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We study the Two-Higgs-Doublet Model with the aligned Yukawa sector (A2HDM)in light of the observed excess measured in the muon anomalous magnetic moment.We take into account the existing theoretical and experimental constraints withup-to-date values and demonstrate that a phenomenologically interesting regionof parameter space exists. With a detailed parameter scan, we show a muchlarger region of viable parameter space in this model beyond the limiting caseType X 2HDM as obtained before. It features the existence of light scalarstates with masses $3$ GeV $\lesssim m_H^{} \lesssim 50$ GeV, or $\ 10$ GeV$\lesssim m_A^{} \lesssim 130$ GeV, with enhanced couplings to tau leptons. Thecharged Higgs boson is typically heavier, with $200$ GeV $ \lesssim m^{}_{H^+}\lesssim 630$ GeV. The surviving parameter space is forced into theCP-conserving limit by EDM constraints. Some Standard Model observables may besignificantly modified, including a possible new decay mode of the SM-likeHiggs boson to four taus. We comment on future measurements and direct searchesfor those effects at the LHC as tests of the model.

Muon $g-2$ in the Aligned Two Higgs Doublet Model