IPMU-19-XXX

Charged Higgs searches in the Georgi-Machacek modelat the LHC
Nivedita Ghosha,1 , Swagata Ghoshb,2 , Ipsita Sahac,3abSchool of Physical Sciences, IACS, Kolkata, India
Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, Indiac
Kavli IPMU (WPI), University of Tokyo, Kashiwa, 277-8583, Japan
Abstract

The Georgi-Machacek Model allows for a large triplet vacuum expectation value (vev) with a custodial
symmetric scalar potential. This manifestly leads to large charged Higgs coupling to SM fermions thus
enhancing the detection probability of the model at the hadron collider. We show that the latest boundfrom LHC searches on charged Higgs scalar decaying to top and bottom quark restricts the triplet vev fromabove. We demonstrate that the combined limit from theoretical constraints and the latest Higgs data
together with this charged Higgs bound can already curb the model parameter space significantly. Further,
we propose the charged Higgs decaying to W ± boson and a Higgs as a prospective channel to probe the yet
unbounded model parameter space at the future run of the LHC.

1

Introduction

The Standard Model (SM) of particle physics has achieved its triumph after the discovery of a 125 GeV scalar
resonance at the Large Hadron Collider (LHC) [1, 2] experiment. Nevertheless, the quest for new physics is
yet to accomplish. Possibility of having an exotic particle in the realm of current collider reach still can not
be discarded and it may just need a closer look at the present LHC data. In the second run of the LHC withincreased energy and luminosity, a greater amount of data is already available for more detailed and intricate
analysis.
Among many, a charged scalar particle is one of the appealing exotic candidates in particle phenomenology andhas been searched for long. Most of the beyond the Standard Model (BSM) scenarios render singly charged scalar
candidate and it has always remained an important probe for the models with SM scalar sector extensions [3–11].
In this paper, we will talk about probing the Georgi-Machacek (GM) model [12–14], a variant of scalar triplet
extension of the SM, through the searches of a singly-charged scalar at the current and future LHC run. The
usual Higgs triplet model (HTM) is favored for the explanation on the neutrino mass generation but it suffersfrom electroweak (EW) ρ-parameter constraint. The GM model, on the other hand, consists of two scalar
triplets, one real and one complex, thus, preserving the custodial SU(2) symmetry and lifting the bound on
the triplet vacuum expectation value (vev). This large triplet vev induces a large mixing between the GM andthe SM sector leading to interesting search processes for the non standard scalars. In particular, the charged
scalar of the GM model couples to the SM fermions with a strength directly proportional to the vev (vt ) anda significantly large vt enhances the detection possibility of such charged scalar at the collider. Such decay
processes are highly suppressed in the HTM and can thus be an important probe of the GM model.
1 tpng@iacs.res.in
2 swgtghsh54@gmail.com
3 ipsita.saha@ipmu.jp

1

Besides the two CP-even scalars, the lightest of which resembles the SM-like Higgs with mass 125 GeV, there lies
seven scalar particles in the GM particle spectrum arising from the custodial triplet and fiveplet respectively.
The singly-charged scalar of the custodial fiveplet (H5± ), however, has no tree-level interaction with the SM
fermions. The singly charged scalar of the custodial triplet (H3± ) can have significant tree level coupling to
SM fermion-anti-fermion pair due to the large overlap with the Higgs field corresponding to the triplet vev. In
particular, H3+ may acquire a considerable branching ratio (BR) to the tb̄ channel in the kinematically possible
mass region. Recently, the ATLAS collaboration [15] has reported their latest analysis on charged Higgs searcheswith the data from the 13 TeV run of the LHC with 36 f b−1 luminosity and has provided a model independent
bound on the production cross-section times the BR for charged Higgs decaying into tb̄ mode. Following theiranalysis, in this paper, we aim to put constraints on the GM model parameter space in the physical basis interms of the scalar masses and mixing angles. This limit will definitely put an upper bound on vt for a particularcharged Higgs mass corresponding to its BR.
On the other hand, the theoretical constraints on the GM scalar potential from EW vacuum stability andperturbative unitarity at tree-level already limits vt from the lower end. Simultaneously, the charged scalarmasses are also restricted from above due to the unitarity constraints. We show the bounds for two variants ofGM potential, with and without the trilinear terms where the potential with vanishing trilinear term results ina more stringent bound. Additionally, the latest LHC Higgs data also cause a severe constraint in the model
parameter space. Therefore, a combination of theoretical constraint, Higgs data and the limit from charged
Higgs analysis by ATLAS will put a definitive restriction on the GM model. In this study, we have given acomprehensive description in this regard. Furthermore, as a future endeavor, we show how the region allowedby the above bounds can be probed at the future run of the LHC. For this, we propose the other competentdecay channel of H3± → W ± h, h being the 125 GeV Higgs resonance. This decay mode is dominant for large
neutral scalar mixing angle α and can be an effective probe in the region where the ATLAS limit is relaxed.
It should be mentioned that though the GM model have been studied extensively in the post-Higgs discovery
era [16–28], implication of charged Higgs searches in association with the latest Higgs data to explore the model
parameter space has not been discussed so far.
The paper is organized in the following manner. In sec. 2, we introduce the model briefly and explain thetheoretical as well as constraint from Higgs data on the model parameter space. In sec. 3, we explain the
production and decay of the charged Higgs state H3± for various parameter space and portray the limits provided
by the ATLAS analysis. In sec. 4, we demonstrate our analysis for the future probe of the model at the LHC
and, in sec. 5 we show our findings collectively. Finally, we conclude in sec. 6.

