We present the muon magnetic moment $g-2$ in the flavour-aligned 2HDM evaluated by employing the recent result of full two-loop computation and making comprehensive use of experimental constraints from Higgs and flavour physics and characterize the parameter regions possible to explain the current $3\sigma$ deviation.
We particularly focus on the light CP-odd neutral Higgs boson $A$ and present the maximum possible Yukawa couplings to leptons and quarks of a light $A$ allowed by the LHC and $B$--physics results, which can enhance $a _\mu ^{\text{2HDM}}$ in this mass region.
As a result we find an overall maximum of $45 \times 10^{−10}$ for $a _\mu ^{\text{2HDM}}$ in the parameter region $20 < M_A < 100$ GeV.