Full text

Turn on search term navigation

Published for SISSA by Springer

Received: November 15, 2012

Accepted: December 8, 2012

Published: January 3, 2013

Cheng-Wei Chianga,b,c and Kei Yagyua

aDepartment of Physics and Center for Mathematics and Theoretical Physics, National Central University, Chungli, Taiwan 32001, ROC

bInstitute of Physics, Academia Sinica,

Taipei, Taiwan 11529, ROC

cPhysics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan 30013, ROC

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

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 parameter at unity at tree level. In the GM model, there are 5-plet (H5), 3-plet (H3) and singlet (H1) Higgs bosons under the classication 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) H5 and H1 couple to the electroweak gauge bosons but not SM quarks, whereas H3 couples to the quarks but not the gauge bosons. We nd that the H5 production from the weak vector boson fusion process and the Drell-Yan process associated with H3 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 as well as h Z decays.

Keywords: Phenomenological Models

ArXiv ePrint: 1211.2658

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

JHEP01(2013)026

SISSA 2013 doi:http://dx.doi.org/10.1007/JHEP01(2013)026

Web End =10.1007/JHEP01(2013)026

Contents

1 Introduction 1

2 The model 3

3 Constraints 93.1 Perturbative unitarity and vacuum stability bounds 93.2 Zbb data 11

4 Higgs decays 11

5 Phenomenology at the LHC 195.1 Production modes 205.2 Signal and background analysis 22

6 Higgs to and Z decays 27

7 Conclusions 28

A Relationships among di erent representations of the Higgs elds 31

B Coupling constants between the triplet-like Higgs bosons and the weak gauge bosons 31

C Loop functions in the h ! and Z decay rates 32

1 Introduction

Recently, a new particle of mass about 125 GeV has been discovered at the CERN Large Hadron Collider (LHC) with a total production rate consistent with that of the standard model (SM) Higgs boson [1, 2]. Conrming this Higgs-like particle as the one responsible for the electroweak symmetry breaking is of paramount importance in particle physics because, for one thing, it explains the origin of mass for elementary particles. While further detailed examinations are required, the current LHC data show some deviations in the pattern of its decay branching ratios from the SM expectation. This leads to the speculation that the Higgs sector may not as simple as the one in SM.

In certain new physics models such as supersymmetry, the Higgs sector has to be extended with additional nontrivial isospin SU(2)L scalar multiplets for consistency or to explain new phenomena. Such an extension also holds the capacity to provide additional CP-violating sources for low-energy phenomena as well as baryon asymmetry of the Universe. For example, the two-Higgs doublet model (2HDM) [3] is an extensively studied

JHEP01(2013)026

prototype in which an additional scalar doublet is introduced. SU(2)L triplet Higgs elds also occur in some new physics models, such as the left-right symmetric model [46] and little Higgs models [7, 8]. By introducing a complex triplet Higgs eld, it is possible to have an e ective dimension-5 operator for generating tiny Majorana mass for neutrinos. Therefore, it is important to determine the true Higgs sector in order to exactly know what kind of new physics models exist at the TeV or higher energy scales. In this paper, we want to focus on the phenomenology of the extended Higgs sector in the model proposed by Georgi and Machacek (GM) [9] in mid-80s. We investigate how one can distinguish it from the other Higgs-extended models at the LHC.

The GM model contains a Higgs doublet eld and a triplet eld , with the latter containing a hypercharge Y = 1 component and a Y = 0 component. The model is of great interest because it can provide tiny mass to neutrinos la the Seesaw Mechanism, dubbed the Type-II Seesaw [1014]. Moreover, it has been shown that the Higgs potential in this model can be constructed to maintain a custodial SU(2)V symmetry at the tree level [15], keeping the electroweak parameter at unity to be consistent with the experimental constraint. In the model, there are 5-plet Higgs bosons H5 (=H5, H5, H05), 3-plet Higgs bosons H3 (=H3, H03) and singlet Higgs boson H01 under the classication of the SU(2)V symmetry. The masses of the Higgs bosons belonging to the same SU(2)V multiplet are the same at the tree level as the consequence of custodial symmetry.

The doubly-charged Higgs boson H5, for example, is an important but not unique feature of the model. Finding particles in one Higgs multiplet and checking their (near)

mass degeneracy would better verify the model. Strategies of discovering such Higgs bosons, however, depend largely on the vacuum expectation value (VEV) of the Higgs triplet eld, v .

