New Analytical Solutions for Bosonic Field Trapping in Thick Branes

Abstract

New analytical solutions for gravity, scalar and vector field localization in Randall-Sundrum(RS) models are found. A smooth version of the warp factor with an associated function $f(z)=\exp (3A(z)/2)$ inside the walls ($|z|<d$) is defined, leading to an associated equation and physical constraints on the continuity and smoothness of the background resulting in a new space of analytical solutions. We solve this associated equation analytically for the parabolic and Pöschl-Teller potentials and analyze the spectrum of resonances for these fields. By using the boundary conditions we are able to show that, for any of these solutions, the density probability for finding a massive mode in the membrane has a universal behavior for small values of mass given by $|{\psi }_m(0){|}^2={\beta }_{1}m+{\beta }_3{m}^3+{\beta }_L{m}^3\log (m)+\cdots$. As a consequence, the form of the leading order correction, for example, to the Newton's law is general and does not depend on the potential used. At the end we also discuss why complications arises when we try to use the method to find analytical solutions to the fermion case.

11 pages, 4 figures; v2: extended version; references and section added; title, conclusions and abstract changed

References in corpus (7)

• Fermion Localization and Resonances on A de Sitter Thick Brane
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• Gravity Trapping on a Finite Thickness Domain Wall: An Analytic Study
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• Generalized non-minimal couplings in Randall-Sundrum scenarios
• Coulomb's law corrections and fermion field localization in a tachyonic de Sitter thick braneworld
• Universal Aspects of $U(1)$ Gauge Field Localization on Branes in $D$-dimensions
• Gauge Field Emergence from Kalb-Ramond Localization
• Massive $p$-form trapping as a $p$-form on a brane
• Consistency Conditions for $p$-Form Fields Localization on Codimension two Braneworlds
• Does Geometric Coupling Generates Resonances?