much greater than ${\cal O}(1)$.

In the GM model, there are ten physical states in the Higgs sector, which are classified as a 5-plet ($H_5^{++}, H_5^{+}, H_5^{0}, H_5^{-}, H_5^{--}$), a 3-plet ($H_3^{+}, H_3^{0}, H_3^{-}$), and two singlets $H_1^0$ and $H_1^{0'}$ under the custodial $SU(2)_{\rm V}$ symmetry. These are given in terms of the original component fields and the doublet-triplet mixing angle $\theta_H$ as [@Gunion:1989ci] &&H\_5\^[++]{}=\^[++]{} ,\
&&H\_5\^[+]{}=(\^[+]{}-\^[+]{})/  ,\
&&H\_5\^[0]{}=(2\_r\^0-\^[0]{}\_r)/ ,\
&&H\_3\^[+]{}=(\^++\^+)/-\^+,\
&&H\_3\^[0]{}=i(-\^0\_i+\^0\_i) ,\
&&H\_1\^[0]{}=\_r\^0,\
&&H\_1\^[0’]{}=(\^0\_r+\_r\^0)/. The 5-plet components do not include the component fields from the isospin doublet field $\Phi$, so that the states of the 5-plet do not couple to the fermions at the tree level. On the other hand, the 3-plet fields can couple to the fermions. Because of invariance under the custodial $SU(2)_{\rm V}$ symmetry, states in the different multiplet cannot mix each other.

All members in the same $SU(2)_{\rm V}$ multiplet are degenerate in mass at the tree level. The masses of the 5-plet and the 3-plet are respectively given by m\_[H\_5]{}\^2&=&(\_4\^2\_H-\_5\^2\_H) v\^2  , \[m5\]\
m\_[H\_3]{}\^2&=&-v\^2  . On the other hand, two $SU(2)_{\rm V}$ singlets can mix, and the mass matrix \^2\_[H\_1\^0,H\_1\^[0’]{}]{}=(

[cc]{}8\^2\_H\_1 &\_H\_H (2\_3+\_5)\
\_H\_H (2\_3+\_5) &\^2\_H(3\_2+\_4)

)v\^2 \[masses\] is diagonalized by introducing the mixing 