Radiative corrections to electroweak parameters in the Higgs triplet model and implication with the recent Higgs boson searches

We study radiative corrections to the electroweak parameters in the Higgs model with the Y=1 triplet field, which is introduced in the scenario of generating neutrino masses based on the so-called type II seesaw mechanism. In this model, the rho parameter deviates from unity at the tree level. Consequently, the electroweak sector of the model is described by the four input parameters such as $\alpha_{\text{em}}$, $G_F$, $m_Z$ and $\sin^2\theta_W$. We calculate the one loop contribution to the W boson mass as well as to the rho parameter in order to clarify the possible mass spectrum of the extra Higgs bosons under the constraint from the electroweak precision data. We find that the hierarchical mass spectrum among $H^{\pm\pm}$, $H^{\pm}$ and $A$ (or $H$) is favored by the precision data especially for the case of $m_A$ $(\simeq m_H)>m_{H^+}>m_{H^{++}}$, where $H^{\pm\pm}$, $H^{\pm}$, $A$ and $H$ are the doubly-charged, singly-charged, CP-odd and CP-even Higgs bosons mainly originated from the triplet field. We also discuss phenomenological consequences of such a mass spectrum with relatively large mass splitting. The decay rate of the Higgs boson decay into two photons is evaluated under the constraint from the electroweak precision data, regarding the recent Higgs boson searches at the CERN LHC.