Analysis of the quark sector in the 2HDM-III with a four-zero Yukawa texture using the most recent data on the CKM matrix

In this letter we analyse, in the context of the general 2-Higgs Doublet Model, the structure of the Yukawa matrices, $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, by assuming a four-zero texture ansatz for their definition. In this framework, we obtain compact expressions for $\widetilde{ \bf Y}_{ _{1,2} }^{q}$, which are reduced to the Cheng and Sher ansatz with the difference that they are obtained naturally as a direct consequence of the invariants of the fermion mass matrices. Furthermore, in order to avoid large flavour violating effects coming from charged Higgs exchange, we consider the main flavour constraints on the off-diagonal terms of Yukawa texture {{$\left( \widetilde{\chi}_{j}^q \right)_{kl}$}} ($k\neq l$). We perform a $\chi^2$-fit based on current experimental data on the quark masses and the Cabibbo-Kobayashi-Maskawa mixing matrix ${ \bf V}_{\rm CKM }$. Hence, we obtain the allowed ranges for the parameters $\widetilde{ \bf Y}_{ _{1,2} }^{q}$ at 1$\sigma$ for several values of $\tan \beta$. The results are in complete agreement with the bounds obtained taking into account constraints on Flavour Changing Neutral Currents reported in the literature.