# Kink modes and effective four dimensional fermion and Higgs brane models

## Abstract

In the construction of a classical smoothed out brane world model in five dimensions, one uses a dynamically generated domain wall (a kink) to localize an effective four dimensional theory. At the level of the Euler-Lagrange equations the kink sets up a potential well, a mechanism which has been employed extensively to obtain localized, four dimensional, massless chiral fermions. We present the generalization of this kink trapping mechanism for both scalar and fermionic fields, and retain all degrees of freedom that were present in the higher dimensional theory. We show that a kink background induces a symmetric modified Poeschl-Teller potential well, and give explicit analytic forms for all the bound modes and a restricted set of the continuum modes. We demonstrate that it is possible to confine an effective four dimensional scalar field with a quartic potential of arbitrary shape. This can be used to place the standard model electroweak Higgs field on the brane, and also generate nested kink solutions. We also consider the limits of the parameters in the theory which give thin kinks and localized and delocalized scalar and fermionic fields.

- Authors:

- School of Physics, Research Centre for High Energy Physics, University of Melbourne, Victoria 3010 (Australia)

- Publication Date:

- OSTI Identifier:
- 20935268

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.105007; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BRANES; CHIRALITY; DEGREES OF FREEDOM; FERMIONS; FOUR-DIMENSIONAL CALCULATIONS; HIGGS MODEL; LAGRANGE EQUATIONS; M-THEORY; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; POTENTIALS; SCALAR FIELDS; SCALARS; STANDARD MODEL; TRAPPING

### Citation Formats

```
George, Damien P., and Volkas, Raymond R..
```*Kink modes and effective four dimensional fermion and Higgs brane models*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.105007.

```
George, Damien P., & Volkas, Raymond R..
```*Kink modes and effective four dimensional fermion and Higgs brane models*. United States. doi:10.1103/PHYSREVD.75.105007.

```
George, Damien P., and Volkas, Raymond R.. Tue .
"Kink modes and effective four dimensional fermion and Higgs brane models". United States.
doi:10.1103/PHYSREVD.75.105007.
```

```
@article{osti_20935268,
```

title = {Kink modes and effective four dimensional fermion and Higgs brane models},

author = {George, Damien P. and Volkas, Raymond R.},

abstractNote = {In the construction of a classical smoothed out brane world model in five dimensions, one uses a dynamically generated domain wall (a kink) to localize an effective four dimensional theory. At the level of the Euler-Lagrange equations the kink sets up a potential well, a mechanism which has been employed extensively to obtain localized, four dimensional, massless chiral fermions. We present the generalization of this kink trapping mechanism for both scalar and fermionic fields, and retain all degrees of freedom that were present in the higher dimensional theory. We show that a kink background induces a symmetric modified Poeschl-Teller potential well, and give explicit analytic forms for all the bound modes and a restricted set of the continuum modes. We demonstrate that it is possible to confine an effective four dimensional scalar field with a quartic potential of arbitrary shape. This can be used to place the standard model electroweak Higgs field on the brane, and also generate nested kink solutions. We also consider the limits of the parameters in the theory which give thin kinks and localized and delocalized scalar and fermionic fields.},

doi = {10.1103/PHYSREVD.75.105007},

journal = {Physical Review. D, Particles Fields},

number = 10,

volume = 75,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}