Scrutinizing a massless dark photon

A new $U(1)_X$ gauge boson field $X$ can have renormalizable kinetic mixing with the standard model (SM) $U(1)_Y$ gauge boson field $Y$. This mixing induces interactions of $X$ with SM particles even though $X$ starts as a dark photon without such interactions. If the $U(1)_X$ is not broken, both the dark photon field $X$ and the photon field $A$ are massless. One cannot determine which one of them is the physical dark photon or the photon by just looking at kinetic terms in the Lagrangian. We further show that the kinetic mixing does not leave traces in electromagnetic and weak interactions if only SM particles are involved. The kinetic mixing provides a portal for probing the dark sector beyond the SM. Missing energy due to the escape of dark sector particles in probes that are sensitive only to SM particles leads to observable effects of the kinetic mixing massless dark photon. We study examples for a Higgs boson decays into a mono-photon plus missing energy, and a $Z$ boson decays into missing energy.