The notion of naturalness is introduced and reviewed which serves as the best guiding principle in high energy physics. The naturalness criterion raises the gauge hierarchy problem which requires the explanations for the discrepancy between the electroweak scale and the Planck scale. Two main candidates for the gauge hierarchy problems are studied in this paper: the supersymmetric models and the brane world scenarios.
We review the basic materials of supersymmetry and explain the minimal supersymmetric Standard Model. Discrete gauged R-symmetry is introduced as a possible alternative to the conventional R-parity, and horizontal U(1) model is proposed to explain the fermion mass hierarchy and other hierarchies in the supersymmetric models. Also we summarize the μ problem and suggest a fancy idea which combines the technicolor idea with supersymmetry to solve the μ problem.
Several brane world ideas have been proposed for recent three years to explain the gauge hierarchy problem in different ways. We focus on the Randall-Sundrum model and find inflationary to explain the gauge hierarchy problem in different ways. We focus on the Randall-Sundrum model and find inflationary solutions for general bulk cosmological constant and brane tensions. Furthermore, the meaning of naturalness in the brane world model is reexamined by investigating the scalar coupled gravity. Generally singularities are developed in the geometry, and a criterion for a physically admissible singularities is suggested.
All the nice models and ideas have their own clues that ultimately allow us to test and falsify them. It would be amusing to watch for which model will turn out to be the one describing nature.