Possible Textures of the Fermion Mass Matrices

Abstract

Texture specific fermion mass matrices have played an important role in understanding several features of fermion masses and mixings. In the present work, we have given an overview of all possible cases of Fritzsch-like as well as non Fritzschlike texture 6 and 5 zero fermion mass matrices. Further, for the case of texture 4 zero Fritzsch-like quark mass matrices, the issue of the hierarchy of the elements of the mass matrices and the role of their phases have been discussed. Furthermore, the case of texture 4 zero Fritzsch-like lepton mass matrices has also been discussed with an emphasis on the hierarchy of neutrino masses for both Majorana and Dirac neutrinos.

Quark sector ofS3models: Classification and comparison with experimental data

“…In this case, the Higgs boson of the SM is an SU(2) L doublet and, since it has no flavour, it is in a singlet representation of S 3 . When S 3 is an exact symmety and the field in the S 3 singlet representation is assigned to the fields in the third generation, then, in a symmetry adapted basis, all elements in the mass matrices should vanish except for the element (3,3). Hence, from the structure of the mass matrices, only the fermion that is assigned to the singlet representation of S 3 acquires mass, and the symmetry should be broken in order to give mass to the other families.…”

“…We have denoted s = sin θ, c = cos θ and t = tan θ. The third column of this table corresponds to the general case, while the fourth column to a case where we have rotated the matrix to a basis where the elements (1, 1), (1,3) and (3, 1) vanish. The primed cases, A' or B', are particular cases of the unprimed ones, A or B, with θ = π/6 or θ = π/3, respectively.…”

“…where the first condition is needed such that the entries (1, 2) and (2, 1) correspond respectively to the complex conjugate of each other, and the second, such that the entries (2, 3) and (3,2) …”

General Lepton Textures and Their Implications

“…In particular, several attempts [1]- [8] have been made to understand the neutrino mixing data by formulating the phenomenological mass matrices with charged lepton matrix being diagonal, usually referred to as the flavor basis case. In addition, for both Majorana as well as Dirac neutrinos, some attempts [9]- [10] have also been made to explain the neutrino mixing data by considering texture specific structures for both the charged lepton and the neutrino mass matrices, referred to as the non flavor basis case. It may be noted that the non flavor basis enables quarks and leptons to be treated at the same footing and also to explore the possibility to arrive at a minimal set of fermion mass matrices which are compatible with the latest mixing data.…”

Fermion mass matrices, textures and beyond

“…Despite large number of attempts from the top-down perspective, 7 we are not in a position to incorporate the vast amount of data related to fermion mixing within a consistent framework. In this context, therefore, it is desirable to look at bottom-up approach [8][9][10][11] consisting of finding the phenomenological fermion mass matrices which are in tune with the low energy data, i.e. observables like quark and lepton masses, mixing angles in both sectors, angles of the unitarity triangle in the quark sector, etc.…”