Fermion localization mechanism with derivative geometrical coupling on branes

In order to localize fermions on branes with codimension 1, one usually introduces the Yukawa coupling between fermions and background scalar fields or the recently proposed derivative fermion-scalar coupling [Phys. Rev. D 89, 086001 (2014)]. In this paper, we explore the coupling between a spinor field Ψ and the scalar curvature of spacetime R, ηΨΓM∂MF(R)γ5Ψ¯ with F(R) a function of R, to investigate the localization of the fermion. Because of the Z2 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 branes without background scalar fields. By investigating three examples, we find that fermions can be localized on branes with the new mechanism. We also study the case of both couplings of fermions, those with the scalar field and those with the curvature.