On the four-zero texture of quark mass matrices and its stability

Abstract

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations.Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl. Phys.

Quark flavor mixings from hierarchical mass matrices

“…The study indicates that there should exist, not one [55], but several viable sets of hierarchical and Hermitian quark mass matrices, which may provide further possible clues for model building in top-down approaches [67][68][69][70][71][72][73][74]. In this context, it has been recently shown [42] that the texture zeros in the quark sector are essentially stable against the one-loop renormalization-group-evolution of the energy scale required in the top-down investigations of such mass matrices. It should be interesting to see if those specific structures of quark mass matrices can be verified in the future B-physics experiments.…”

“…Even more, it has recently been found in Ref. [42] that the relation |D q | |B q | |C q | is valid. By contrast, the Fritzsch ansatz with |A q | |B q | |C q | seems to reflect the strong hierarchies of quark mass spectra and flavor mixings in a more transparent and natural way.…”

“…As a consequence of texture zeros [32][33][34][35][36][37][38][39][40][41][42], a few simple but instructive relations among flavor mixing angles and quark mass ratios can be established [34,36,[43][44][45][46][47][48][49] and tested in experiments. Unfortunately, the Fritzsch ansatz failed to reconcile a large top-quark mass with the observed value of |V cb | [50,51].…”

Occam's razor in quark mass matrices

“…Our textures have been analyzed at the electroweak scale in this paper. The stability of texture zeros of the quark mass matrix has been examined against the renormalization-group evolution from the GUT scale to the electroweak scale by Xing and Zhao [11]. They found that texture zeros of the quark mass matrix are essentially stable against the evolution.…”

Exploring the predictability of symmetric texture zeros in quark mass matrices

“…Dong-Sheng Du and Zhi Zhong Xing [52] introduced a new structure for texture four zero quark mass matrices, which was a modification of the famous Fritzsch type texture six zero matrices [11]. This new structure, also referred to as Fritzsch-like texture four zero was later pursued in [15,36,[53][54][55][56][57][58] and was observed to offer a promising explanation for observed flavor mixing both in the quark as well as the lepton sectors [15,55,[59][60][61][62][63][64][65][66][67]. Initial observations on the non-viability of this structure on account of sin2β predictions in [42] were investigated [68,69] to establish that these matrices must involve two non-trivial phases in the quark mass matrices to account for observed CP-violation in the quark sector but predicted the following relation for the Cabibbo angle and quark mass ratios…”