Flavor structure of anomaly-free hidden photon models

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.