  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.
