  Extensions of the Standard Model with an Abelian gauge group are constrained
by gauge anomaly cancellation, so that only a limited number of possible charge
assignments is allowed without the introduction of new chiral fermions. For
flavour universal charges, couplings of the associated hidden photon to
Standard Model fermions are flavour conserving at tree-level. We show
explicitly that even the flavour specific charge assignments allowed by anomaly
cancellation condition lead to flavour conserving tree-level couplings of the
hidden photon to quarks and charged leptons \emph{if} the CKM or PMNS matrix
can be successfully reconstructed. Further, loop-induced flavour changing
couplings are strongly suppressed. As a consequence, the structure of the
Majorana mass matrix is constrained and flavour changing tree-level couplings
of the hidden photon to neutrino mass eigenstates are identified as a means to
distinguish the $U(1)_{B-L}$ gauge boson from any other anomaly-free extension
of the Standard Model without new chiral fermions. We present a comprehensive
analysis of constraints and projections for future searches for a
$U(1)_{B-3L_i}$ gauge boson, calculate the reach of resonance searches in $B$
meson decays and comment on the implications for non-standard neutrino
interactions.
