Neutrino-two-Higgs-doublet model with the inverse seesaw mechanisms

In this paper, we combine the $\nu$-two-Higgs-doublet-model with the inverse seesaw mechanisms. In this model, the Yukawa couplings involving the sterile neutrinos and the exotic Higgs bosons can be of order 1 in the case of a large $\tan \beta$. We calculated the corrections to the $Z$-resonance parameters $R_{l_i}$, $A_{l_i}$, and $N_{\nu }$, together with the $l_1\to l_2\gamma$ branching ratios and the muon anomalous $g-2$. Compared with the current bounds and plans for the future colliders, we find that the corrections to the electroweak parameters can be constrained or discovered in much of the parameter space.

Figure 1

(a) to the $Z-l^{+}-l^0$ vertices.

Figure 2

(c) Diagrams to $l^{\pm }$ propagators.

Figure 3

(a) Diagrams to the $Z-\nu -\overline{\nu }$ vertices.

Figure 4

(c) Diagrams to $\nu$ propagators.

Figure 5

The diagram for $l_1\to l_2\gamma$. This diagram can also be used to calculate the muon anomalous $g-2$.

Figure 6

$R_{l_i}$ (left panel) and $A_{l_i}$ (right panel) together with the $l_1\to l_2\gamma$ bounds and the $3\text{−}\sigma g-2$ range. Here, $m_H=m_{H^{\pm }}=m_A=200\mathrm{GeV}$. $\tan \beta =1000$, $\sin (\beta -\alpha )=0.9999$, and $m_{N_0}=20\mathrm{GeV}$. The purple, green, and blue lines indicate $\delta R/\delta A_{e,\mu ,\tau }$, respectively. As for the $l_i\to l_j\gamma$ constraints, the lower area has been excluded, and as for the “Planck bound” constraint, the upper area has been excluded.

Figure 7

$R_{l_i}$ (left panel) and $A_{l_i}$ (right panel) together with the $l_1\to l_2\gamma$ bounds and the $3\text{−}\sigma g-2$ range. Here, $m_H=m_{H^{\pm }}=m_A=200\mathrm{GeV}$. $\tan \beta =1000$, $\sin (\beta -\alpha )=0.9999$, and $m_{N_0}=20\mathrm{GeV}$. The purple, green, and blue lines indicate $\delta R/\delta A_{e,\mu ,\tau }$, respectively. As for the $l_i\to l_j\gamma$ constraints, the lower area has been excluded, and as for the Planck bound constraint, the upper area has been excluded.

Figure 8

$l_1\to l_2\gamma$ diagram up to the lowest order in case 3.

Figure 9

$R_{l_i}$ (left panel) and $A_{l_i}$ (right panel) together with the $3-\sigma g-2$ range. Here, $m_H=m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}>125\mathrm{GeV}$; however, $m_H=125.1\mathrm{GeV}$ and $m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}<125\mathrm{GeV}$. $\tan \beta =1000$, $\sin (\beta -\alpha )=0.9999$, and $m_{N_0}=20\mathrm{GeV}$.

Figure 10

$R_{l_i}$ (left panel) and $A_{l_i}$ (right panel) together with the $3-\sigma g-2$ range. Here, $m_H=m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}>125\mathrm{GeV}$; however, $m_H=125.1\mathrm{GeV}$ and $m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}<125\mathrm{GeV}$. $\tan \beta =1000$, $\sin (\beta -\alpha )=0.9999$, and $m_{N_0}=m_{H^{\pm }}$.

Figure 11

$R_{l_i}$ (left panel) and $A_{l_i}$ (right panel) together with the $3-\sigma g-2$ range. Here, $m_H=m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}>125\mathrm{GeV}$; however, $m_H=125.1\mathrm{GeV}$ and $m_{H^{\pm }}=m_A$ when $m_{H^{\pm }}<125\mathrm{GeV}$. $\tan \beta =300$, $\sin (\beta -\alpha )=0.9999$, and $m_{N_0}=20\mathrm{GeV}$.

Figure 12

Comparison of the $\delta N_{\nu }^{l,\mathrm{h}}$. Here, $m_H=m_A$ $m_{H^{\pm }}=200\mathrm{GeV}$, $\tan \beta =1000$, $\sin (\beta -\alpha )=0.9999$, $m_{N_0}=20\mathrm{GeV}$, and $y_{\mathrm{SM}}/\cos \beta =1.5$.