angle $\alpha$. The eigenvalues correspond to the masses $m_{\tilde H_1^0}$ and $m_{\tilde H_1^{0'}}$ for the mass eigenstates ${\tilde H_1^0}$ and ${\tilde H_1^{0'}}$.

From Eqs.(\[m5\]) - (\[masses\]), the quartic couplings $\lambda_i$ are expressed in terms of the masses and the mixing angles as \_1&=&(m\_[H\_1\^0]{}\^2\^2+m\_[H\_1\^[0’]{}]{}\^2\^2)/(8v\^2\^2\_H) , \[lambda1\]\
\_2&=&(m\_[H\_1\^0]{}\^2\^2+m\_[H\_1\^[0’]{}]{}\^2\^2-m\_[H\_5]{}\^2+3m\_[H\_3]{}\^2\^2\_H)/(3v\^2\^2\_H) , \[lambda2\]\
\_3&=&(m\_[H\_1\^[0’]{}]{}\^2-m\_[H\_1\^0]{}\^2)/(v\^2\_H\_H)+m\_[H\_3]{}\^2/v\^2 , \[lambda3\]\
\_4&=&(m\_[H\_5]{}\^2-3m\_[H\_3]{}\^2\^2\_H)/(v\^2\^2\_H) ,\
\_5&=&-2m\_[H\_3]{}\^2/v\^2  . \[lambda5\] \[lambda\]

The $SU(2)_{\rm V}$ 3-plet fields receive the constraints from the current data of $Z\to b\bar b$, $B_0-\bar B_0$ and $K_0-\bar K_0$ mixings [@Kundu:1995qb; @Chakraverty:1995zw]. These data give bounds on the mass $m_{H_3}^{}$ with the mixing angle $\theta_H$. The most stringent experimental constraint comes from $Z \to b \bar b$. The mass $m_{H_3}^{}$ is constrained to be smaller than 1 (0.5) TeV for $\tan\theta_H~<$ 2 (1).

Although the 5-plet fields do not couple to the fermions, the singly-charged state in the 5-plet has a characteristic coupling of $H_5^\pm W^\mp Z$, which only appears beyond the tree level in multi-Higgs-doublet models [@Grifols:1980uq]. Experimental confirmation of a sizable coupling of $H_5^\pm W^\mp Z$ with $\rho \simeq 1$ should be a strong indication for the GM model[@Mukho:1990]. This coupling is testable via the process $p\bar p\to W^\pm H^\mp$ at the Fermilab Tevatron [@Cheung:2002gd], also via $pp\to W^{\pm\ast} 