On gapped continuum resonance spectra

Abstract: In this work we study a warped five-dimensional (5D) model with ultraviolet (UV) and infrared (IR) branes, that solves the hierarchy problem with a fundamental 5D Planck scale $M$, and curvature parameter $k$, of the order of the 4D Planck mass $M_{\textrm{Planck}}\equiv 2.4\times 10^{15}$ TeV. The model exhibits a continuum of Kaluza-Klein (KK) modes with different mass gaps, at the TeV scale, for all fields. We have computed the Green's functions and spectral densities, and shown how the presence of a continuum KK spectrum can produce an enhancement in the cross section of some Standard Model processes. The metric is linear near the IR, in conformal coordinates, as in the linear dilaton and 5D clockwork models, for which $M\sim$ TeV. We also analyze a pure (continuum) linear dilaton scenario, solving the hierarchy problem with more conventional fundamental $M$ and $k$ scales of the order of $M_{\textrm{Planck}}$, and a continuum spectrum.