2

The Model

Here, we present a brief description of the scalar potential of the GM model. in addition to the SM particle
content, the scalar sector of the GM model [12–14] consists of one real SU (2)L triplet ξ and one complex SU (2)Ltriplet χ with hypercharges Y = 0 and Y = 2 forming a bi-triplet X. Now, the most general scalar potential
for the GM model can be written as [19, 26]
V (Φ, X)=µ2φµ2
Tr(Φ† Φ) + X Tr(X † X) + λ1 [Tr(Φ† Φ)]2 + λ2 Tr(Φ† Φ) Tr(X † X)
22
+λ3 Tr(X † XX † X) + λ4 [Tr(X † X)]2 − λ5 Tr(Φ† τa Φτb ) Tr(X † ta Xtb )−M1 Tr(Φ† τa Φτb ) U XU † ab − M2 Tr(X † ta Xtb ) U XU † ab ,(1)

where, τa ≡ σa /2, (a = 1, 2, 3) with σa ’s being the Pauli matrices and ta ’s are the generators of triplet
representation of SU (2) which are expressed as






0 1 0
0 −i 01 0 0
1
1
t1 = √  1 0 1  ,t2 = √  i 0 −i  ,t3 =  0 0 0  .
(2)
2
2
0 1 0
0 i
0
0 0 −1
2

Furthermore, the matrix U in the trilinear terms of Eq. (1) is given by,


−1 0
1
1 
−i √0 −i  .
U=√
2
0
2 0

(3)

It is worth mentioning here that the absence of these trilinear term would enhance the symmetry of the potential.
Moreover, it should be noted that the GM potential has no explicit CP violation since there are no non-Hermitian
terms.
Now, the bi-doublet Φ and the bi-triplet X are represented as
 0∗
 0∗

χ
+
φ
φ
−

−χ
Φ=
,
X
=
−φ− φ0
−−
χ

ξ+
ξ0
−ξ −


χ++
χ+  .
χ0(4)

After the electroweak symmetry breaking (EWSB), the neutral components of the bi-doublet and the bi-triplet
can be expanded around their vacuum expectation values(vev) as φ0 = √12 (vd + hd + iηd ), ξ 0 = (vt + hξ ) andh +iη

χ0 = (vt + χ√2 χ ). The equality in vevs to the real and the complex triplets corresponds to the preserved
custodial symmetry of the potential. The EW vev in terms of the vevs of the scalar multiplets turns out to beq
vd2 + 8vt2 = v = 246 GeV .
(5)
Thus, there will be two independent minimization conditions corresponding to the two vevs of the bi-doublet
and the bi-triplet (vd and vt ) which can be used to extract the bilinear coefficients of the potential µ2φ and µ2X
as
µ2φ

3
= −4λ1 vd2 − 3 (2λ2 − λ5 ) vt2 + M1 vt ,2µ2X

= − (2λ2 − λ5 ) vd2 − 4 (λ3 + 3λ4 ) vt2 +(6a)
M1 vd2+ 6M2 vt .
4vt

(6b)

The scalar potential consists of a custodial quintuplet (H5++ , H5+ , H50 , H5− , H5−− ) of common mass m5 anda custodial triplet (H3+ , H0 , H3− ) of mass m3 . Alongside, there are two CP-even scalars that are custodial
singlets, namely h and H with masses mh and mH respectively. The neutral scalar mixing angle α diagonalizes
the CP even sector to obtain the mass eigenstates h and H. Hereby, we refrain ourselves from giving a detailed
description of the diagonalization procedure and we refer the reader to Refs. [17, 19]. We only show the mass
eigenstate for the charged scalars and the custodial singlets.
1
H3± = − sin β φ± + cos β √ χ± + ξ ± ,
2
!
r
r
1
2
hξ +
hχ ,
h = cos α hd + sin α
3
3
!
r
r
1
2
H = − sin α hd + cos α
hξ +
hχ ,
3
3

H5±

=


1
√ χ± − ξ ± ,
2

(7a)
(7b)

(7c)

where, hd , hχ , hξ are the fields corresponding to the neutral components of the doublet and the triplets after
the electroweak symmetry breaking. The angle α represents the neutral mixing angle while tan β is defined as√
2 2vt
tan β =.
(8)vd
In total, there are nine independent parameters in the GM scalar potential with two bilinears (µ2φ and µ2X ),five quartic couplings (λi , i = 1, . . . , 5) and two trilinear couplings (M1 and M2 ). Among these, the bilinears
3have already been traded in favor of the vevs, vd and vt as in Eq. (6). Besides the trilinear terms (M1 , M2 ),the five quartic couplings can now be exchanged with the four physical scalar masses, m5 , m3 , mH and mh
and the mixing angle, α. It should be mentioned here that, h is the lightest among all the CP -even scalars
corresponding to the Higgs-like scalar discovered at the LHC with mass mh ≈ 125 GeV. Below, we present therelation between the λi -s with the physical masses and mixings [26].
λ1

