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Trapping of spin-0 fields on tube-like topological defects. (English) Zbl 1381.81075

Summary: We have considered the localization of resonant bosonic states described by a scalar field \(\Phi\) trapped in tube-like topological defects. The tubes are formed by radial symmetric defects in \((2,1)\) dimensions, constructed with two scalar fields \(\phi\) and \(\chi\), and embedded in the \((3,1)\)-dimensional Minkowski spacetime. The general coupling between the topological defect and the scalar field \(\Phi\) is given by the potential \(\eta F(\phi ,\chi)\Phi^2\). After a convenient decomposition of the field \(\Phi\), 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 \(F(\phi,\chi)=\chi^2\) for a fourth-order potential and, the second one is a sixth-order interaction characterized by \(F(\phi ,\chi)=(\phi \chi)^2\). 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.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
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