Vacuum Polarization Effects from Dark Fermion Loops in $Z'$ Mediator Models and their Impact on Angular Observables in $B \to K^* μ^+μ^-$ Decays

Rare flavour changing neutral current decays such as $B \to K^{*}μ^{+}μ^{-}$ provide sensitive probes of physics beyond the Standard Model (SM), being forbidden at tree level and arising only through loop induced processes. Angular analyses yield observables sensitive to short distance dynamics. The