Large Star/Rose Extra Dimension with Small Leaves/Petals

Abstract

Scenarii with Large Extra Dimensions (LEDs) compactified on a (q ≤ 7)D torus and with the Standard Model (SM) fields localized on a 3-brane reformulate the gauge hierarchy problem between the 4D Planck scale Λ (4) P ∼ 10 18 GeV and the electroweak scale Λ EW ∼ 100 GeV as a geometrical hierarchy problem: gravity is strongly coupled at the (4 + q)D Planck scale Λ (4+q) P ∼ O(1) TeV, but the compactification radii need to be stabilized at large values compared to the (4 + q)D Planck length 1/Λ (4+q) P. In this article, we propose to compactify a single LED on a star/rose graph with a large number of identical leaves/petals of length/circumference of O(1/Λ EW ), where the 5D Planck scale is Λ(5) P ∼ O(1) TeV (without a large geometrical hierarchy to stabilize). The 4D SM fields are localized at the central vertex of the star/rose graph. We predict a feebly coupled tower of KK-gravitons invisible in current experiments with a KK scale of O(Λ EW ). Our scenarii lead also to TeV scale strongly coupled gravitational phenomena and to an infinite tower of trans-TeV semi-classical black holes. If there is a stable black hole remnant after evaporation, the Planckion, it could constitute a part of dark matter. Moreover, we propose a toy model to generate light Dirac neutrinos, where the right-handed neutrinos are KK modes of gauge singlet fermions propagating in the extra dimension. In our models, a large number of KK-gravitons and of sterile KK-neutrinos interact only with gravity and constitute a hidden sector.