Electroweak corrections to the SM-like Higgs boson decays and the Higgs trilinear coupling in the real Higgs triplet model

We study new physics effects on the decays of the standard model-like Higgs boson ($h$) and the Higgs trilinear coupling including the full one-loop corrections in the real Higgs triplet model (RHTM). We adopt the on-shell renormalization scheme, in which the scalar mixing angles are renormalized in a gauge-independent way using the pinch technique. We found that sizable one-loop effects can arise in the decay rates through the Higgs wave-function (external-leg) corrections, while the tree-level effects are rather small due to the constraint on the vacuum expectation value of the triplet field from the electroweak precision measurements. In addition, the $h\toγγ$ decay rate and the $hhh$ coupling are sensitive to loop contributions. The RHTM may be distinguishable from other extended Higgs models by studying the correlations among the $h\toττ$, $h\to ZZ^{*}$, and $h\toγγ$ decay modes, and such characteristic predictions can be tested at the High-Luminosity LHC or future Higgs factories.