Linear sigma models in QCD and S3 symmetry for neutrinos

This thesis has two parts with different topics in particle physics. In part I, we consider various linear sigma models and their applications to scalar mesons. It is shown that the tree amplitude for ππ scattering in the minimal linear sigma model has an exact expression which induces an infinite geometric series in which the pattern for both the I = 0 and I = 2 s-wave scattering lengths to orders $p^2$, $p^4$ and $p^6$ seems to agree with chiral perturbation theory predictions. The model is then gauged to study the mass differences between the vector meson and the axial vector meson as a possibly useful "template" for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) the "global" region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of "bare" sigma mass parameter for describing these two regions. By including the parity reversed partner we study a simple two Higgs dou-blet model which reflects, in a phenomenological way, the idea of compositeness for the Higgs sector. It is relatively predictive. In one scenario, it allows for a "hidden" usual Higgs particle in the 100 GeV region and a possible dark matter candidate. Poles in unitarized [pi pi] scattering amplitude are studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseu- doscalar nonets. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. Some comparison is made to the situation in the usual SU(3) linear sigma model with a single scalar nonet. We show that the mixing of two "bare" nonets, one of which is of quark- antiquark type and the other of two quark- two antiquark type is, before chiral symmetry breaking terms are included, only possible for three flavors. Specif ically, our criterion would lead one to believe that scalar and pseudoscalar states containing charm would not have "four quark" admixtures. We also discuss some aspects associated with the possibility of getting new experi- mental information about scalars from semileptonic decays of heavy charged mesons into an isosinglet scalar or pseudoscalar plus leptons. In part II we explore a predictive model based on permutation symmetry S3 for the masses and mixing matrix of three Majorana neutrinos. At zeroth order the model yielded degenerate neutrinos and a generalized "tribimaximal" mixing matrix. We first study the effects of the perturbation which violates S3 but preserves the well known (23) interchange symmetry. This is done in the presence of an arbitrary Majorana phase ψ which serves to insure the degeneracy of the three neutrinos at the unperturbed level. At this order the mass splitting was incorporated and the tribimaximal mixing matrix emerged with very small corrections but with a zero value for the parameter s13. Next a different, assumed weaker, perturbation is included which gives a non zero value for s13 and further corrections to other quantities. These corrections are worked out and their consequences discussed under the simplifying assumption that the conventional CP violation phase vanishes. It is shown that the existing measurements of the parameter s23 provide strong bounds on s13 in this model.

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