=

λ2

=

λ3

=

λ4

=

λ5

2.1

=

1


m2h cos2 α + m2H sin2 α ,
√

√

1
2
2
2
6
m
sin
2α
+
12m
2v
cos
βM
,
−
m
sin
β
cos
β
−
3
1
h
H
3
12v 2 cos β sin β


√
√
1
m25 − 3m23 cos2 β + 2v cos β cot βM1 − 3 2v sin βM2 ,22v sin β√12m2H cos2 α + 2m2h sin2 α − 2m25 + 6 cos2 βm23 − 3 2v cos β cot βM1226v sin β√+9 2v sin βM2 ,
√
2m23
2M1
−
.
v2
v sin β8v 2 cos2 β

(9a)
(9b)
(9c)

(9d)
(9e)

Theoretical Constraint and Higgs data

In this section, we discuss the consequences of theoretical constraints, such as the electroweak stability and theperturbative unitarity on the GM scalar potential as well as the parameter constraints coming from the latest
Higgs data. We will thus use Eq. (9) to translate the scalar couplings in terms of the physical masses andmixings.
We first consider the theoretical constraints on the model parameter space. In Fig. 1, we show the region allowed
simultaneously by the electroweak vacuum stability and the perturbative unitarity bounds on the scalar quartic
couplings [19, 29]. For illustration purpose, we have shown the allowed region in the vt -m3 plane and in them3 -m5 plane. In doing so, we choose two different possibilities for the GM scalar potential, with and without
the trilinear couplings. For nonzero trilinear couplings, we choose M1 = M2 = 100 GeV as a benchmark. It isclearly evident from the nature of the plots that the theoretical constraints impose a lower bound on the triplet
vev vt as well as an upper bound on the mass of the custodial triplet m3 and custodial fiveplet m5 . Moreover,it also draws a correlation between m3 and m5 as can be seen from the lower panel of Fig. 1. These limits are
actually a direct consequence of the unitarity condition on the scalar quartics as has been discussed in detailin Ref [26] for the zero trilinear term scenario. In particular, the triplet is required to obtain a reasonable vev
to get a simultaneous solution of all the unitarity conditions. The limits are relaxed for non-vanishing trilinear
term as can be seen from the right panel of Fig. 1. Since, the additional contribution of the nonzero trilinear
couplings to the scalar quartic couplings, given in Eq. (9), will help to alleviate the bounds on the masses andthe vev vt . Next, one should also consider the bounds on the model parameter space placed by the updated 13
TeV LHC Higgs data [30, 31]. Here, it is to be mentioned that the the lightest among all the CP-even states(mh ) corresponds to the 125 GeV SM-like Higgs in our model scenario. Therefore, its tree-level couplings to
the SM fermions and vector bosons must be matched with the LHC data. Additionally, the charged scalarparticles coming from both the custodial multiplets of masses m3 and m5 contributes to the loop-induced Higgs
to diphoton decay mode. Therefore, the observed limit from h → γγ decay [30, 31] should also be considered
for lighter charged Higgs masses. In fact, the combined limits from Higgs decay to fermions, weak gauge bosons
together with di-photon channel severely constraint the model parameter space as shown in Fig. 2. To implement
the current limit, we define the Higgs coupling modifiers as the ratio of the theoretical model prediction to theSM value, i.e,ghii(GM ), i = f, W ± , Z, γ .
(10)
κi =
ghii(SM )4

Figure 1: Allowed regions in the vt -m3 plane (upper panel) and in the m3 -m5 plane (lower panel) from theoreticalconstraints for zero (left panel) and non-zero (right panel) trilinear couplings.
The model prediction for the coupling modifiers are well-known [26] and it depend on the mixing angles α and β
for a fixed m3 and m5 . In Fig. 2, we show the allowed region in the (sin α−vt ) plane from the latest 13 TeV LHC
Higgs result [30, 31]. The blue shaded region in the figure is allowed by all Higgs channels including the loop
induced diphoton mode. For the diphoton decay mode, we have fixed the charged scalar masses at m3 = 300 GeV
and m5 = 400 GeV. The benchmark of such mass points are followed by the maximum allowed value by thetheoretical constraints, as is evident from Fig. 1. Now, in Fig. 2, the solid(red) and dashed(black) lines further
corresponds to the equivalent theoretical limits in the (sin α − vt ) plane for two cases, vanishing trilinear terms(M1 = M2 = 0) and non-vanishing trilinear terms (M1 = M2 = 100 GeV) respectively. Obviously, the limit
is more relaxed in the later case, allowing vt as low as around 10 GeV at small sin α ∼ O(0.1). The mostimportant point in Fig. 2, is however, the region allowed by the Higgs data. It shows a clear preference towards
larger sin α at large vt allowing only sin α > 0.3 for vt & 30 GeV. This has notable consequences on the charged
Higgs decay modes as we will explain in our subsequent analysis.

