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We study how the custodial symmetry in the Higgs sector of theGeorgi-Machacek (GM) model can be tested at the LHC. As the minimal extensionof the Higgs triplet model, in which tiny neutrino masses are generated via theType-II Seesaw Mechanism, the GM model keeps the electroweak $\rho$ parameterat unity at tree level. In the GM model, there are 5-plet ($H_5$), 3-plet($H_3$) and singlet ($H_1$) Higgs bosons under the classification of thecustodial $SU(2)_V$ symmetry, in addition to the standard model-like Higgsboson ($h$). These new Higgs bosons have the following characteristic featuresat the tree level: (1) the masses of the Higgs bosons belonging to the same$SU(2)_V$ multiplet are degenerate; and (2) $H_5$ and $H_1$ couple to theelectroweak gauge bosons but not SM quarks, whereas $H_3$ couples to the quarksbut not the gauge bosons. We find that the $H_5$ production from the weakvector boson fusion process and the Drell-Yan process associated with $H_3$ areuseful in testing the custodial symmetry of the Higgs sector at the LHC. Inaddition, these processes can also be used to discriminate from other modelsthat contain singly-charged Higgs bosons and extra neutral Higgs bosons. Wealso investigate a possible enhancement in the $h\to \gamma\gamma$ as well as$h\to Z\gamma$ decays.

Testing the custodial symmetry in the Higgs sector of the Georgi-Machacek model