ar X iv : h ep - p h / 99 08 49 1 v 1 2 7 A ug 1 99 9 LBNL - 41874 UCB - PTH

In the Standard Model of elementary particle physics, electroweak symmetry breaking is achieved by a Higgs scalar doublet with a negative (mass). The Standard Model has the well known gauge hierarchy problem: quadratically divergent quantum corrections drive the Higgs mass and thus the weak scale to the scale of new physics. Thus, if the scale of new physics is say the Planck scale, then correct electroweak symmetry breaking requires a fine tuning between the bare Higgs mass and the quantum corrections. Supersymmetry, a symmetry between fermions and bosons, solves the gauge hierarchy problem of the Standard Model: the quadratically divergent corrections to the Higgs mass cancel between fermions and bosons. The remaining corrections to the Higgs mass are proportional to the supersymmetry breaking masses for the supersymmetric partners (the sparticles) of the Standard Model particles. The large top quark Yukawa coupling results in a negative Higgs (mass). Thus, electroweak symmetry breaking occurs naturally at the correct scale if the masses of the sparticles are close to the weak scale. In this thesis, we argue that the supersymmetric Standard Model, while avoiding the fine tuning in electroweak symmetry breaking, requires unnaturalness/fine tuning in some (other) sector of the theory. For example, Baryon and Lepton number violating operators are allowed which lead to proton decay and flavor changing neutral currents. We study some of the constraints from the latter in this thesis. We have to impose an R-parity for the theory to be both natural and viable. In the absence of flavor symmetries, the supersymmetry breaking masses for the squarks and sleptons lead to too large flavor changing neutral currents. We show that two of the solutions to this problem, gauge mediation of supersymmetry breaking and making the scalars of the first two generations heavier than a few TeV, reintroduce fine tuning in electroweak symmetry breaking. We also construct a model of low energy gauge mediation with a non-minimal messenger sector which improves the fine tuning and also generates required Higgs mass terms. We show that this model can be derived from a Grand Unified Theory despite the nonminimal spectrum.