Fermion Localization Mechanism On Brane And Methods For Resonances

In the last two decades,the idea that our universe is embedded in a higher-dimensional spacetime has attracted much attention.Extra dimensions not only provide a new view of spacetime,but can also solve some outstanding problems that the standard model of particle physics cannot deal with,such as the gauge hierarchy problem and the cosmological constant problem.In the braneworld scenarios,the localization mechanisms of bulk matter fields on a brane are very significant,which could reconstruct the standard model on branes and also give experimental predictions in future.In this thesis we will mainly investigate the new localization mechanism of the fermions,the solution of Schr¨odinger equation and new approach to get the resonances of the five-dimensional matter fields on the branes.Firstly,we briefly introduce the background of the theory of extra dimension and its development history.We review several important models,including the KaluzaKlein（KK）theory,the Arkani-Hamed-Dimopoulos-Dvali（ADD）model,and the RandallSundram（RS）model.Besides,we discuss the related theoretical knowledge about the localization and resonance states of matter fields and the latest developments in these areas.Secondly,we investigate a new localization mechanism of the fermions in the braneworld.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 coupling mechanism.In this thesis,we explore the coupling between a spinor field Ψ and the scalar curvature of spacetime R,ηΨΓ^M_MF（R）γ⁵（?） with F（R） a function of R,to investigate the localization of the fermion.Because of 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 work for the brane models without background scalar fields.By investigating three examples,we find that fermions can be localized on the branes with the new mechanism.Finally,we discuss in detail a numerical method and WKB approximation to study resonances in membranes generated by domain walls in RS-like scenarios.It is based on similar work on quantum mechanical tunneling across barrier potentials.We apply numerical and semi-analytic methods to fermion resonances as examples.The two methods match very well and we find a rich structure of resonances.