3

Charged Higgs production and decay

As mentioned earlier, the GM model contains two singly charged Higsses, one from each of the custodial triplet(H3± ) and the custodial quintuplet (H5± ). However, the quintuplet component H5± does not couple to SM quarks
since it has a pure triplet origin, as can also be seen from Eq. (7a). On the other hand, the triplet candidate

5Figure 2: Model parameter space allowed in the (sin α-vt ) plane from the latest Higgs data (shaded blue) [30, 31]
for a benchmark scenario m3 (m5 ) = 300(400) GeV allowed by the theoretical constraints. The dot-dashed (red)and dashed (black) lines correspond to the bound coming from theoretical constraint for vanishing and nonvanishing trilinear term of the GM potential respectively.
H3± can mix with SM quarks through doublet mixing. Therefore, in this article, we will venture the possibilityof limiting or probing the GM model from direct searches of the triplet charged candidate, namely, H3± . To
begin with, we show the decay branching ratio of this particle for various mass regions. In Fig. 3, we depicts
the BR of (H3± ) of mass m3 for two different choices of vt = (30, 45) GeV and each for four different valuesof sin α = (0.001, 0.01, 0.1, 1.0)), represented by four different color variations. It must be mentioned that our
choice of vt relies on the parameter space available after satisfying the theoretical constraints, as described inSec. 2.1. Although, the non-zero trilinear scenario allows much lower vt , the allowed range of sin α is large forlarge vt . The BRs though has no dependence on the parameter values M1 and M2 . Therefore, in our following
analysis, we will mainly focus on vt & 30 GeV.
vt = 30 GeV

100

Colour Codesin(α) = 1 , 0.1 , 0.01, 0.001±±● : H3 → wh, ■ : H3 → tb

Br (H3±)

60

60

40

40

20

20

0
200

250

300

350

400

450

Colour Codesin(α) = 1 , 0.1 , 0.01, 0.001● : H3±→ wh, ■ : H3±→ tb

80±

Br (H3 )80

vt = 45 GeV

100

0
200

500

m3 (GeV)

250

300

350

400

450

500

m3 (GeV)Figure 3: The branching ratio of charged Higgs H3± for two different choices of the triplet vev, vt = 30 GeV(left panel) and vt = 45 GeV (right panel). The box and circular points define the two distinct decay modesof the charged scalar, H3± → tb and H3± → W h channel respectively while the four different colors (red, green,
magenta, blue) corresponds to four different orders of magnitude for sin α (1,0.1,0.01,0.001).
Let us first briefly understand the nature of Fig. 3. As one can see, H3± has two dominant decay channels,
H3+ → tb̄ and H3+ → W + h (similarly for the anti-particle), h being the 125 GeV resonance. It is clear from6

Fig. 3, that as the mass of H3 reaches 205 GeV (threshold to produce W ± h), the BR(H3± → W ± h) increases
considerably with an increase in sin α reducing the BR(H3± → tb). This turns out to be the crucial point forthe charged Higgs searches in this model. As we showed in Sec. 2.1 that the current Higgs data preferred larger
sin α for larger vt . Hence, the combined limit of theoretical constraints with the Higgs data points towards aninclination of a lighter charged Higgs mass m3 < 300 GeV and a larger mixing angle in the CP-even sector.
From this viewpoint and referring to Fig. 3, one can interpret that probing the charged Higgs candidate in thismodel would be more probable in W ± h channel instead of the quark final state.

10.1

sin(α) = 0.1

30 GeV
45 GeV
60 GeV
Observed dataσ(pp → tbH3±) * Br(H3± → t b) (pb)

±

10

±

σ(pp → tbH3 ) * Br(H3 → t b) (pb)Nevertheless, it is mandatory to validate the model parameter space first with the current limit on charged Higgs
decaying to tb final state, as reported by the ATLAS collaboration [15] with the 13 TeV data. There is a similar
analysis by CMS collaboration lately [32], however there limits for low charged Higgs mass m3 < 500 GeV are
weaker and hence we will only consider the ATLAS bound. In Fig. 4, we draw the limits on the charged Higgs
production cross sec times its BR to tb channel, as observed in experiment. The observed limit on the effective
cross section from ATLAS for a range of charged Higgs masses has been shown for three distinct triplet vev
vt = 30, 45 & 60 GeV with two different sin α ≡ (0.1, 1) values. As anticipated, even for low charged Higgs
masses m3 . 300 GeV, the null result from observed data can only exclude vt > 45 GeV for sin α = 0.1. The
limit is much relaxed for higher mixing angles.

0.01

0.001

10

30 GeV
45 GeV
60 GeV
Observed datasin(α) = 1

1

0.1

0.01

0.001
250

300

350

400

450

500

250

m3 (GeV)

300

350

400

450

500

m3 (GeV)Figure 4: The production cross-section times the branching ratio for the charged Higgs decaying to tb channel isshown for two different values of sin α, 0.1 (left panel) and 1.0 (right panel). The three colored lines, orange(dotdashed), blue(dotted) and magenta(dashed) stands for three different values of triplet vev vt = 30, 45 & 60 GeV
respectively. The solid black line corresponds to the current limit from ATLAS analysis [15].
Following the above findings, in the next section we will carry out a simple signal-to-background (cut-based)
analysis to predict the efficiency of probing the model parameter space still allowed by theoretical constraints
and the present experimental observation made for both the Higgs and the charged Higgs.

