Localization of 5D Elko Spinors on Minkowski Branes

TL;DR

This paper studies the localization properties of 5D Elko spinors on Minkowski branes, revealing that zero modes can be localized under certain conditions, but massive modes generally cannot, differing from standard fermions and scalars.

Contribution

It provides a detailed analysis of Elko spinor localization on Minkowski branes, including effects of mass terms and Yukawa couplings, highlighting differences from conventional fields.

Findings

Zero mode localized on Randall-Sundrum brane without mass term.

Massive KK modes are not localized on these branes.

Yukawa coupling enables zero mode localization on some thick branes.

Abstract

Recently, a new spin-1/2 fermionic quantum field with mass dimension one in four dimensions--Elko field $\lambda$ was introduced as a candidate of dark matter. In this paper, we investigate the localization of 5D Elko {spinors} on Minkowski branes by presenting the equation of {the} Elko KK modes. For the 5D free massless Elko field, the zero mode can be localized on Randall-Sundrum thin brane but can not be localized on the majority of thick branes. There {do} not exist bound massive KK modes on all these branes. If the 5D mass term is introduced, there will exist bound Elko zero mode in Randall-Sundrum brane model. And when we introduce the Yukawa type coupling $\eta \phi^2 \mathop \lambda\limits^\neg\lambda$ with $\phi$ the background scalar field, the Elko zero mode can be localized on some special thick branes with a particular coupling constant $\eta$. Nevertheless, the massive KK modes still can not be localized on these branes. These results are very different from that of the conventional Dirac spinor {field} and the scalar field.