One-loop renormalized Higgs boson vertices in the Georgi-Machacek model

We compute renormalized vertices of the 125 GeV Higgs boson h with the weak gauge bosons ($hVV$), fermions (hff̄), and itself ($hhh$) in the Georgi-Machacek model at one-loop level. The renormalization is performed based on the on-shell scheme with the use of the MS̄ scheme only for the $hhh$ vertex. We explicitly show the gauge dependence in the counterterms of the scalar mixing parameters in the general R_ξ gauge and that the dependence can be removed by using the pinch technique in physical scattering processes. We then discuss the possible allowed deviations in these one-loop corrected Higgs couplings from the standard model predictions by scanning model parameters under the constraints of perturbative unitarity and vacuum stability as well as those from experimental data.