Testing the Higgs triplet model with the mass difference at the LHC

Abstract: In general, there can be mass differences among scalar bosons of the Higgs triplet field with the hypercharge of Y=1. In the Higgs triplet model, when the vacuum expectation value $v_\Delta$ of the triplet field is much smaller than that $v$ ($\simeq 246$ GeV) of the Higgs doublet field as required by the electroweak precision data, a characteristic mass spectrum $ m_{H^{++}}^2-m_{H^+}^2\simeq m_{H^+}^2-m_{\phi^0}^2(\equiv \xi)$ appears, where $m_{H^{++}}$, $m_{H^+}$, $m_{\phi^0}$ are the masses of the doubly-charged ($H^{++}$), the singly-charged ($H^+$) and the neutral ($\phi^0=H^0$ or $A^0$) scalar bosons, respectively. It should be emphasized that phenomenology with $\xi\neq 0$ is drastically different from that in the case with $\xi=0$ where the doubly-charged scalar boson decays into the same sign dilepton $\ell^+\ell^+$ or the diboson $W^+W^+$ depending on the size of $v_\Delta$. We find that, in the case of $\xi > 0$, where $H^{++}$ is the heaviest, $H^{++}$ can be identified via the cascade decays such as $H^{++}\to H^+W^{+(*)}\to \phi^0 W^{+()}W^{+()}\to b\bar{b}\ell^+\nu\ell^+\nu$. We outline how the Higgs triplet model can be explored in such a case at the LHC. By the determination of the mass spectrum, the model can be tested and further can be distinguished from the other models with doubly-charged scalar bosons.