Muon g-2 in the 2HDM: maximum results and detailed phenomenology

We present a comprehensive analysis of the muon magnetic moment $a_\mu$ in the flavour-aligned two-Higgs doublet model (2HDM) and parameter constraints relevant for $a_\mu$. We employ a recent full two-loop computation of $a_\mu$ and take into account experimental constraints from Higgs and flavour physics on the parameter space. Large $a_\mu$ is possible for light pseudoscalar Higgs A with large Yukawa couplings to leptons, and it can be further increased by large A coupling to top quarks. We investigate in detail the maximum possible Yukawa couplings to leptons and quarks of a light A, finding values of around 50...100 (leptons) and O(0.5) (quarks). As a result we find that an overall maximum of $a_\mu$ in the 2HDM of more than $45\times10^{-10}$ is possible in a very small parameter region around M_A=20 GeV. The parameter regions in which the currently observed deviation can be explained are characterized.