That is, we replace Eqs. (6) and (7) as respectively. Note that phase factors are added into { 12 } , { 21 } , { 23 } and { 32 } elements for each matrix. The phases θ 1 and φ 1 are responsible for the up- and down-quark masses. If we regard ( e iθ$_{1}$ − 1) and ( e iφ$_{1}$ − 1) as perturbations, we obtain as we expected. The phases θ 2 and φ 2 are added to account for the CP violating Dirac phase in the CKM matrix. In the following, we will present our numerical analysis to illustrate our result. In our calculation, without loss of generality, we will normalize Eqs. (18) and (19) with B$_{u,d}$ = 1. We will also ignore the terms associated with A$_{u}$ because they are suppressed by ξ$_{u}$ = λ $^{4}$. As a result, the model has three real parameters: A$_{d}$ and C$_{u,d}$ , and three CP violating phases: θ 1 and φ 1 , 2 . For these six parameters, we use the following experimental values from the Particle Data Group (PDG) [18]: as input parameters. Figure 1 shows the allowed region in the | V$_{us}$ | − | V$_{td}$/V$_{ts}$ | plane with the bounds [18] One can easily see from Fig. 1 that our results on | V$_{us}$ | and | V$_{td}$/V$_{ts}$ | are consistent with 6 | V$_{ub}$ | = (3 . 57 − 4 . 29) × 10 − $^{3}$, | V$_{td}$/V$_{ts}$ | = 0 . 202 − 0 . 216 . (24) m$_{u}$/m$_{c}$ = (0 . 112 − 0 . 284) × 10 − $^{2}$, m$_{c}$ /m$_{t}$ = (0 . 669 − 0 . 792) × 10 − $^{2}$, (21) m$_{s}$/m$_{d}$ = 17 − 22 , m$_{s}$/m$_{b}$ = (0 . 160 − 0 . 315) × 10 − $^{1}$, (22) | V$_{us}$ | = 0 . 2236 − 0 . 2274 , | V$_{cb}$ | = 0 . 0401 − 0 . 0423 , (23) m$_{u}$ m$_{c}$ ≃ ∣ 2 η 2 $_{u}$( e iθ$_{1}$ − 1) ∣ , m$_{d}$ m$_{s}$ ≃ ∣ 2 η 2 $_{d}$( e iφ$_{1}$ − 1) ∣ , (20) M d =    ( B$_{d}$ + C$_{d}$ξ$_{d}$ ) η 2 d − B$_{d}$η$_{d}$ e iφ$_{1}$ − C$_{d}$η$_{d}$ − B$_{d}$η$_{d}$ e iφ$_{1}$ A$_{d}$ξ$_{d}$ + B$_{d}$ − A$_{d}$ e iφ$_{2}$ − C$_{d}$η$_{d}$ − A$_{d}$ e iφ$_{2}$ ( A$_{d}$ + C$_{d}$ ) /ξ$_{d}$   $^{,}$ (19) M u =    ( B$_{u}$ + C$_{u}$ξ$_{u}$ ) η 2 u − B$_{u}$η$_{u}$ e iθ$_{1}$ − C$_{u}$η$_{u}$ − B$_{u}$η$_{u}$ e iθ$_{1}$ A$_{u}$ξ 2 u + B$_{u}$ − A$_{u}$ξ$_{u}$ e iθ$_{2}$ − C$_{u}$η$_{u}$ − A$_{u}$ξ$_{u}$ e iθ$_{2}$ A$_{u}$ + C$_{u}$/ξ$_{u}$   $^{,}$ (18)