Abstract
Abstract We have carried out an extensive analysis of all possible minimal texture quark mass matrices implying 169 texture-6 zero combinations. One finds that all these combinations are ruled out: a good number of these analytically, the other possibilities being excluded by the present quark mixing data. Interestingly, even if there are future changes in the ranges of the light quark masses, these conclusions remain valid.
Highlights
The concept of texture zeros was introduced implicitly by Weinberg [7] and explicitly by Fritzsch [8, 9], the original Fritzsch ansatz being given by MU = A∗U 0 BU, MD = A∗D 0 BD, (1)
It may be noted that the maximum number of texture zeros which can be introduced in the quark mass matrices is 3 in each sector, resulting in minimal number of parameters or elements of the mass matrices
We have examined in a detailed and comprehensive manner the viability of all these possible mass matrices keeping in mind the improvements in the measurements of light quark masses mu, md and ms as well as ‘precision measurements’ of the Cabibbo Kobayashi Maskawa (CKM) parameters
Summary
It may be mentioned that the rest of the 5 matrices belonging to class I of the table can be expressed in terms of a real matrix Mir and the corresponding phase matrix Pi. An essential step for the construction of the diagonalization transformation is to consider the invariants trace Mir, trace Mir2 and determinant Mir to yield relations involving elements of mass matrices. In order to have a better understanding of the above mentioned results as well as for the sake of completion, we present the magnitudes of the CKM matrix elements, obtained by considering the masses mentioned in equation (27) as inputs and both Vus and Vub values as constraints, i.e.,
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