Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-07-25
JHEP 1002:080,2010
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, 17 figures, published version
Scientific paper
10.1007/JHEP02(2010)080
By presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of various bulk matter fields on an AdS thick brane. For a spin 0 scalar $\Phi$ coupled with itself and the domain-wall-forming field $\phi$ via a coupling potential $V=(\lambda \phi^{2}-u^{2})\Phi^{2}+\tau\Phi^{4}$, the localization and spectrum are decided by a critical coupling constant $\lambda_{0}$. When $\lambda>\lambda_0$, the potential of the scalar KK modes in the corresponding Schr\"{o}dinger equation tends to infinite when far away from the brane, which results in that there exist infinite discrete scalar bound KK states, and the massless modes could be trapped on the AdS brane by fine-tuning of parameters. When $\lambda<\lambda_0$, the potential of the scalar KK modes tends to negative infinite when far away from the brane, hence there does not exist any scalar bound KK state. For a spin 1 vector, the situation is same like the scalar with a coupling constant $\lambda>\lambda_0$, but the zero mode can not be localized on the brane. For a spin 1/2 fermion, we introduce the usual Yukawa coupling $\eta\bar{\Psi}\phi\Psi$, and find that the localization of the fermion is decided by a critical coupling constant $\eta_0$. For $\eta > \eta_0$, the four-dimensional massless left chiral fermion and massive Dirac fermions consisted of the pairs of coupled left-hand and right-hand KK modes could be localized on the AdS brane, and the massive Dirac fermions have a set of discrete mass spectrum. While for the case $0<\eta < \eta_{0}$, no four-dimensional Dirac fermion can be localized on the AdS brane.
Fu Chun-E
Guo Heng
Liu Yu-Xiao
Ren Ji-Rong
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