Localization and mass spectra of various matter fields on Weyl thin brane

It has been shown that the thin brane model in a five-dimensional Weyl gravity can deal with the wrong-signed Friedmann-like equation in the Randall–Sundrum-1 (RS1) model. In the Weyl brane model, there are also two branes with opposite brane tensions, but the four-dimensional graviton (the gravity zero mode) is localized near the negative tension brane, while our four-dimensional universe is localized on the positive tension brane. In this paper, we consider the mass spectra of various bulk matter fields (i.e., scalar, vector, and fermion fields) on the Weyl brane. It is shown that the zero modes of those matter fields can be localized on the positive tension brane under some conditions. The mass spectra of the bulk matter fields are equidistant for the higher excited states, and relatively sparse for the lower excited states. The size of the extra dimension determines the gap of the mass spectra. We also consider the correction to the Newtonian potential in this model and it is proportional to $$1/r^{3}$$ .