content_image/336060.jpg content_image/336059.jpg content_image/336058.jpg content_image/336057.jpg content_image/336056.jpg content_image/336055.jpg content_image/336054.jpg content_image/336053.jpg
and 

<img src='content_image/336060.jpg'>

respectively. In this basis, we impose 

<img src='content_image/336059.jpg'>

We note that with Eq. (8), the down-type quark mass matrix becomes similar to the hy- brid texture discussed in Ref. [17]. On the other hand, the up-type one is almost diagonal. Since M u,d are real and symmetric matrices, they can be diagonalized by real orthogonal matrices: V T q M $^{q}$V$_{q}$ = diag( m$_{q}$ 1 , m$_{q}$ 2 , m$_{q}$ 3 ). With Eq. (8), V$_{q}$ can approximately be written as 

with m$_{u}$/m$_{c}$ ≃ η 2 u and m$_{c}$/m$_{t}$ ≃ | ξ$_{u}$ | for the up-quark sector, and 

<img src='content_image/336058.jpg'>

<img src='content_image/336057.jpg'>

with m$_{d}$/m$_{s}$ ≃ η 2 d and m$_{s}$/m$_{b}$ ≃ 1 / 2 | ξ$_{d}$ | for the down-quark sector, respectively. Note that the factor 1 / 2 in Eq. (10) arises from the { 33 } element of Eq. (7). From the mass ratios, we can deduce that 

<img src='content_image/336056.jpg'>

<img src='content_image/336055.jpg'>

with λ ≃ 0 . 22. Therefore, in what follows, we consider the following hierarchical FL translation: 

<img src='content_image/336054.jpg'>

<img src='content_image/336053.jpg'>

