厚膜上的费米子共振态
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摘要
本文,我们主要研究了两个拓扑非平庸的厚膜上费米子的局域化和共振态问题。
首先,我们简要介绍了额外维物理和膜世界理论。综述了三个额外维理论,即Kaluza-Klein理论,ADD模型,以及RS模型。接着,我们介绍了厚膜的构造原理,并将其与薄膜进行了比较。
其次,我们研究了由多个背景标量场产生的厚膜上的费米子共振态问题。具体来说,我们主要研究了三场厚膜上的费米子的局域化和共振态问题。数值结果表明,和单场以及两场构成的厚膜模型一样,在三场厚膜中也存在费米子共振态。我们发现,Kaluza-Klein手征分解实际上是宇称一手征分解。对于由整体时空标量场的幂指数函数构成的推广Yukawa耦合,共振态的数目随幂指数的增加而增加。这一结果和单场de Sitter厚膜中得到的结果是相反的。
最后,我们构造了一个具有分段卷曲因子且光滑衔接的由单个标量场构成的厚膜,并研究了这个膜上费米子的共振态问题。为了满足正确的衔接条件,我们在参数之间引入了三个关系,这使得两个边界之间的距离和其它的参数可以由一个自由参数决定。对于推广的Yukawa耦合,我们发现,没有内在结构的厚膜也可以导致左右手费米子的共振态的出现。标量—费米耦合和膜的厚度均对有质量费米子的共振行为产生影响。
In this thesis, we focus on the fermion localization and quasi-localization (resonances) on two topologically non-trivial thick branes.
Firstly, we give an overview of extra-dimensional physics and the braneworld theories. Three different pictures of an extra dimension are reviewed, namely, Kaluza-Klein(KK) theory, ADD model and RS model. We then move on to the construction of thick brane and compare it with the thin brane.
Secondly, we study the fermion resonances on multi-scalar generated thick branes. Specifically, the fermion localization and resonances on the three-field thick brane are investigated. Our numerical results show that the resonant states also exist on the brane as that on the single-field thick branes and the two-field thick branes. It is found that the Kaluza-Klein chiral decomposition of massive fermion resonances is the parity-chiral decomposition. For a generalized Yukawa coupling with a power function of the bulk scalar field with an odd exponent, the number of the resonant states decreases with the power exponent. This result is opposite to the one obtained in the single-field de Sitter thick brane.
Finally, we construct a thick brane with a piecewise warp factor matching smoothly and investigate the problem of resonances of massive KK fermions on the thick brane. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling, it is found that the brane without internal structure also favors the appearance of resonant states for both left-and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.
首先,我们简要介绍了额外维物理和膜世界理论。综述了三个额外维理论,即Kaluza-Klein理论,ADD模型,以及RS模型。接着,我们介绍了厚膜的构造原理,并将其与薄膜进行了比较。
其次,我们研究了由多个背景标量场产生的厚膜上的费米子共振态问题。具体来说,我们主要研究了三场厚膜上的费米子的局域化和共振态问题。数值结果表明,和单场以及两场构成的厚膜模型一样,在三场厚膜中也存在费米子共振态。我们发现,Kaluza-Klein手征分解实际上是宇称一手征分解。对于由整体时空标量场的幂指数函数构成的推广Yukawa耦合,共振态的数目随幂指数的增加而增加。这一结果和单场de Sitter厚膜中得到的结果是相反的。
最后,我们构造了一个具有分段卷曲因子且光滑衔接的由单个标量场构成的厚膜,并研究了这个膜上费米子的共振态问题。为了满足正确的衔接条件,我们在参数之间引入了三个关系,这使得两个边界之间的距离和其它的参数可以由一个自由参数决定。对于推广的Yukawa耦合,我们发现,没有内在结构的厚膜也可以导致左右手费米子的共振态的出现。标量—费米耦合和膜的厚度均对有质量费米子的共振行为产生影响。
In this thesis, we focus on the fermion localization and quasi-localization (resonances) on two topologically non-trivial thick branes.
Firstly, we give an overview of extra-dimensional physics and the braneworld theories. Three different pictures of an extra dimension are reviewed, namely, Kaluza-Klein(KK) theory, ADD model and RS model. We then move on to the construction of thick brane and compare it with the thin brane.
Secondly, we study the fermion resonances on multi-scalar generated thick branes. Specifically, the fermion localization and resonances on the three-field thick brane are investigated. Our numerical results show that the resonant states also exist on the brane as that on the single-field thick branes and the two-field thick branes. It is found that the Kaluza-Klein chiral decomposition of massive fermion resonances is the parity-chiral decomposition. For a generalized Yukawa coupling with a power function of the bulk scalar field with an odd exponent, the number of the resonant states decreases with the power exponent. This result is opposite to the one obtained in the single-field de Sitter thick brane.
Finally, we construct a thick brane with a piecewise warp factor matching smoothly and investigate the problem of resonances of massive KK fermions on the thick brane. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling, it is found that the brane without internal structure also favors the appearance of resonant states for both left-and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.
引文
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