Shedding light on dark matter with recent muon $(g-2)$ and Higgs exotic decay measurements

Recently, we have witnessed two hints of physics beyond the standard model: A 3.3$\sigma$ local excess ($M_{A_0} = 52$ GeV) in the search for $H_0\to A_0 A_0\to b\bar{b}\mu^{+}\mu^{-}$ and a 4.2$\sigma$ deviation from the SM prediction in the $(g-2)_\mu$ measurement. The first excess was found by the ATLAS Collaboration using 139 fb$^{-1}$ data at $\sqrt{s}=13$ TeV. The second deviation is a combination of the results from the Brookhaven E821 and the recently reported Fermilab E989 experiment. We attempt to explain these deviations in terms of a renormalizable simplified dark matter model. Inspired by the null signal result from dark matter (DM) direct detection, we interpret the possible new particle, $A_0$, as a pseudoscalar mediator connecting DM and the standard model. On the other hand, a new vector-like muon lepton can explain these two excesses at the same time while contributiong to the DM phenomenology.