Selected topics on dynamical symmetry breaking
Abstract
The chapters of this thesis contain four somewhat unrelated studies. In chapter two the fermion number induced by nontrivial topological configurations in the O(3) nonlinear $\sigma$ model in 2 + 1 dimensions is studied in the presence of a parity breaking fermion mass term. We consider a scalar background configuration that adiabatically evolves from the normal vacuum to a soliton of winding number unity. The appearance of zero energy modes is analyzed as a function of the relative magnitudes of the explicit, odd parity, fermion mass, $m\sb{odd},$ the fermion mass induced by the Yukawa coupling, $m\sb{Y},$ and the inverse soliton width, 1/$\rho\sb{s}.$ We find $\rho\sb{c},$ the maximum value of $\rho = \rho\sb{s}m\sb{Y}$ for which a fermion zero energy level crossing occurs during the adiabatical evolution. We obtain that whenever the ratio $M\sb{f} = m\sb{odd}/m\sb{Y} < 1$ and $\rho > \rho\sb{c}(M\sb{f})$ the ground state charge of the soliton is wholly determined by its topological charge. Otherwise, it vanishes. In chapter three the top quark mass prediction in supersymmetric top condensate models is found to be insensitive to the inclusion of the effects of higher dimensional operators. For associated coefficients of characteristically moderate strength, the supersymmetric renormalization group trajectories are strongly focused to the infrared quasi-fixed point of the top Yukawa coupling constant. In chapter four the sensitivity of the top quark and Higgs boson masses in the top condensate model to two loop radiative corrections is studied. Both the top quark and the Higgs boson masses vary by a few GeV with respect to their values in the one loop calculation. Finally, in chapter five an upper bound on the mass of the lightest neutral scalar Higgs boson is calculated in an extended version of the minimal supersymmetric standard model that contains an additional Higgs singlet. Radiative corrections induced by a large top quark Yukawa coupling are included in our analysis, and we find the allowed values for the mass of the Higgs boson as a function of the mass of the top quark. Typically, for a top quark mass $m\sb{t} = 150 GeV,$ the upper bound on the Higgs boson mass is about 25 GeV higher than in the minimal model.
Degree
Ph.D.
Advisors
Clark, Purdue University.
Subject Area
Particle physics
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