry, and orbifold extra dimensions. These foundations underly the research presented in this dissertation, which is from three separate projects.; Texture models are Ansatze for the undiagonalized Yukawa matrices in which some of the matrix elements have been chosen to vanish. Recent precise measurements of sin 2beta from the B-factories (BABAR and BELLE) and a better known strange quark mass from lattice QCD make precision tests of predictive texture models possible. We show that in a set of these models, their maximal sin 2beta values rule them out at the 3sigma level. While at present sin 2beta and |Vub/Vcb| are equally good for testing N-zero texture models, in the near future the former will surpass the latter in constraining power.; We construct a supersymmetric SO(10) x D3 grand unified model with an orbifold extra dimension S1/(Z2 x Z2'). The model uses 11 parameters to fit the 13 independent low energy observables of the charged fermion Yukawa matrices and predicts the values of two quark mass combinations, mu/mc and mdmsmb, to each be approximately 1sigma above their experimental values. The remaining observables are successfully fit at the 5% level. This model is shown to have a gauge anomaly on one of the fixed points and we discuss the alterations in field content necessary to repair it.; Extra dimensional orbifold theories have gauge anomaly structures which are more complicated than those of Minkowski space. We review previous work done by von Gersdorff and Quiros to derive general expressions for orbifold gauge anomalies. These equations are applied to a supersymmetric 6D orbifold model with E6 gauge symmetry presented by Kobayashi, Raby, and Zhang in order to verify the gauge anomaly cancellations. From this illustration we conclude that the constraining power of orbifold gauge anomalies on the field content of the theory is about as great as the usual case in Minkowski space and depends highly on the gauge groups and number of dimensions present.