5D Elko spinor field non-minimally coupled to nonmetricity in $f(Q)$ gravity

TL;DR

This paper explores the localization of a five-dimensional Elko spinor field non-minimally coupled to nonmetricity in $f(Q)$ gravity, using braneworld scenarios and a Schrödinger-like approach to analyze zero and massive modes.

Contribution

It introduces a novel geometrical Yukawa-like coupling for Elko fields in $f(Q)$ gravity and studies their localization and mass spectrum in braneworld models.

Findings

Zero-mode can be localized with a linear coupling function.

Massive modes require an exotic term for real solutions.

Effective potential resembles that of scalar fields.

Abstract

This paper aims to investigate the localization of the five-dimensional spinor field known as Elko (dual-helicity eigenspinors of the charge conjugation operator) by employing a Yukawa-like geometrical coupling in which the Elko field is non-minimally coupled to nonmetricity scalar $Q$. We adopt the braneworld scenarios in which the first-order formalism with sine-Gordon and linear superpotentials is employed to obtain the warp factors. A linear function supports the zero-mode trapping within the geometric coupling, leading to the same effective potential as the scalar field. Moreover, an exotic term must be added to obtain real-valued massive modes. Such modes are investigated through the Schr\"{o}dinger-like approach.