gauge coupling $g_Y$ given as $$g_Y=\frac{g_R g_V}{\sqrt{g_R^2+g_V^2}}.$$

The scalar potential of this model is given as: $$\begin{aligned}
V(\Delta,\Phi)&=& -\mu_{1}^2{\text{Tr}}\left(\Phi^\dagger \Phi \right)-\mu_2^2{\text{Tr}}\left[\widetilde{\Phi}\Phi^\dagger+\widetilde{\Phi}^\dagger\Phi\right]-\mu_3^2 H_R^\dagger H_R -  \mu_4^2 H_L^\dagger H_L- \mu_5^2 \delta^+ \delta^-+ \left(M_1 H_L^\dagger \Phi H_R \right.  \notag \\
&+& \left. M_2 H_L^\dagger \widetilde\Phi H_R + H.C.\right) + \l_1\left[{\text{Tr}}(\Phi^\dagger\Phi)\right]^2 + \l_2\left[\left\{{\text{Tr}}(\widetilde\Phi\Phi^\dagger)\right\}^2+\left\{{\text{Tr}}(\widetilde\Phi^\dagger\Phi)\right\}^2\right]+\l_3{\text{Tr}}(\widetilde\Phi\Phi^\dagger){\text{Tr}}(\widetilde\Phi^\dagger\Phi)\notag\\
&+&\l_4{\text{Tr}}(\Phi\Phi^\dagger)\left[{\text{Tr}}(\widetilde\Phi\Phi^\dagger)+{\text{Tr}}(\widetilde\Phi^\dagger\Phi)\right] + \left[ i \a_1 {\text{Tr}}(H_L^T \tau_2 \Phi H_R \delta^-) + i \a_2 {\text{Tr}}(H_L^T \tau_2 \widetilde\Phi H_R \delta^-)  + H.C.\right] \notag \notag\\
&+& \a_3(H_L^\dagger \Phi \Phi^\dagger H_L)  + \a_4\left[{\text{Tr}}(\widetilde\Phi\Phi^\dagger+\widetilde{\Phi}^\dagger\Phi)H_L^\dagger H_L\right]+\a_5{\text{Tr}}(\Phi\Phi^\dagger)H_L^\dagger H_L +\a_6 (H_R^\dagger \Phi^\dagger \Phi H_R)  \notag\\ 
&+&\a_7\left[{\text{Tr}}(\widetilde\Phi\Phi^\dagger+\widetilde{\Phi}^\dagger\Phi)H_R^\dagger H_R\right] + \a_8{\text{Tr}}(\Phi\Phi^\dagger)H_R^\dagger H_R + \b_1 (H_L^\dagger H_L)^2 + \b_2 (H_R^\dagger H_R)^2 +\b_3 (H_R^\dagger H_R)(H_L^\dagger H_L)  \notag \\
&+&\g_1 {\text{Tr}}(\Phi^\dagger \Phi) \delta^+ \delta^- + \g_2 {\text{Tr}}\left[\widetilde{\Phi}\Phi^\dagger+\widetilde{\Phi}^\dagger\Phi\right]\delta^+ \delta^- + \g_3 H_L^\dagger H_L \delta^+ \delta^- +\g_4 H_R^\dagger H_R  \delta^+ \delta^- + \g_5 (\delta{^+} \delta{^-})^2.
\label{eq:spot}\end{aligned}$$

This gives four CP-even, two CP-odd and three charged Higgs boson states. Two CP-odd and two charged states are eaten up to give mass to the $Z_R,~Z,~W_R,W$ gauge bosons respectively. We will mainly focus our discussion on the charged Higgs sector, as that is the most important for the neutrino masses and the collider analysis which will be studied in this paper.

Minimizing the scalar potential of Eq. \[eq:spot\] we 