UC Berkeley

While the standard model successfully describes a wide array of phenomena among

the fundamental particles and interactions, some significant problems remain. These

include the hierarchy problem in the Higgs sector, the hierarchy of the Yukawa cou-

plings, and the nature of dark matter.

These problems are addressed in this thesis. First, the standard model and its

problems are reviewed; supersymmetry is identified as possible framework for solving

all three problems. Second, brief reviews of supersymmetry and dark matter phe-

nomenology are provided. Then, using gamma rays and neutrinos, novel astrophysi-

cal constraints on the dark matter interpretation of the recently observed cosmic-ray

e± anomalies are developed. Finally, a class of supersymmetric models is described

wherein the first and second generation squarks and sleptons are pseudo-Nambu-

Goldstone bosons, making their standard model counterparts naturally light, thereby

resolving the Yukawa hierarchy problem. We show that this model an be easily iden-

tified at the Large Hadron Collider after a few months of running at 14 TeV. This

class of models also provides a promising dark matter candidate which evades the

derived gamma ray and neutrino bounds, and may be relevant to the cosmic ray e±

anomalies in a certain parameter region.