Implications of θ13 on Fritzsch-like lepton mass matrices

Quark flavor mixings from hierarchical mass matrices

“…Therefore, phenomenological approaches on specific textures of quark mass matrices have been widely adopted to obtain vital clues on the underlying flavor dynamics [10][11][12][13][14][15][16][17]. However, experience shows that there exist a vast number of texture zero structures, [18][19][20][21][22][23][24][25][26][27][28][29][30][31] both for the quark and lepton sectors, which in principle, may not be ruled out by experiments. This suggests that the texture approach alone is perhaps not sufficient to account for the flavor dynamics and one may require to use additional assumptions (based on observations) to extract some useful information on the gross possible structures of these matrices from a model-independent prospective, particularly, for the quark sector.…”

Generic lepton mass matrices and neutrino oscillations

“…It has been recently shown [10,16] that for Hermitian lepton mass matrices M 0 e and M 0 νD and for a real diagonal M R ¼ m R I, where I is a unit matrix and m R denotes a very large mass scale, the left diagonalizing transformations for M 0 νD and M 0 ν remain the same, as shown in Eqs. (9) and (11) below.…”

“…In this context, following FSTY, we have considered M R ¼ m R I. In such a case, it can be shown [10,16] that the light neutrino mass matrix takes the following form,…”

“…(11) above [10,16]. In such a case, the ratios m ν12D , m ν13D , and m ν23D get replaced by m ν12D → ffiffiffiffiffiffiffiffiffi m ν12 p ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m ν1 =m ν2 p and so on.…”

“…(4), (5), (11), (12), the product Q e P νD in Eq. (11) is a diagonal phase matrix given by Q e P νD ¼ diagðe −iϕ 1 ; 1; e iϕ 2 Þ [16], where the phases ϕ 1 ¼ α e − α νD and ϕ 2 ¼ β e − β νD are also free parameters.…”