The kinetic mixing of the vector boson of hypercharge with the vector boson(s) associated with particle sectors beyond the Standard Model is one of the best motivated windows to new physics. The resulting phenomenology depends on whether the new vector boson is massive or massless. The phenomenology associated with the massive phase has received considerable attention in recent years with many theoretical explorations and new experimental efforts, while the massless phase is linked to the phenomenology of milli-charged particles. In this paper we introduce the more general case where the kinetic mixing is with a vector boson that is a linear combination of both a massive and a massless state (as hypercharge is in the Standard Model). We demonstrate that the general phase is only weakly constrained when the mass scale associated with it is above about 100 MeV. Finally, we show that a new dedicated experiment at the LHC, proposed recently in Ref. [1], can explore large parts of the parameter space in the mass range between 100 MeV and 100 GeV. In particular, it is uniquely sensitive to a new signature that only arises in the general phase.
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