Implications of a Running Dark Photon Coupling

For an "invisible" dark photon $Z_d$ that dominantly decays into dark states, the running of its fine structure constant $\alpha_d$ with momentum transfer $q > m_{Z_d}$ could be significant. A similar running in the kinetic mixing parameter $\varepsilon^2$ can be induced through its dependence on $\alpha_d(q)$. The running of couplings could potentially be detected in "dark matter beam" experiments, for which theoretical considerations imply $\alpha_d (m_{Z_d}) \lesssim 0.5$.