Large Star/Rose Extra Dimension with Small Leaves/Petals

In this paper, we propose to compactify a single large extra dimension (LED) on a star/rose graph with a large number of identical leaves/petals. The 5D Planck scale can be chosen to be $\Lambda_P^{(5)} \sim \mathcal{O}(1)$ TeV which can provide a path to solve the gauge hierarchy problem. The leaf/petal length scale is of $\mathcal{O}(1/\Lambda_{EW})$, where $\Lambda_{EW} \sim 100$ GeV is the weak scale, without the large geometrical hierarchy of the traditional LED models to stabilize. The 4D fields of the SM are localized on a 3-brane at the central vertex of the star/rose graph. We predict a tower of feebly coupled weak scale Kaluza-Klein (KK) gravitons below a regime of strongly coupled gravitational phenomena above the TeV scale. Moreover, we reformulate in our setup the LED mechanism to generate light Dirac neutrinos, where the right-handed neutrinos are KK-modes of gauge singlet fermions propagating in the bulk. A large number of KK-gravitons and KK-neutrinos interact only gravitationally, and thus constitute a hidden sector.