# Dynamical generation of quark/lepton mass hierarchy in an extra dimension

## TL;DR

This paper proposes a model where the quark and lepton mass hierarchy is generated dynamically through point interactions in an extra dimension, with the positions stabilized by Casimir energy minimization, matching experimental quark masses.

## Contribution

It introduces a novel mechanism using point interactions and Casimir energy to dynamically generate and stabilize the quark/lepton mass hierarchy in an extra-dimensional framework.

## Key findings

- Successfully reproduces quark mass values with stabilized point interactions.
- Demonstrates the role of scalar vacuum expectation values in the model.
- Shows potential for improved lepton mixing predictions.

## Abstract

We show that the observed quark/lepton mass hierarchy can be realized dynamically on an interval extra dimension with point interactions. In our model, the positions of the point interactions play a crucial role to control the quark/lepton mass hierarchy and are determined by the minimization of the Casimir energy. By use of the exact extra-dimensional coordinate-dependent vacuum expectation value of a gauge singlet scalar, we find that there is a parameter set, where the positions of the point interactions are stabilized and fixed, which can reproduce the experimental values of the quark masses precisely enough, while the charged lepton part is less relevant. We also show that possible mixings among the charged leptons will improve the situation significantly.