Radiatively induced flavour violation in the general two-Higgs doublet model with Yukawa alignment

The most general two Higgs doublet model contains new sources of flavour violation that are usually in conflict with the experimental constraints. One possibility to suppress the exotic contribution to the flavour changing neutral currents consists on imposing the alignment of the Yukawa couplings. This condition presumably holds at a high-energy scale and is spoiled by the radiative corrections. We compute in this letter the size of the radiatively induced flavour violating Higgs couplings at the electroweak scale. These also yield the absolute lower bound on the size of the exotic contributions to the flavour changing neutral currents in any two Higgs doublet model, barring cancellations and the existence of discrete symmetries. We show that these contributions are well below the experimental bounds in large regions of the parameter space.