The muon magnetic moment in the ${\rm{2HDM}}$: complete two-loop result

We study the ${\rm{2HDM}}$ contribution to the muon anomalous magnetic moment $a_\mu$ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned ${\rm{2HDM}}$, which has general Yukawa coupling constants and is more general than the type I, II, X, Y models. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document the general behavior. Taking into account constraints on parameters, we find that the full ${\rm{2HDM}}$ contribution to $a_\mu$ can accommodate the current experimental value, and the complete two-loop bosonic result contribution can amount to $(2\cdots 4)\times 10^{-10}$, more than the future experimental uncertainty.