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

We study how the custodial symmetry in the Higgs sector of the Georgi-Machacek (GM) model can be tested at the LHC. As the minimal extension of the Higgs triplet model, in which tiny neutrino masses are generated via the Type-II Seesaw Mechanism, the GM model keeps the electroweak $\rho$ parameter at 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 the custodial $SU(2)_V$ symmetry, in addition to the standard model-like Higgs boson ($h$). These new Higgs bosons have the following characteristic features at 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 the electroweak gauge bosons but not SM quarks, whereas $H_3$ couples to the quarks but not the gauge bosons. We find that the $H_5$ production from the weak vector boson fusion process and the Drell-Yan process associated with $H_3$ are useful in testing the custodial symmetry of the Higgs sector at the LHC. In addition, these processes can also be used to discriminate from other models that contain singly-charged Higgs bosons and extra neutral Higgs bosons. We also investigate a possible enhancement in the $h\to \gamma\gamma$ as well as $h\to Z\gamma$ decays.