Abstract
Theories beyond the Standard Model often contain mass scales hierarchically different from the electroweak scale and the Planck scale. It has been shown that such hierarchical mass scales can be realized as typical energy scales of multiple 3-branes in a 5D warped spacetime. We present a mechanism for stabilizing the intervals between the multiple 3-branes in the warped extra dimension, by introducing a single 5D scalar field with brane-localized potentials. We discuss the radion stabilization by solving the Einstein equation and the scalar field equation of motion so that a backreaction effect on the geometry due to the presence of the scalar field is taken into account. Perturbations from the background configuration are then considered with proper identification of multiple radion degrees of freedom. By solving their equations of motion, we compute the mass spectrum of the radion-scalar field system and the radion couplings to brane-localized matter fields, which are found to be suppressed by typical energy scales and radion profiles at the branes. We also compute the mass spectrum of Kaluza-Klein gravitons and their profiles in the extra dimension. Some applications of the setup are briefly described. Our analysis provides a solid ground to build 5D warped extra dimension models with multiple 3-branes.
Highlights
Background configurationWe consider a spacetime geometry described by R4 × S1/Z2 with the metric, ds2 = gMN dxM dxN = e−2A(y)ημν dxμdxν − dy2 . (2.1)Here, M = (μ, y) with μ running from 0 to 3, ημν is the flat 4D metric, y ∈ [0, yIR] denotes the coordinate for the S1/Z2 orbifold and A(y) is some function of y
We present a mechanism for stabilizing the intervals between the multiple 3-branes in the warped extra dimension, by introducing a single 5D scalar field with brane-localized potentials
Perturbations from the background configuration are considered with proper identification of multiple radion degrees of freedom. By solving their equations of motion, we compute the mass spectrum of the radion-scalar field system and the radion couplings to brane-localized matter fields, which are found to be suppressed by typical energy scales and radion profiles at the branes
Summary
V (φ) denotes the potential of the scalar field which includes bulk cosmological constants. Where all the γ2’s are constants with mass dimension 1 and φUV, I, IR are values of φ at the UV, intermediate and IR branes, respectively. By using the explicit forms of W (φ) in eq (2.4) and the brane-localized potentials (2.6), the solution is obtained as φUV e−u1y (subregion 1). All the distances between the 3-branes are determined in terms of the values of φ on the branes by solving the Einstein equation and the scalar field equation of motion simultaneously. The potential of the GW scalar field including bulk cosmological constants is assumed to have the same form as eq (2.3) with W (φ) for the subregion p defined in yp−1 < y < yp, Wp(φ) = 6kp − upφ (subregion p) , κ2. In terms of the scalar field values on the branes φ0,p(yp−1), φ0,p(yp)
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