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

TL;DR

This paper explores how to test the custodial symmetry in the Higgs sector of the Georgi-Machacek model at the LHC, focusing on characteristic Higgs boson production processes and decay enhancements.

Contribution

It proposes specific collider processes to test custodial symmetry and distinguish the GM model from other Higgs models at the LHC.

Findings

Higgs bosons in the same multiplet are mass-degenerate at tree level.

Production processes like vector boson fusion and Drell-Yan are effective for testing custodial symmetry.

Potential enhancements in h→γγ and h→Zγ decay channels.

Abstract

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.