The Universal Extra Dimensional Model with S²/Z₂ extra-space

We propose a new Universal Extra Dimensional model that is defined on a six-dimensional spacetime which has a two-sphere orbifold $S^2/Z_2$ as an extra-space. We specify our model by choosing the gauge symmetry as SU(3)$\timesSU(2)\timesU(1)_Y \timesU(1)_X$, introducing field contents in six-dimensions as their zero modes correspond to the Standard model particles, and determining a boundary condition of these fields on orbifold $S^2/Z_2$. A background gauge field that belongs to U(1)$_X$ is introduced there, which is necessary to obtain massless chiral fermions in four-dimensional spacetime. We then analyze Kaluza-Klein(KK) mode expansion of the fields in our model and derive the mass spectrum of the KK particles. We find that the lightest KK particles are the 1st KK particle of massless gauge bosons at tree level. We also discuss the KK parity of the KK modes in our model and confirm the stability of the lightest KK particle which is important for dark matter physics.