down quark mass matrix $M_d$ and a charged lepton mass matrix $M_e$ of the form \[matrixMd\] M\_d

0 & (\^d\_2)\^2 \^d\_3/M\^3 & -(\^d\_2)\^2 \^d\_3/M\^3\
-(\^d\_2)\^2 \^d\_3/M\^3 & \^d\_2 \^d\_3/M\^2 & -\^d\_2 \^d\_3/M\^2 + (\^d\_2)\^2 \^d\_3/M\^3\
0 & 0 & \^d\_3/M

v\_d and \[matrixMe\] M\_e

0 & -(\^d\_2)\^2 \^d\_3/M\^3 & 0\
(\^d\_2)\^2 \^d\_3/M\^3 & -3 \^d\_2 \^d\_3/M\^2 & 0\
-(\^d\_2)\^2 \^d\_3/M\^3 & 3 \^d\_2 \^d\_3/M\^2 + (\^d\_2)\^2 \^d\_3/M\^3 & \^d\_3/M

v\_d (with $v_d$ being the VEV of the light combination of electroweak doublets contained in $H_{\ol{5}}$ and $H_{\ol{45}}$). The Dirac neutrino mass matrix and the right-handed neutrino mass matrix read M\_D = y\_D

1 & 0 & 0\
0 & 0 & 1\
0 & 1 & 0

v\_u , \[matrixMR\] M\_R =

\^\_1 + 2 \^\_[3’]{} & \^\_2 - \^\_[3’]{} & \^\_2 -\^\_[3’]{}\
\^\_2 - \^\_[3’]{} & \^\_2 + 2 \^\_[3’]{} & \^\_1 - \^\_[3’]{}\
\^\_2 -\^\_[3’]{} & \^\_1 - \^\_[3’]{} & \^\_2 + 2 \^\_[3’]{}

($v_u$ is the VEV of the electroweak doublet contained in $H_{5}$). The matrix $M_R$ is of the most general form compatible with TB mixing. For $\varphi^u_2$, $\wt\varphi^u_2 \sim \la^4 M$, $\la \approx \theta_C \approx
0.22$, the up and charm quark mass, $m_u \approx \varphi^u_2 