We explore constraints on gauge bosons of a weakly coupled $U(1)_{B-L}$, $U(1)_{L_mu-L_e}$, $U(1)_{L_e-L_tau}$ and $U(1)_{L_mu-L_tau}$. To do so we apply the full constraining power of experimental bounds derived for a hidden photon of a secluded $U(1)_{X}$ and translate them to the considered gauge groups. In contrast to the secluded hidden photon that acquires universal couplings to charged Standard Model particles through kinetic mixing with the photon, for these gauge groups the couplings to the different Standard Model particles can vary widely. We take finite, computable loop-induced kinetic mixing effects into account, which provide additional sensitivity in a range of experiments. In addition, we collect and extend limits from neutrino experiments as well as astrophysical and cosmological observations and include new constraints from white dwarf cooling. We discuss the reach of future experiments in searching for these gauge bosons.
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