Four-Dimensional Planck Scale Is Not Universal in Fifth Dimension in Randall-Sundrum Scenario

T. Ozeki, N. Shimoyama
2000 Progress of theoretical physics  
It has recently been proposed that the hierarchy problem can be solved by considering the warped fifth dimension compactified on S^1/Z_2. Many studies in the context have assumed a particular choice for an integration constant σ_0 that appears when one solves the five-dimensional Einstein equation. Since σ_0 is not determined by the boundary condition of the five-dimensional theory, σ_0 may be regarded as a gauge degree of freedom in a sense. To this time, all indications are that the
more » ... sional Planck mass depends on σ_0. In this paper, we carefully investigate the properties of the geometry in the Randall-Sundrum model, and consider in which location y the four-dimensional Planck mass is measured. As a result, we find a σ_0-independent relation between the four-dimensional Planck mass M_ Pl and five- dimensional fundamental mass scale M, and remarkably enough, we can take M to TeV region when we consider models with the Standard Model confined on a distant brane. We also confirm that the physical masses on the distant brane do not depend on σ_0 by considering a bulk scalar field as an illustrative example. The resulting mass scale of the Kaluza-Klein modes is on the order of M.
doi:10.1143/ptp.103.1227 fatcat:lmwjme2ymvf53iwy7w3jekbbiu