Suppression of $H\to VV$ decay channels in the Georgi-Machacek model

The $H\to ZZ$ decay mode is usually considered as one of the most promising ways to discover new heavy neutral scalar $H$. We show that in the Georgi-Machacek model it is possible to get large enhancement of double SM-like Higgs boson production due to $H$ decays while $ZZ$ and $WW$ decay channels could be highly suppressed.


I. INTRODUCTION
Models with extended Higgs sector provide a very rich phenomenology. In many models there is a heavy neutral scalar H which has the admixture of the neutral component of the Standard Model (SM) doublet. As one of the consequences this new heavy scalar can provide us with the significant enhancement of double SM-like Higgs boson (h) production.
In our previous paper [1] we considered extensions of the SM by isotriplets with hypercharges Y = 0 and Y = 2. In see-saw type II (one extra triplet with Y = 2) double Higgs boson production can be increased by the value which is comparable with what we have in the SM. In the Georgi-Machacek (GM) model [2] we obtained that H production cross section is significantly enhanced so 2h production can be much larger than in the SM.
If H is produced with large cross section then in principle it can be discovered in ZZ final state. Direct searches in this mode at the LHC [3] can set limits on model parameters which in some ranges of M H can be stronger than that from h couplings. However it is not the case in the GM model since we show that Br (H → ZZ) < 1% could occur.

II. THE MODEL
In the GM model (see [4] for a detailed review of this model 1 ) in addition to SM Higgs doublet two isotriplets with hypercharges Y = 0 and Y = 2 are introduced: We took the potential in the following form (for a detailed description see [4]): where Φ (0) , ξ and ∆ are combined into matrices Φ and X: U is a rotational matrix: τ a = σ a /2 where σ a are Pauli matrices. Let us note that we consider simplified potential which corresponds to λ 2 , λ 3 , λ 4 , λ 5 , M 2 = 0 choice in the potential considered in paper [4].
The value of v ∆ is generated by the term proportional to M 1 and the following relations In paper [1] v ∆ is defined to be √ 2 times larger.
Since the potential is written in the way that vevs of two triplets are the same then the custodial symmetry is preserved and the relation between W and Z boson masses is the same as in the SM so the experimental data on W mass does not lead to new limits on model parameters. It means that main restrictions originate from the measurement of h couplings to SM particles. Since the accuracy of these measurements is not very good at the moment, these restrictions are not very tough and v ∆ up to approximately 30 GeV is allowed.
Only one scalar, a combination of ξ 0 and ∆ 0 , mixes with neutral component Φ 0 of SM doublet forming mass eigenstates, h and H, which correspond to the scalar discovered at LHC (so M h = 125 GeV) and new heavy scalar. Since this new scalar H has doublet admixture, it couples to quarks and therefore it can be produced in gluon-gluon fusion so its production cross section at LHC can be much larger than that for the other scalars of the GM model which can be produced only in electroweak processes. It was stressed in [1] that in some region of parameters space H decays can provide great enhancement of double h production at LHC.