Abstract
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.
Highlights
The motivations for building a specific model based on a compactified Extra Dimension can be of different origins, ranging from phenomenological ones to more formal ones related for example to string theory
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 this paper we focus on the issue of Dark Matter in Universal Extra Dimension (UED) type of models
Summary
The motivations for building a specific model based on a compactified Extra Dimension can be of different origins, ranging from phenomenological ones to more formal ones related for example to string theory. In the following we shall consider an effective theory defined on a d dimensional manifold which is the direct product of the standard four-dimensional Minkowski space-time M4 and a (d − 4)-dimensional orbifold defined as the quotient space of R(d−4) modulo a discrete symmetry group Γ This general framework can be constrained by few important theoretical requirements which will select, in our case, a unique geometry. The scenario we discuss here, based on the real projective plane orbifold, has a special status as the stability of the dark matter candidate is not imposed, but is the result of an exact residual space-time symmetry after compactification. The divergences appearing in loop corrections require counter-terms localised on these fixed points Another important theoretical and phenomenological requirement is the presence of 4-dimensional chiral fermions as zero modes in the low energy spectrum of the effective theory.
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