Quark mixing in an $S_3$ symmetric model with two Higgs doublets

We construct a model where the smallness of the masses of first quark generations implies the near block diagonal nature of the CKM matrix and vice-versa. For this set-up, we rely on a 2HDM structure with an $S_3$ symmetry. We show that an SM-like Higgs emerges naturally from such a construction. Moreover, the ratio of two VEVs, $\tan \beta$ can be precisely determined from the requirement of the near masslessness of the up- and down-quarks. The FCNC structure that arises from our model is also very predictive.