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Belchior, F. M., & Maluf, R. V. (2023). One-loop radiative corrections in bumblebee-Stueckelberg model. Phys. Lett. B, 844, 138107–9pp.
Abstract: This work aims to study the radiative corrections in a vector model with spontaneous Lorentz symmetry violation, known in the literature as the bumblebee model. We consider such a model with self -interaction quadratic smooth potential responsible for spontaneous Lorentz symmetry breaking. The spectrum of this model displays a transversal nonmassive mode, identified as Nambu-Goldstone, and a massive longitudinal mode. Besides the Lorentz symmetry, this model also exhibits gauge symmetry violation. To restore the gauge symmetry, we introduce the Stueckelberg field and calculate the two -point function by employing the principal-value (PV) prescription. The result is nontransversal, leading to a massive excited mode.
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Belchior, F. M., Moreira, A. R. P., Maluf, R. V., & Almeida, C. A. S. (2023). Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on f(T, B)-thick brane. Eur. Phys. J. C, 83(5), 388–14pp.
Abstract: In the context of f (T, B) modified teleparallel gravity, we investigate the influence of torsion scalar T and boundary term B on the confinement of both the gauge vector and Kalb-Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and f(4)-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.
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Belchior, F. M., Moreira, A. R. P., Maluf, R. V., & Almeida, C. A. S. (2023). 5D Elko spinor field non-minimally coupled to nonmetricity in f (Q) gravity. Phys. Lett. B, 843, 138029–8pp.
Abstract: This paper aims to investigate the localization of the five-dimensional spinor field known as Elko (dual-helicity eigenspinors of the charge conjugation operator) by employing a Yukawa-like geometrical coupling in which the Elko field is non-minimally coupled to nonmetricity scalar Q. We adopt the braneworld scenarios in which the first-order formalism with sine-Gordon and linear superpotentials is employed to obtain the warp factors. A linear function supports the zero-mode trapping within the geometric coupling, leading to the same effective potential as the scalar field. Moreover, an exotic term must be added to obtain real-valued massive modes. Such modes are investigated through the Schrodinger-like approach.
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Moreira, A. R. P., Belchior, F. M., Maluf, R. V., & Almeida, C. A. S. (2023). Bulk fields localization on thick string-like brane in f(T) gravity. Eur. Phys. J. Plus, 138(8), 730–15pp.
Abstract: This paper aims to investigate the influence of torsion on bulk fields in the codimension two thick brane in f(T) modified teleparallel gravity. It is shown that the brane supports the localization of gauge field zero mode without an extra coupling. However, Kalb-Ramond and fermionic fields require a suitable coupling. Then, it is proposed a geometrical coupling based on results in 5D thick brane in modified teleparallel gravities. The Kalb-Ramond field is coupled to torsion scalar T through a gauge-invariant interaction. For the case of fermionic fields, we study the Dirac fermions and gravitino with a derivative geometrical coupling. For all of the fields, it obtained massive and resonant modes by employing the Schodinger-like approach.
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