A Consistent Theory of Kinetic Mixing and the Higgs Low-Energy Theorem

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.