  Extensions of the Standard Model of particle physics with new Abelian gauge
groups allow for kinetic mixing between the new gauge bosons and the
hypercharge gauge boson, resulting in mixing with the photon. In many models
the mixing with the hypercharge gauge boson captures only part of the kinetic
mixing term with the photon, since the new gauge bosons can also mix with the
neutral component of the $SU(2)_L$ gauge bosons. We take these contributions
into account and present a consistent description of kinetic mixing for general
Abelian gauge groups both in the electroweak symmetric and the broken phase. We
identify an effective operator that captures the kinetic mixing with $SU(2)_L$
and demonstrate how renormalisable contributions arise if the charged fields
only obtain their masses from electroweak symmetry breaking. For the first
time, a low-energy theorem for the couplings of novel Abelian gauge bosons with
the Standard Model Higgs boson is derived from the one-loop kinetic mixing
amplitudes.
