More about unphysical zeroes in quark mass matrices

TL;DR

This paper systematically explores all weak bases with minimal parameters that produce texture zeroes in quark mass matrices, analyzing their physical relevance and compatibility with experimental data.

Contribution

It classifies all possible texture zero configurations in quark mass matrices within the standard model and assesses their physical significance and experimental viability.

Findings

Maximum of nine texture zeroes distributed between quark sectors.

All nine-zero texture pairs are incompatible with current data.

Many zero-zero configurations are equivalent to weak basis choices.

Abstract

We look for all weak bases that lead to texture zeroes in the quark mass matrices and contain a minimal number of parameters in the framework of the standard model. Since there are ten physical observables, namely, six nonvanishing quark masses, three mixing angles and one CP phase, the maximum number of texture zeroes in both quark sectors is altogether nine. The nine zero entries can only be distributed between the up- and down-quark sectors in matrix pairs with six and three texture zeroes or five and four texture zeroes. In the weak basis where a quark mass matrix is nonsingular and has six zeroes in one sector, we find that there are 54 matrices with three zeroes in the other sector, obtainable through right-handed weak basis transformations. It is also found that all pairs composed of a nonsingular matrix with five zeroes and a nonsingular and nondecoupled matrix with four zeroes simply correspond to a weak basis choice. Without any further assumptions, none of these pairs of up- and down-quark mass matrices has physical content. It is shown that all non-weak-basis pairs of quark mass matrices that contain nine zeroes are not compatible with current experimental data. The particular case of the so-called nearest-neighbour-interaction pattern is also discussed.