A Solution of the Randall-Sundrum Model and the Mass Hierarchy Problem

TL;DR

This paper presents an analytical solution to the simplified Randall-Sundrum model using a thin wall expansion, exploring implications for the mass hierarchy problem and the nature of 4D fermions.

Contribution

It provides a new analytical solution for the Randall-Sundrum model with a single wall, incorporating a 5D Higgs potential and examining physical quantities relevant to the mass hierarchy.

Findings

Derived a $1/k^2$-expansion solution for the model.

Analyzed the impact on Planck mass, cosmological constant, and fermion masses.

Explored the possibility of 4D chiral fermions as bound states in 5D.

Abstract

A solution of the Randall-Sundrum model for a simplified case (one wall) is obtained. It is given by the $1/k^2$-expansion (thin wall expansion) where $1/k$ is the {\it thickness} of the domain wall. The vacuum setting is done by the 5D Higgs potential and the solution is for a {\it family} of the Higgs parameters. The mass hierarchy problem is examined. Some physical quantities in 4D world such as the Planck mass, the cosmological constant, and fermion masses are focussed. Similarity to the domain wall regularization used in the chiral fermion problem is explained. We examine the possibility that the 4D massless chiral fermion bound to the domain wall in the 5D world can be regarded as the real 4D fermions such as neutrinos, quarks and other leptons.