Tests of the Atomki anomaly in lepton pair decays of heavy mesons

The anomalies recently reported in lepton pair transitions of $^8$Be$^*$ and $^4$He nuclei may be attributed to the existence of a feebly interacting light vector boson $X17$. We study the effects of this hypothetical particle in the semileptonic $H^* \to H e^+e^-$ decays ($H$ a $Q\bar{q}$ meson) in the framework of the HQET+VMD model. Using current bounds and the universality assumption of the $X17$ boson to quarks, we find that decays of $D^{*+}$ and $D_s^{*+}$ mesons can be importantly enhanced relative to the dominant photon-mediated contributions. Dedicated experimental searches at current heavy meson factories may confirm the existence of this light boson or set stronger bounds of their couplings to ordinary matter.