A Three three-brane Universe:New Phenomenology for the New Millennium?

TL;DR

The paper extends the Randall–Sundrum framework by introducing a three-brane construction in $AdS_5$, placing SM fields on a positive brane and predicting a distinctive ultralight first KK graviton bound state that can dominate gravity under certain conditions. It derives the KK spectrum and couplings, showing that the first KK mode has mass $m_1=2 k w e^{-2x}$ and coupling $c_1= w M_{\\rm Pl}$ (with higher modes increasingly decoupled as $e^{x}$ grows), and maps viable regions of parameter space using collider cross sections and Cavendish tests. The authors also propose a Bi-Gravity scenario where gravity is mediated by both the massless graviton and the ultralight KK state, leading to modifications at cosmological and submillimeter scales and offering new observational signatures. Overall, the work reveals rich phenomenology for multi-brane warped geometries and guides experimental searches for deviations in gravity and high-energy processes.

Abstract

We consider an extension of the Randall-Sundrum model with three parallel 3-branes in a 5-dimensional spacetime. This new construction, apart from providing a solution to the Planck hierarchy problem, has the advantage that the SM fields are confined on a positive tension brane. The study of the phenomenology of this model reveals an anomalous first KK state which is generally much lighter than the remaining tower and also much more strongly coupled to matter. Bounds on the parameter space of the model can be placed by comparison of specific processes with the SM background as well as by the latest Cavendish experiments. The model suggests a further exotic possibility if one drops the requirement of solving the hierarchy problem. In this case gravity may result from the exchange of the ordinary graviton plus an ultralight KK state and modifications of gravity may occur at both small and extremely large scales.

Figures (8)

• Figure 1: Randall-Sundrum Model with two branes at the orbifold $S^1/Z_2$ fixed points. Here and further a brane with positive cosmological constant is called positive or $"+"$ brane and a brane with negative cosmological constant is called negative or $"-"$ brane.
• Figure 2: $+-+$ model with two $"+"$ branes at the fixed points and moving $"-"$ branes. In the limiting case when $x \rightarrow 0$ we have a RS configuration.
• Figure 3: $++-$ model which is a RS configuration on Figure 1 with an insertion of a moving $"+"$ brane. This configuration can be obtained from a configuration with only $"-"$ branes at the orbifold points and several moving $"+"$ branes.
• Figure 4: $e^+e^-\rightarrow \mu^+ \mu^-$
• Figure 5: $e^+e^-\rightarrow\mu^+\mu^-$ Resonance of the third mode for $k=10^{17} {\rm GeV}$, $w=e^{-35}$ and $x=1$. The higher curve is the theoretical curve, the smaller one is the result of the smoothing by the convolution of the theoretical curve and the experimental resolution of the beam. The SM background lies below them.