Dark Photons as Kaluza-Klein Gauge Modes in Warped Gauge-Higgs Unification: Geometric Kinetic Mixing from Wavefunction Overlap

We extend the SO(5) × U(1)X gauge Higgs unification framework in a slice of five dimensional anti de Sitter space (warp factor kL = 38.44) by embedding a hidden U(1)′ gaugefield in the bulk. The dark photon A′ emerges as the lightest Kaluza-Klein excitation of thishidden gauge symmetry, with massmA′ ≈x1ke−kL (x1 ≈ 3.83)spanning 0.15–2.8 GeV, where the precise value is modulated by the Wilson line vacuumexpectation value ⟨θ⟩ controlling the effective infrared scale.The kinetic mixing ϵ with the Standard Model photon arises purely from geometricwavefunction overlap between the ultraviolet localized photon zero mode and the infraredlocalized first Kaluza-Klein dark photon mode.