A new ansatz: Fritzsch Mass Matrices with least modification

Abstract

We investigate how the Fritzsch ansatz for the quark mass matrices can be modified in the least possible way to accommodate the observed large top quark mass and the measured values of the CKM elements. As one of the solutions, we find that the \{23\} and the \{32\} elements of the up quark mass matrix are unequal. The rest of the assumptions are same as in Fritzsch ansatz. In this formalism we have an extra parameter i.e. the ratio of the \{{23\}} and the \{{32\}} element, which gets fixed by the large top quark mass. The predicted values for $\frac{V_{ub}}{V_{cb}}$ , $\frac{V_{td}}{V_{ts}}$ from this new ansatz are in the correct experimental range even for the smaller values of $\tan \beta $. In the end, we write down the $SO(10)$ motivated superpotential for these new mass matrices.