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Muon g-2 and galactic centre $γ$-ray excess in a scalar extension of the 2HDM type-X

We consider an extension of the lepto-specific 2HDM with an extra singlet $S$ as a dark matter candidate. Taking into account theoretical and experimental constraints, we investigate the possibility to address both the $γ$-ray excess detected at the Galactic centre and the discrepancy between the Standard Model prediction and experimental results of the anomalous magnetic moment of the muon. Our analyses reveal that the $SS \to τ^+ τ^-$ and $SS \to b \bar b$ channels reproduce the Galactic centre excess, with an emerging dark matter candidate which complies with the bounds from direct detection experiments, measurements of the Higgs boson invisible decay width and observations of the dark matter relic abundance. Addressing the anomalous magnetic moment of the muon imposes further strong constraints on the model. Remarkably, under these conditions, the $SS \to b \bar b$ channel still allows for the fitting of the Galactic centre. We also comment on a scenario allowed by the model where the $SS \to τ^+ τ^-$ and $SS \to b \bar b$ channels have comparable branching ratios, which possibly yield an improved fitting of the Galactic centre excess.