Probing the explanation of the muon (g-2) anomaly and thermal light dark matter with the semi-visible dark photon channel.

We report the results of a search for a new vector boson ( $$ A'$$ ) decaying into two dark matter particles $$\chi _1 \chi _2$$ of different mass. The heavier $$\chi _2$$ particle subsequently decays to $$\chi _1$$ and an off-shell Dark Photon $$ A'^* \rightarrow e^+e^-$$ . For a sufficiently large mass splitting, this model can explain in terms of new physics the recently confirmed discrepancy observed in the muon anomalous magnetic moment at Fermilab. Remarkably, it also predicts the observed yield of thermal dark matter relic abundance. A detailed Monte-Carlo simulation was used to determine the signal yield and detection efficiency for this channel in the NA64 setup. The results were obtained re-analyzing the previous NA64 searches for an invisible decay $$A'\rightarrow \chi \overline{\chi }$$ and axion-like or pseudo-scalar particles $$a \rightarrow \gamma \gamma $$ . With this method, we exclude a significant portion of the parameter space justifying the muon g-2 anomaly and being compatible with the observed dark matter relic density for $$A'$$ masses from 2 $$m_e$$ up to 390 MeV and mixing parameter $$\varepsilon $$ between $$3\times 10^{-5}$$ and $$2\times 10^{-2}$$ .