Localization of Matters on Pure Geometrical Thick Branes

In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza–Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincaré invariance, and some of them break Z2–symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schrödinger problem and obtain the lowest KK mode. Just as the case of scalar, the massless mode of spin 1 vectors is found to be normalizable on the brane. The result is different from the famous case of RS model in AdS5 space, in which vector fields are not localized neither on a brane with positive tension nor on a brane with negative tension. It is also show that there exist a continuum gapless spectrum of KK states with m2 > 0. However, for the massless left or right chiral fermion localization, there must be some kind of Yukawa coupling. These features show that these thick branes arising from a pure geometric Weyl integrable manifold are different from others.