4

Analysis

In this section, we address the question that we posed in the last section, i.e. how efficiently we can probe theparameter space of GM model allowed by the experimental and theoretical bounds together. Charged Higgs
decaying into W h channel is the signal that we will be interested in. The single production of the charged Higgs
can however be made either in the 4-flavor or in the 5-flavor scheme, where the production processes will be
pp → tb̄H3+ and pp → tH3+ respectively. In our subsequent analysis, we will work in the 5-flavor scheme. In
Fig. 5, we show the production cross section times the BR for sin α = 1, 0.1. Following our previous line ofargument, a direct comparison between Fig. 4 and Fig. 5 shows that for larger sin α, the W h decay mode forthe charged higgs imparts larger effective cross-section. Hence, we may expect to discover or restrict the model7

σ(pp → tH3±)* Br(H3± → W± h)(pb)±±

σ(pp → tH3 )* Br(H3 → W h)(pb)

1

±

0.1
sin(α) = 0.1
30 GeV
45 GeV
60 GeV

0.01

1

0.1
sin(α) = 1
30 GeV
45 GeV
60 GeV

0.01
250

300

350

400

450

500

250

300

m3 (GeV)

350

400

450

500

m3 (GeV)Figure 5: The production cross section times branching ratio plot for charged Higgs decaying to W ± h channel
for two values of sin α = 0.1 (left panel) and sin α = 1.0 (right panel). The color coding is same as in Fig. 4.
sin α
BP1
BP2

0.6
0.5

vt
(in GeV)35
45

m3(in GeV)
250
300

m5
(in GeV)
300
350

σprod
(in fb)
14.80
18.53

Table 1: Benchmark points valid by all constraints and the corresponding production cross-section of our signal.
in its full parameter region with larger efficiency in the future run of the LHC probing the specified channel.
In the following, we will give a simple cut-based analysis to give a prediction of probing the GM model at the
future LHC run from the charged Higgs searches through W h final state. Therefore, we consider the following
signal channel:
pp → tH3− → bW + W − h → 3b + 2` + E/T(11)

where, we assume that the two W bosons decays leptonically and the Higgs decay yields two b-tagged jets.
Thus as a final state we look for 3 b-tagged jets, two opposite signed leptons and missing transverse energy.
The irreducible SM background contribution will come from tt̄j with at least one extra hard jet, tt̄h andtt̄V, V = W ± , Z processes. It should be noted here that the tt̄ plus jets background has the largest cross section
among all and in turn it is the most dominant background in this analysis. Below we present our cut-based
analysis for the signal-to-background event ratio computation. For our analysis, we choose two benchmark
points in consistent with all the above limits, and the relevant parameter values are shown in Table. 1. In
passing, we would like to mention that our benchmark value for m5 is consistent with the latest bound fromATLAS collaboration [33] where a doubly-charged Higgs mass between 200 and 220 GeV is excluded at 95%
CL from same-sign W boson signal.
The model has been implemented in FeynRules [34] to obtain the UFO model files required for event generation in madgraph. We generate both the signal and SM backgrounds events at the Leading Order (LO) in
Madgraph5(v2.3.3) [35] using the NNPDF3.0 parton distributions [36]. The parton showering and hadronisation is done using the built-in Pythia [37] in the madgraph. The showered events are then passed throughDelphes(v3) [38] for the detector simulation where the jets are constructed using the anti-KT jet algorithmwith minimum jet formation radius ∆R = 0.4. The isolated leptons are considered to be separated from the jets
and other leptons by ∆R`i & 0.4, i = j, `. For the background processes with hard jets, proper MLM matching
scheme [39] has been chosen.
To generate our signal and background events, we employ the following pre-selection cuts.
pT (j, b) >30 GeV ;|η(j)| < 4.7 ;8|η(b)| < 2.5 ,pT (`) >10 GeV ,|η(`)| < 2.5 .

(12)The b-jets are tagged with the pT -dependent b-tag efficiency following the medium criteria of Ref. [40] which
has an average 75% tagging efficiency of the b-jets with 50 GeV < pT < 200 GeV and 1% mis-tagging efficiency
for light jets.
Additionally, we propose the following selection cuts to dis-entangle the signal from the SM backgrounds thatwould enhance the signal significance.
• Selecting jets and leptons:To affirm that our signal has 3 b jets, we select 3 b jets with pT (b) > 30
GeV while rejecting any fourth b jet with pT > 35 GeV. In addition to this, we demand two opposite sign
leptons with pT (`) > 10 GeV.
• Selecting E/T : Both for signal and backgrounds, the missing energy(E/T ) comes from the decay of W ±boson. From the left panel of Fig. 6, one can see that the distributions for signal and backgrounds are
peaking around similar E/T value. However, the SM background has a large tail of the distribution. We,
thus, impose an upper bound of E/T < 175 GeV as an optimum cut to enhance the signal over backgroundratio.
• Higgs mass reconstruction: In our signal, two b-tagged jets among the three are produced by the decayof the Higgs. Therefore, the invariant mass of the two b-jets are expected to peak around 125 GeV. On theother hand, only the tt̄h can yield similar peak structure for the Mbb̄ . The right panel of Fig. 6 depicts thenature of Mbb̄ distribution for both the signal and background. It is to be mentioned that the pair of b-jets
is selected after rejecting any third b-jet that has the minimum azimuthal angle φ. This follows from theargument that the third b-jet is a remnant of direct top decay in our signal and therefore expected to lie
closer to the beam direction than the other two. Following Fig. 6, we select 100 GeV < Mbb̄ < 150 GeV
for significant background reduction. This cut turns out to be the most effective to reduce the large tt̄jbackground events.

