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In the L_{\mu} - L_{\tau} model the 3.6$\sigma$ discrepancy between thepredicted and measured values of the anomalous magnetic moment of positivemuons can be explained by the existence of a new dark boson Z' with a mass inthe sub-GeV range, which is coupled at tree level predominantly to the secondand third lepton generations. However, at the one-loop level, the Z' couplingto electrons or quarks can be induced via the \gamma -Z' kinetic mixing, whichis generated through the loop involving the muon and tau lepton. This loopholehas important experimental consequences since it opens up new possibilities, inparticular for the complementary searches of the Z' in the ongoing NA64 andincoming dark photon experiments with high-energy electrons. An extension ofthe model able to explain relic Dark Matter density is also discussed.

Probing the muon g_\mu-2 anomaly, L_{\mu} - L_{\tau} gauge boson and Dark Matter in dark photon experiments