Higgs triplets at like-sign linear colliders and neutrino mixing

We study the phenomenology of the type-II seesaw model at a linear $e^{-}{e}^{-}$ collider. We show that the process $e^{-}{e}^{-}\to {\alpha }^{-}{\beta }^{-}$ ($\alpha$, $\beta =e$, $\mu$, $\tau$ being charged leptons) mediated by a doubly charged scalar is very sensitive to the neutrino parameters, in particular, the absolute neutrino mass scale and the Majorana $CP$-violating phases. We identify the regions in parameter space in which appreciable collider signatures in the channel with two like-sign muons in the final state are possible. This includes Higgs triplet masses beyond the reach of the LHC.

Figure 1

Feynman diagrams for the doubly charged Higgs mediated bilepton channel (left) and $WW$ channel (right).

Figure 2

Upper limits of cross sections $e^{-}{e}^{-}\to {\alpha }^{-}{\beta }^{-}$ with respect to $m_1$ at a linear collider with $\sqrt{s}=1\mathrm{TeV}$. The Higgs triplet mass $m_{\Delta }=800\mathrm{GeV}$ has been assumed as an example, while the choices of $\sin {\theta }_{13}$ are labeled on each plot. Furthermore, we take the Majorana $CP$-violating phases ${\varphi }_1$ and ${\varphi }_2$ to be zero for the plots on the upper panel, and the Dirac $CP$-violating phase $\delta =0$ for the plots on the lower panel. For comparison, the SM Møller scattering cross section is also shown on the plots with black solid lines. The luminosity one can assume is $80{\mathrm{fb}}^{-1}$.

Figure 3

Upper bounds of the total cross section $\sigma (e^{-}{e}^{-}\to {\mu }^{-}{\mu }^{-})$ (in units of fb) with respect to the effective mass $|m_{ee}|$. The experimental setup and the mass of the Higgs triplet are the same as those in Fig. 2, while the input values of $s_{13}$ as well as the neutrino mass hierarchies are labeled on the plot. The Majorana $CP$-violating phases are allowed to vary between 0 and $\pi$, while $\delta =0$ is assumed.

Figure 4

Upper bounds of the total cross section $\sigma (e^{-}{e}^{-}\to {\mu }^{-}{\mu }^{-})$ (in units of fb) for $\sqrt{s}=1\mathrm{TeV}$ in the $\sin {\theta }_{13}-\delta$ plane with the experimental setup and the mass of the Higgs triplet are the same as those in Fig. 2. For the plots in the upper row, we consider the normal mass ordering, while in the lower row the inverted mass ordering is assumed. The lightest neutrino mass can be read off from the plots, and for the sake of simplicity, we take all the Majorana phases to be zero. For an integrated luminosity $80{\mathrm{fb}}^{-1}$, the solid, dashed and dotted curves show the regions with expected number of events greater than 5, 50 and 500, respectively.

Figure 5

Upper bounds of the total cross section $\sigma (e^{-}{e}^{-}\to {\mu }^{-}{\mu }^{-})$ (in units of fb) in the ${\varphi }_1-{\varphi }_2$ plane with the same experimental setting of Fig. 4. The input values of $s_{13}$ and $m_1$ are labeled on the plots, while $\delta$ is taken to be zero. The luminosity one can assume is $80{\mathrm{fb}}^{-1}$.

Figure 6

The bare cross section ${\sigma }_0$ (in units of fb) as a function of $\sqrt{s}$, with solid, dashed and dotted lines corresponding to $m_{\Delta }=0.8\mathrm{TeV}$, 0.5 TeV and 1.5 TeV, respectively. The black star on the plot indicates the values of the parameters used in plotting Figs. 2, 3, 4, 5, 6). For the definition of ${\sigma }_0$, see Eq. (8).

Figure 7

Upper limits of the cross section $e^{-}{e}^{-}\to {\mu }^{-}{\mu }^{-}$ with $\sqrt{s}=1\mathrm{TeV}$ (solid lines) and $\sqrt{s}=4\mathrm{TeV}$ (dashed lines). The Higgs triplet masses are labeled on the plot. Here we consider the normal mass ordering case, and assume all the $CP$-violating phases and $s_{13}$ to be zero for simplicity. The blue and green solid lines for $\sqrt{s}=1\mathrm{TeV}$ and $m_{\Delta }=800$ and 1500 GeV are lying basically on top of each other and are hardly distinguishable. 100 events correspond to $\sigma =1.25\mathrm{fb}$ (black solid line) and $\sigma =0.078\mathrm{fb}$ (black dashed line), respectively.