0.10

0.12

SignalSignalSM Background

0.08

SM Background

1/N dN/dMbb (GeV-1)

1/N dN/dET (GeV-1)

0.10

0.08

0.06

0.04

0.06

0.04

0.02

0.02

0.00

0.00

50

100 150 200 250 300 350 400 450 500

50

100 150 200 250 300 350 400 450 500

ET (GeV)Mbb (GeV)

(a)

(b)

Figure 6: Normalized distribution of the (left panel) Missing transverse energy (E/T ) and (right panel) theinvariant mass of bb̄ pair after the basic kinematical acceptance cuts(Eq. 12) for the benchmark BP1.
The cut-flow is presented in Table. 2 for our two chosen benchmarks (BP1, BP2) of Table. 1. The signal
Ssignificance is defined as S = √S+B
, S and B being the number of signal and background events after all thecuts respectively. As is evident from Table. 2, one can reach more than 5σ significance at the High Luminosity
run of LHC (HL-LHC) with 3000 f b−1 luminosity and more than 3σ significance with only 1000 f b−1 in thespecified parameter space of this model with this particular signal channel.
9Effective cross-section after the cut(fb)SM-backgroundtt̄+jettt̄htt̄W ±
tt̄Z
Total SM BackgroundMH ± = 250 GeV
3MH ± = 300 GeV
3Preselection cuts
124.41
1.05
0.21
0.84
126.51
1.49
1.87

E/T cut
119.52
0.97
0.19
0.79
121.491.42
1.78

Invmass cut
27.17
0.32
0.049
0.21
27.75
0.52
0.65

Significancereach at3(1) ab−1
integrated
luminosity
at 14 TeV
LHC–
5.37 (3.10)
6.68 (3.86)

Table 2: No. of events obtained after each cut for both signal (`+ `− + 3b + E/T ) and background and thesignificance obtained for 3(1) ab−1 integrated luminosity at 14 TeV LHC.

5

Results

Let us now present our findings in a comprehensive manner. In Fig. 7, we show our complete results spannedin the model parameters {sin α − vt } plane for two particular choices of m3 and m5 masses corresponding toour benchmark points in Table 1. The region allowed by the latest LHC Higgs data [30, 31] and the bounds
from the theoretical constraints for the two distinct cases of trilinear terms follows the same color combinations
as in Fig. 2. On top of it, we show the bounds imposed by the ATLAS analysis for 13 TeV data on charged
Higgs searches in tb channel [15] which is shown by the gray shaded region bounded by the solid black line. As
can be seen from the Fig. 2, this bound can only restrict a small parameter space in association with the Higgs
data. Quantitatively, for charged Higgs masses around 250 GeV, vt > 50 GeV can only be discarded. For such
vt , the bound on sin α though comes solely from the Higgs data. As already mentioned, for smaller vt , Higgs
data only allows large sin α which can only be probed by the other significant decay mode of the charged scalar
to W h channel. Hence, we present the 3σ and 5σ discovery reach at the HL-LHC with 3 ab−1 luminosity fromour proposed signal channel for charged Higgs decaying to W ± h mode, depicted as solid (orange) and dashed(green) lines respectively. The areas above those lines shaded in Orange and Green describe the parameter
space that can be probed at the future HL-LHC with more than 3σ and 5σ signal significance respectively. To
illustrate further, one can see that a 5σ discovery is possible for vt & 31(35) GeV for m3 =250(300) GeV. In anutshell, Fig. 7 shows the complete allowed parameter space of GM model from theoretical constraints, latest
LHC Higgs data and charged Higgs searches altogether, while simultaneously showing the future reach of charge
Higgs searches for the unbounded parameter space.

