# Fermion localization mechanism with derivative geometrical coupling on branes

## TL;DR

This paper proposes a new derivative geometrical coupling mechanism involving scalar curvature to localize fermions on branes, effectively addressing limitations of previous methods and working even without background scalar fields.

## Contribution

It introduces a novel fermion localization mechanism using scalar curvature coupling, applicable to branes with or without background scalar fields, overcoming previous challenges.

## Key findings

- Fermions can be localized using the new curvature coupling.
- The mechanism works for branes without scalar backgrounds.
- It addresses issues faced by Yukawa coupling methods.

## Abstract

In order to localize fermions on branes with codimension one, one usually introduces the Yukawa coupling between fermions and background scalar fields or the recently proposed derivative fermion-scalar coupling in [Phys. Rev. D 89 (2014) 086001]. In this paper, we explore the coupling between a spinor field $\Psi$ and the scalar curvature of spacetime $R$, $\eta\Psi\Gamma^M\partial_M F(R)\gamma^5\bar{\Psi}$ with $F(R)$ a function of $R$, to investigate localization of the fermion. Because of $Z_2$ symmetry of the extra dimension, the new coupling mechanism proposed here can easily deal with the problem encountered in the Yukawa coupling with even background scalar fields. More importantly, the new mechanism will also work for the branes without background scalar fields. By investigating three examples, we find that fermions can be localized on the branes with the new mechanism.