Trapping of spin-0 fields on tube-like topological defects

We have considered the localization of resonant bosonic states described by a scalar field Φ trapped in tube-like topological defects. The tubes are formed by radial symmetric defects in (2,1) dimensions, constructed with two scalar fields ϕ and χ, and embedded in the (3,1)-dimensional Minkowski spacetime. The general coupling between the topological defect and the scalar field Φ is given by the potential ηF(ϕ,χ)Φ2. After a convenient decomposition of the field Φ, we find that the amplitudes of the radial modes satisfy Schrödinger-like equations whose eigenvalues are the masses of the bosonic resonances. Specifically, we have analyzed two simple couplings: the first one is F(ϕ,χ)=χ2 for a fourth-order potential and, the second one is a sixth-order interaction characterized by F(ϕ,χ)=(ϕχ)2. In both cases the Schrödinger-like equations are numerically solved with appropriated boundary conditions. Several resonance peaks for both models are obtained and the numerical analysis showed that the fourth-order potential generates more resonances than the sixth-order one.