6

Summary

To summarise, we consider the GM model as a preferred variant of scalar triplet extension of the SM that
preserves the custodial symmetry allowing for a larger triplet vev unlike the usual HTMs. Such large triplet vev
leads to interesting search prospects for the singly charged scalar of the model that can decay to SM fermion
with large coupling. The latest LHC search result on charged Higgs decaying to tb channel thus impose an upperbound on the triplet vev. On the other hand, the theoretical constraints on the model parameter restricts thetriplet vev from the lower end and can be as strong as 30 GeV for vanishing triliinear term of the GM potential.
Moreover, the theoretical constraints entails an upper bound on the triplet and quintuplet masses which puts
significant upper bound on the singly and doubly charged Higgs mass. Additionally, the non-standard triplet
scalars mixing will modify the SM-like Higgs coupling to the SM fermions and gauge bosons. Therefore, it ismandatory to match the model prediction for the SM-like Higgs coupling with the latest LHC Higgs data. In
the first part of this paper, we show the complete limit on the model parameter space from both the theoreticalconstraints as well as the 13 TeV LHC Higgs results. We show that these two constraints together put astringent bound on the model parameter space in neutral mixing angle sin α and triplet vev vt plane. As shown,a large positive sin α & 0.1(0.3) with vt > 10(30) GeV is preferred by these bounds for the two distinct casesof vanishing and non-vanishing trilinear terms. In the second part of our paper, we intended to combine these10Figure 7: The combined results on the model parameter space in the (sin α − vt ) plane for charged Higgs masses
m3 = 250 GeV (left panel) and m3 = 300 GeV (right panel). The color coding for Higgs data and theoreticalconstraint is same as in Fig. 2. The gray shaded region with black solid boundary corresponds to the current
ATLAS limit from charged Higgs analysis. The Green(dashed) and Orange(Solid) lines are respectively the 5σ
and 3σ signal significance reach at 14 TeV LHC with 3 ab−1 luminosity in the charged Higgs decaying to W hmode.
limits with the latest bound from LHC on the charged scalar searches to tb channel. We show that this limit
excludes vt > 50 GeV for sin α . 0.4 for a 250 GeV charged Higgs in the region allowed by the theoreticalconstraints and the Higgs data. We also described that for a larger sin α, the singly charged Higgs predominantly
decays to W h channel. Therefore, we showed a simple cut-based signal-to-background analysis for the singly
charged Higgs decaying to W h mode. Our analysis revealed that this search channel can probe the unboundedregion of the model parameter by all the above-mentioned constraints at 5σ signal significance at the futurehigh luminosity run of the LHC.

Acknowledgements
IS would like to thank Michihisa Takeuchi and Satoshi Shirai for useful discussions. The work of IS was
supported by World Premier International Research Center Initiative (WPI), MEXT, Japan. NG would liketo acknowledge the Council of Scientific and Industrial Research (CSIR), Government of India for financial
support.

References[1] ATLAS collaboration, G. Aad et al., Observation of a new particle in the search for the Standard Model
Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B716 (2012) 1–29, [1207.7214].
[2] CMS collaboration, S. Chatrchyan et al., Observation of a New Boson at a Mass of 125 GeV with the
CMS Experiment at the LHC, Phys. Lett. B716 (2012) 30–61, [1207.7235].
[3] K. Cheung and D. K. Ghosh, Triplet Higgs boson at hadron colliders, JHEP 11 (2002) 048,
[hep-ph/0208254].
[4] G. Bhattacharyya and D. Das, Nondecoupling of charged scalars in Higgs decay to two photons andsymmetries of the scalar potential, Phys. Rev. D91 (2015) 015005, [1408.6133].
11

