Scrutinizing a massless dark photon: basis independence

Understand

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.