Kaluza–Klein towers in warped spaces with metric singularities

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 extra dimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kaluza–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.