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In this manuscript, we discuss the confinement of the spin $\frac{1}{2}$ field on a plethora of branewords models. Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), we studied the consistency of the Standard Model (SM) fields localization on braneworlds with the Einstein equation. In that paper, we discussed the consistency of the spinor field confinement and, by using a Yukawa-like interaction given by $\mathcal{L}_{int}\propto f(y)\bar{\Psi}\Psi$, we obtained that the function must be defined as $f(y)\propto e^{-A}A'$. This shape of the scalar function emerge from the requirement that the spin $\frac{1}{2}$ (zero-mode) localization cannot modify the metric on bulk. This ensures that the confinement of gravity on the brane is preserved. In the present manuscript, we find a covariant scalar-coupling function that can generate this interaction. This provide a new mechanism for localizing fermion fields over the brane. We also discuss massive modes and we found some gravitational configuration where there are confined and discretized massive modes., Comment: 28 pages, 2 figures; We add a new subsection in section VI

Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), the present authors obtained general stringent conditions on the localization of fields in braneworlds by imposing that its zero-mode must satisfy Einstein's equations (EE). Here, we continue this study by considering free $p$-form. These fields present an on-shell equivalency relation between a $p$-form and a $(D-p-2)$-form, provided by Hodge duality (HD). This symmetry will impose a new consistency condition, namely, confinement of a $p$-form must imply the localization of its dual. We apply the above conditions to $6$D braneworlds. With this, we find that in global string-like defects, for example, the $1$-form has a normalizable zero-mode. By using the HD, we show that its bulk dual $3$-form also has a normalizable zero-mode, making the confinement consistent with HD. However, these solutions cannot be made consistent with EE, therefore, these fields must be ruled out. In fact, by imposing both conditions, only the scalar and its dual field can be consistently localized. In this way, all the literature so far in which the free $1$-form is localized in codimension two models should be reviewed. These results also point to the fact that the symmetries of the fields can be used to verify the consistency of their localization and even prohibit it., Comment: 39 pages and 2 figures. Final version

The general procedure for analyzing the localization of matter fields in Brane models is by integrating, in the action, its zero mode solutions over the extra dimensions. If this is finite, the field is said to be localized. However, the zero mode solutions must also satisfy the Einstein equations. With this in mind, we obtain stringent constraints on a general energy-momentum tensor by analyzing the Einstein's equations. These {\it consistency conditions} must be satisfied for any Braneworld model. We apply it for some fields of the Standard Model. For a free massless scalar field, the zero-mode localization is consistent only if the field does not depend on the extra dimensions. About the spin $\frac{1}{2}$ field with Yukawa-like interactions, we find a very specific relation between Yukawa function and the warp factor. As a consequence, the spinor field localization becomes inconsistent for most of the models studied in the literature. For the free vector field case we find that, independent of the braneworld or the number of extra dimensions, the zero-mode do not satisfy the consistency conditions. Finally, we consider the mechanisms proposed to localize this field. We find that a few survive, and even for these, the consistency conditions fix the free parameters or the possible class of solutions allowed., Comment: 20 pages

In this manuscript we study the confinement of bosonic and spinning test particles in smooth Randall-Sundrum models. For this, we show that it is possible to find an effective potential which describe the motion of the particle over the extra dimension. For the bosonic case it is a known fact that free test particles cannot be localized neither in thin nor thick branes. Recently, a coupling to a scalar field has been used to localize a limited range of masses. Up to now, no mechanism has been found that can trap test particles of any mass over the brane. To solve this, we show that a coupling with the dilaton can trap particles of any mass. Next we analyze the spinning particle. The spin variables $\psi^{P}$ introduces an interaction with the curvature Riemann tensor. This introduces a correction to the effective potential. By analyzing it, we find that the spinning particle can be localized at a position different of the brane. We also show that a spinning particle over the brane can escape to infinity. Therefore, we can conclude that free bosonic and spinning particles are not trapped to the brane.

In this work, we study the general properties of the $D$-vector field localization on $(D-d-1)$-brane with co-dimension $d$. We consider a conformally flat metric with the warp factor depending only on the transverse extra dimensions. We employ the geometrical coupling mechanism and find an analytical solution for the $U(1)$ gauge field valid for any warp factor. Using this solution we find that the only condition necessary for localization is that the bulk geometry is asymptotically AdS. Therefore, our solution has an universal validity for any warp factor and is independent of the particular model considered. We also show that the model has no tachyonic modes. Finally, we study the scalar components of the $D$-vector field. As a general result, we show that if we consider the coupling with the tensor and the Ricci scalar in higher co-dimensions, there is an indication that both sectors will be localized. As a concrete example, the above techniques are applied for the intersecting brane model. We obtain that the branes introduce boundary conditions that fix all parameters of the model in such a way that both sectors, gauge and scalar fields, are confined., Comment: 26 pages, 5 figures, Accepted version for publication in JHEP

We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect., Comment: 13 pages. Two figures

We have investigated the possibility of discerning mass from flavor changing neutrino interactions induced $\nu_\mu \to \nu_\tau$ oscillations in the long baseline neutrino experiments K2K and MINOS. We have found that for virtually any value of the flavor conserving parameter $\epsilon^\prime$ it will be possible to, independently, distinguish these two mechanisms at K2K, if the flavor changing parameter $\epsilon$ is in the range $\epsilon \gsim 0.77$, and at MINOS, if $\epsilon \gsim 0.2$. Moreover, if K2K measures a depletion of the expected $\nu_\mu$ flux then MINOS will either observe or discard completely flavor changing neutrino oscillations., Comment: 21 pages with 7 figures, uses Elsart style and epsfig

We investigate the sensitivity of some weak processes to the simplest extension of the Standard Model with Majorana neutrinos mixing in the leptonic sector. Values for mixing angles and masses compatible with several experimental accelerator data and the most recent neutrinoless double--$\beta$ decay limit were found., Comment: 19 pages, 2 figures

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples., Comment: 34 pages, ps file, no figures

A precise meaning is given to the notion of continuous iteration of a mapping. Usual discrete iterations are extended into a dynamical flow which is a homotopy of them all. The continuous iterate reveals that a dynamical map is formend by independent component modes envolving without interference with each other., Comment: 24 pages, ps file