Dark Matter in a twisted bottle

TL;DR

This paper explores a novel universal extra dimensional model based on the real projective plane, analyzing its implications for dark matter stability, mass spectrum, and co-annihilation effects within a six-dimensional framework.

Contribution

It introduces a new UED model on a real projective plane geometry, highlighting unique symmetry origins and small mass splittings affecting dark matter phenomenology.

Findings

Stable dark matter candidate due to geometric symmetry

Small mass splitting enhances co-annihilation effects

Higher Kaluza-Klein tiers significantly influence dark matter relic density

Abstract

The real projective plane is a compact, non-orientable orbifold of Euler characteristic 1 without boundaries, which can be described as a twisted Klein bottle. We shortly review the motivations for choosing such a geometry among all possible two-dimensional orbifolds, while the main part of the study will be devoted to dark matter study and limits in Universal Extra Dimensional (UED) models based on this peculiar geometry. In the following we consider such a UED construction based on the direct product of the real projective plane with the standard four-dimensional Minkowski space-time and discuss its relevance as a model of a weakly interacting Dark Matter candidate. One important difference with other typical UED models is the origin of the symmetry leading to the stability of the dark matter particle. This symmetry in our case is a remnant of the six-dimensional Minkowski space-time symmetry partially broken by the compactification. Another important difference is the very small mass splitting between the particles of a given Kaluza-Klein tier, which gives a very important role to co-annihilation effects. Finally the role of higher Kaluza-Klein tiers is also important and is discussed together with a detailed numerical description of the influence of the resonances.