Scrutinizing a massless dark photon: basis independence

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 revisit this issue and show explicitly that when all contributions are included, all physical processes do not depend on which basis is used and the kinetic mixing effects do not show up in electromagnetic and weak interactions if only SM particles are involved in the calculations. On the other hand, the kinetic mixing provides a portal for probing the dark sector beyond the SM. We update constraints on the millicharged dark sector particles from the Lamb shift and lepton $g-2$ measurements.