Corrections To Newtonian And Coulomb Potentials From Extra Dimensions

From Kaluza and Klein(KK)unified the gravitational and electromagnetic interactions by introducing an extra spatial dimension to Rubakov et al.described the extra dimension through the image of the brane world,and from Arkani-Hamed et al.and Randall et al.for solving the problem of the gauge hierarchy by introducing the extra dimension with different properties to many thick brane models with different structures constructed by various mechanisms,the brane world theory has provided some new research ideas for solving some related fundamental problems in theoretical physics,e.g.,the problems of gauge hierarchy,cosmological constants,and dark matter.In the brane world theory,the four-dimensional world we live in can be considered as a brane which is embedded into a high-dimensional space-time.Therefore,in order to consistent with the current experimental results,we need to provide some reasonable mechanisms to ensure that the zero-mass modes of various matter fields in high-dimensional space-time can be localized on the brane.In addition,the brane world theory predicts a series of massive particles which are beyond the Standard Model of particle physics,such as massive gravitons and vector particles.These massive particles which are beyond the Standard Model will make a certain correction to the Newtonian and Coulomb potentials which we have observed,and make corresponding predictions in the experiments.In chapter 1,we introduce the related development process of extra dimension and brane world theory,briefly.We also introduce several important models,such as Karuza-Klein model,large extra-dimensional model,warp extra-dimensional model,and thick brane model.For the Karuza-Klein model,an additional spatial dimension was introduced in order to unify gravity and electro-magnetic forces.The large extra-dimensional model and the warp extra-dimensional model mainly solved the problem of the gauge hierarchy by introducing extra dimension,and opened a new era for the later development of brane world theory.While,the large extra-dimensional model and the warp extra-dimensional model ignored the problem of thickness of the brane,and this defect can be compensated by the thick brane model constructed by coupling the background field and gravity.In chapter 2,we construct three thick brane models with different structures by introducing mimetic scalar field.For these three brane structures,we analyze the stability of the tensor fluctua-tion of the metric and the localization of the zero-mass mode of the gravitational field,specifically.In addition,we also consider the localization properties of the zero-mass mode for scalar field,vector field and fermion field on the three thick brane with different structures.The warp factors of these three brane structures are attenuated differently with the extra dimension,and the graviton KK modes will feel different effective potentials along the direction of the extra dimension.Then,these different effective potentials will result a series gravitons massive KK modes with different massive spectra.So,for these three thick brane models with different structures,we talk about the correc-tion to the Newtonian potential which is contributed by the hole graviton massive KK modes.And combining with the current gravitational experiments,we can get the restrictions on the relevant parameters in the mimetic thick brane model.In chapter 3,in order to ensure that the zero-mass mode of the five-dimensional vector field can be localized on the thick brane in anti-de Sitter space-time,we introduce a mass term for the vector field.This mass term is the combination of five-dimensional Ricci scalar and Ricci tensor.According to the transverse condition,we can decompose the vector field A_Minto vector part?A_?,scalar part?and A₅.And the result shows that the two parts are not coupled.Therefore,we can consider the localization condition of the vector part?A_?,separately.Under the localization condition,the tachyton modes of the vector part?A_?can be excluded,and it ensures the stability of vector part?A_?.In addition,we also consider the resonance state properties of the vector field?A_?.We find that both the mass and the lifetime on the brane of the first resonance state of the vector field?A_?can be fitted as the functions of the related parameters.By assuming that the first resonance state of the vector field can be considered as a candidate for dark matter,and based on the current observation results,we get the constrictions on the relevant parameters of the thick brane in anti-de Sitter space-time.In chapter 4,we get the correction to the Coulomb potential by considering the exchange of vector massive KK modes between two fermions which are localized on a purely geometric Weyl thick brane.We find that the five-dimensional Yukawa interaction term between vector field and the fermion field can be reduced into an effective four-dimensional electromagnetic interaction.In this four-dimensional effective action,various vector massive KK modes will contribute to the corre-sponding four-dimensional effective electromagnetic interaction coupling coefficient.By selecting the specific localization mechanism of fermion field and vector field,we obtain the expression of the correction to the Coulomb potential.The total correction behavior to the Coulomb potential depends on the mass spectrum of the massive vector KK modes,and the mass spectrum is related with the coupling parameters.Therefore,we analyze the influence of the coupling parameters on the correction of the Coulomb potential.And according to the current experiment,we also get re-striction of the relevant parameters of the pure geometric Weyl thick brane model.