Kaluza-Klein towers in warped spaces with metric singularities

TL;DR

This paper extends a warp model with metric singularities to analyze Kaluza-Klein towers, establishing boundary conditions and showing how low-lying mass eigenvalues can explain the hierarchy problem, with potential collider signatures.

Contribution

It introduces singularities into the warp model and systematically determines boundary conditions, providing a detailed analysis of Kaluza-Klein spectra and their implications for mass hierarchy.

Findings

Low-lying mass eigenvalues are of the order of TeV.

The model predicts a characteristic Kaluza-Klein mass tower structure.

Numerical calculations illustrate the mass spectrum and potential collider signatures.

Abstract

The version of the warp model that we proposed to explain the mass scale hierarchy has been extended by the introduction of one or more singularities in the metric. We restricted ourselves to a real massless scalar field supposed to propagate in a five dimensional bulk with the extradimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kakuza Klein operators, we have established all the allowed boundary conditions to be imposed on the fields. From them, for given positions of the singularities, one can deduce either mass eigenvalues building up a Kaluza Klein tower, or a tachyon, or a zero mass state. Assuming the Planck mass to be the high mass scale and by a choice, unique for all boundary conditions, of the major warp parameters, the low lying mass eigenvalues are of the order of the TeV, in this way explaining the mass scale hierarchy. In our model, the physical masses are related to the Kaluza Klein eigenvalues, depending on the location of the physical brane which is an arbitrary parameter of the model. Illustrative numerical calculations are given to visualize the structure of Kaluza Klein mass eigenvalue towers. Observation at high energy colliders like LHC of a mass tower with its characteristic structure would be the fingerprint of the model.