# Fermion Resonances on Multi-field Thick Branes

## TL;DR

This paper investigates fermion resonances on multi-field thick branes, revealing the existence of resonance states influenced by brane structure and scalar-fermion couplings, with numerical analysis showing how resonance counts vary with coupling parameters.

## Contribution

It extends previous work on fermion resonances to multi-scalar thick branes, analyzing how internal structure and couplings affect resonance states.

## Key findings

- Resonance states exist in multi-field thick branes.
- Resonance states are related to the brane's internal structure and scalar-fermion couplings.
- The number of resonant states decreases with increasing coupling parameter k, opposite to single-field results.

## Abstract

Motivated by the recent work on the fermion resonances on scalar-constructed thick branes (arXiv:0901.3543 and arXiv:0904.1785), we extend the idea to multi-scalar generated thick branes and complete previous work. The fermion localization and resonances on the three-field and two-field thick branes are investigated. With the Numerov method, our numerical results show that the resonance states also exist in the brane besides the single-field thick branes and the two-field thick branes in the former cases. This interesting phenomenon is related to the internal structure of the brane and the coupling of fermions and scalars. We find that the Kaluza-Klein chiral decomposition of massive fermion resonances is the parity-chiral decomposition. For the couplings $\eta\bar{\Psi}\phi^{k}\chi\rho\Psi$ and $\eta\bar{\Psi}\phi^{k}\chi\rho\Psi$ for three-field and two-field models with odd positive $k$, respectively, the number of the resonant states decreases with $k$. This result is opposite to the one obtained in the single-field de Sitter thick brane (arXiv:0904.1785).