  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 $\alpha_d
(m_{Z_d}) \lesssim 0.5$.
