Abstract
Green’s functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension z, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS5, thus solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to z → ∞. This simplified metric, which can be considered as an approximation of a more complicated (and smooth) one, leads to analytical Green’s functions (with a mass gap mg ∼ TeV and a continuum for s > {m}_g^2 ) which could then be easily incorporated in the experimental codes. The theory contains Standard Model gauge bosons in the bulk with Neumann boundary conditions in the UV brane. To cope with electroweak observables the theory is also endowed with an extra custodial gauge symmetry in the bulk, with gauge bosons with Dirichlet boundary conditions in the UV brane, and without zero (massless) modes. All Green’s functions have analytical expressions and exhibit poles in the second Riemann sheet of the complex plane at s = {M}_n^2 − iMnΓn, denoting a discrete (infinite) set of broad resonances with masses (Mn) and widths (Γn). For gauge bosons with Neumann or Dirichlet boundary conditions, the masses and widths of resonances satisfy the (approximate) equation s = −4 {m}_g^2{mathcal{W}}_n^2 [±(1 + i)/4], where mathcal{W} n is the n-th branch of the Lambert function.
Highlights
Theories [11], which predict discrete spectra with a TeV mass gap and a mass separation between modes ∼ 30 GeV
Green’s functions with continuum spectra are a way of avoiding the strong bounds on new physics from the absence of new narrow resonances in experimental data. We model such a situation with a five-dimensional model with two branes along the extra dimension z, the ultraviolet (UV) and the infrared (IR) one, such that the metric between the UV and the IR brane is AdS5, solving the hierarchy problem, and beyond the IR brane the metric is that of a linear dilaton model, which extends to z → ∞
In this paper we have studied a 5D model which naturally leads to gapped continuum spectra
Summary
We will assume a Z2 symmetry (y → −y) across the UV brane, which translates into boundary conditions on the fields, while we will impose matching conditions for bulk fields across the IR brane. Due to the Z2 symmetry across the UV brane, the localized terms impose the following boundary conditions in the UV. Simple brane potentials satisfying the boundary conditions of eq (2.8), the jumping conditions of eq (2.9) with ∆W (φ(y1)) = ∆W (φ(y1)) = 0, and fixing dynamically the values vα of φ at the branes, i.e. vα = φ(yα), are given by λ0(φ). This formalism has been extensively discussed in e.g. refs. This formalism has been extensively discussed in e.g. refs. [39, 40]
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