[5] Z.-L. Han, R. Ding and Y. Liao, LHC Phenomenology of Type II Seesaw: Nondegenerate Case, Phys. Rev.
D91 (2015) 093006, [1502.05242].
[6] M. Mitra, S. Niyogi and M. Spannowsky, Type-II Seesaw Model and Multilepton Signatures at Hadron
Colliders, Phys. Rev. D95 (2017) 035042, [1611.09594].
[7] A. Arbey, F. Mahmoudi, O. Stal and T. Stefaniak, Status of the Charged Higgs Boson in Two Higgs
Doublet Models, Eur. Phys. J. C78 (2018) 182, [1706.07414].
[8] J.-Y. Cen, J.-H. Chen, X.-G. He, G. Li, J.-Y. Su and W. Wang, Searching for a charged Higgs boson withboth H ± W ∓ Z and H ± tb couplings at the LHC, JHEP 01 (2019) 148, [1811.00910].
[9] M. Guchait and A. H. Vijay, Probing Heavy Charged Higgs Boson at the LHC, Phys. Rev. D98 (2018)
115028, [1806.01317].
[10] D. K. Ghosh, N. Ghosh, I. Saha and A. Shaw, Revisiting the high-scale validity of the type II seesaw
model with novel LHC signature, Phys. Rev. D97 (2018) 115022, [1711.06062].
[11] D. Kumar Ghosh, N. Ghosh and B. Mukhopadhyaya, Distinctive Collider Signals for a Two Higgs Triplet
Model, Phys. Rev. D99 (2019) 015036, [1808.01775].
[12] H. Georgi and M. Machacek, DOUBLY CHARGED HIGGS BOSONS, Nucl. Phys. B262 (1985) 463–477.
[13] M. S. Chanowitz and M. Golden, Higgs Boson Triplets With M (W ) = M (Z) cos θω, Phys. Lett. 165B
(1985) 105–108.
[14] J. F. Gunion, R. Vega and J. Wudka, Higgs triplets in the standard model, Phys. Rev. D42 (1990)
1673–1691.
[15] ATLAS collaboration,
M. Aaboud et al., Search for charged Higgs bosons decaying into top and bottom√
quarks at s = 13 TeV with the ATLAS detector, JHEP 11 (2018) 085, [1808.03599].
[16] S. Kanemura and K. Yagyu, Radiative corrections to electroweak parameters in the Higgs triplet modeland implication with the recent Higgs boson searches, Phys. Rev. D85 (2012) 115009, [1201.6287].
[17] C.-W. Chiang and K. Yagyu, Testing the custodial symmetry in the Higgs sector of the Georgi-Machacekmodel, JHEP 01 (2013) 026, [1211.2658].
[18] K. Hartling, K. Kumar and H. E. Logan, Indirect constraints on the Georgi-Machacek model andimplications for Higgs boson couplings, Phys. Rev. D91 (2015) 015013, [1410.5538].
[19] K. Hartling, K. Kumar and H. E. Logan, The decoupling limit in the Georgi-Machacek model, Phys. Rev.
D90 (2014) 015007, [1404.2640].
[20] C.-W. Chiang, S. Kanemura and K. Yagyu, Novel constraint on the parameter space of the
Georgi-Machacek model with current LHC data, Phys. Rev. D90 (2014) 115025, [1407.5053].
[21] C.-W. Chiang, A.-L. Kuo and T. Yamada, Searches of exotic Higgs bosons in general mass spectra of the
Georgi-Machacek model at the LHC, JHEP 01 (2016) 120, [1511.00865].
[22] J. Chang, C.-R. Chen and C.-W. Chiang, Higgs boson pair productions in the Georgi-Machacek model atthe LHC, JHEP 03 (2017) 137, [1701.06291].
[23] C. Degrande, K. Hartling and H. E. Logan, Scalar decays to γγ, Zγ, and W γ in the Georgi-Machacekmodel, Phys. Rev. D96 (2017) 075013, [1708.08753].
[24] S. Blasi, S. De Curtis and K. Yagyu, Effects of custodial symmetry breaking in the Georgi-Machacekmodel at high energies, Phys. Rev. D96 (2017) 015001, [1704.08512].
[25] A. Biswas, D. K. Ghosh, S. K. Patra and A. Shaw, b → c`ν anomalies in light of extended scalar sectors,
Int. J. Mod. Phys. A34 (2019) 1950112, [1801.03375].
12

[26] D. Das and I. Saha, Cornering variants of the Georgi-Machacek model using Higgs precision data, Phys.
Rev. D98 (2018) 095010, [1811.00979].
[27] C.-W. Chiang, G. Cottin and O. Eberhardt, Global fits in the Georgi-Machacek model, Phys. Rev. D99(2019) 015001, [1807.10660].
[28] A. Banerjee, G. Bhattacharyya and N. Kumar, Impact of Yukawa-like dimension-five operators on the
Georgi-Machacek model, Phys. Rev. D99 (2019) 035028, [1901.01725].
[29] M. Aoki and S. Kanemura, Unitarity bounds in the Higgs model including triplet fields with custodial
symmetry, Phys. Rev. D77 (2008) 095009, [0712.4053].
√[30] C. Collaboration, Combined measurements of the Higgs boson’s couplings at s = 13
TeV,CMS-PAS-HIG-17-031, .
[31] T. A. collaboration, Combined measurementsof Higgs boson production and decay using up to 80 fb−1 of√proton–proton collision data at s = 13 TeV collected with the ATLAS
experiment,ATLAS-CONF-2018-031, .
[32] C. Collaboration, Search for charged Higgs bosons decaying into top and a bottom quark in the fully
hadronic final state at 13 TeV,CMS-PAS-HIG-18-015, .
[33] ATLAS collaboration, M. Aaboud et al., Search for doubly charged scalar bosons decaying into same-sign
W boson pairs with the ATLAS detector, Eur. Phys. J. C79 (2019) 58, [1808.01899].
[34] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0 - A complete toolbox fortree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250–2300, [1310.1921].
[35] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer et al., The automatedcomputation of tree-level and next-to-leading order differential cross sections, and their matching toparton shower simulations, JHEP 07 (2014) 079, [1405.0301].
[36] NNPDF collaboration, R. D. Ball et al., Parton distributions for the LHC Run II, JHEP 04 (2015) 040,
[1410.8849].
[37] T. Sjostrand, S. Mrenna and P. Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026,
[hep-ph/0603175].
[38] DELPHES 3 collaboration, J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaı̂tre,
A. Mertens et al., DELPHES 3, A modular framework for fast simulation of a generic collider
experiment, JHEP 02 (2014) 057, [1307.6346].
[39] S. Hoeche, F. Krauss, N. Lavesson, L. Lonnblad, M. Mangano, A. Schalicke et al., Matching parton
showers and matrix elements, in HERA and the LHC: A Workshop on the implications of HERA for
LHC physics: Proceedings Part A, pp. 288–289, 2005. hep-ph/0602031. DOI.
[40] CMS collaboration, A. M. Sirunyan et al., Identification of heavy-flavour jets with the CMS detector inpp collisions at 13 TeV, JINST 13 (2018) P05011, [1712.07158].

13