In the minimal Higgs triplet model (HTM) where only one additional complex Higgs triplet is introduced, the doubly-charged Higgs bosons couples dominantly to a pair of like-sign leptons when v [lessorsimilar] 104 GeV. The collider phenomenology of this scenario has been extensively studied recently [1621]. The doubly-charged Higgs boson has been searched for at the Tevatron [2225] and the LHC [26, 27] by looking for like-sign lepton pairs with the same or di erent avors. A lower mass bound of about 400 GeV has been obtained for most scenarios. On the other hand, the doubly-charged Higgs bosons couples dominantly to a pair of like-sign W bosons when v [greaterorsimilar] 104 GeV.1 This possibility is less explored experimentally. Besides, the triplet VEV in the HTM is constrained by the parameter to be less than a few GeV, limiting signicantly the discovery reach at the LHC.

In the GM model, a larger triplet VEV is allowed due to the custodial symmetry. It is therefore interesting to consider signatures of the like-sign gauge boson decays. In ref. [28], collider phenomenology of the GM model has been discussed in the case of light triplet-like Higgs bosons, e.g., less than 100 GeV. A recent study by one of the authors and collaborators [29] nds that with v = 55 GeV and appropriate cuts, the current LHC can reach up to 450 GeV for the doubly-charged Higgs mass. In this work, we further explore

1When there is a non-zero mass splitting among the scalar bosons in the triplet Higgs eld and the doubly-charged Higgs boson mass is the heaviest, the cascade decays of the doubly-charged Higgs boson become dominant. Phenomenology of this scenario has been discussed in refs. [3032].

JHEP01(2013)026

consequences of the custodial symmetry in the Higgs sector of the GM model and study the phenomenology of its entire Higgs sector at the LHC. We nd that the single production of H5 via the weak vector boson fusion process is useful to test the mass degeneracy among the

H5 bosons. We also nd that the Drell-Yan process, where H5 and H3 are simultaneously produced can be used to check the mass degeneracy among H3.

The structure of this paper is organized as follows. We review the GM model in section 2. The Higgs bosons are rst classied according to their group representations under the custodial symmetry. We then consider possible mixings between the two triplets and between the two singlets, and work out their masses. A mass relation among the Higgs bosons of di erent representations is obtained in the decoupling limit when the triplet VEV vanishes. Finally, we show the Yukawa couplings between SM fermions and the physical Higgs bosons. In section 3, we consider both theoretical constraints of perturbative unitarity and vacuum stability and the experimental constraint from the Z-pole data of Z b

b decay at one-loop level. In particular, they impose bounds on the triplet VEV and the Higgs triplet mass. In section 4, we discuss in detail how the Higgs bosons decay in scenarios with or without hierarchy in the masses of the physical Higgs singlet, 3-plet, and 5-plet. The collider phenomenology of the model can be drastically di erent in di erent regions of the v - m ( m is the mass di erence between H5 and H3) space. section 5 discusses how the Higgs bosons can be searched for at the LHC. Finally, we compute the decay rates of h and Z in the model in section 6. Our ndings are summarized in

section 7.

2 The model

In the GM model, the Higgs sector is composed of the SM isospin doublet Higgs eld with hypercharge Y = 1/2 and two isospin triplet Higgs elds with Y = 1 and with Y = 0. These elds can be expressed in the form:

= 0 + 0

12(r + ii) + v, 0 = r + v, (2.2)

where v, v and v are the VEVs for 0, 0 and 0, respectively. When the two triplet VEVs v and v are taken to be the same, i.e., v = v v , the SU(2)L SU(2)R

symmetry is reduced to the custodial SU(2)V symmetry. The phase convention for the component scalar elds are chosen to be = (++), = (+), = (+), = (+) and 0 = (0).

JHEP01(2013)026

!, =

0 + ++

0 +

, (2.1)

where and are transformed under SU(2)L SU(2)R as UL UR and UL UR

with UL,R = exp(iaL,RT a) and T a being the SU(2) generators. The neutral components in eq. (2.1) can be parametrized as

0 = 1

2(r + v + ii), 0 =

The relevant Lagrangian involving the Higgs elds can be written as

LGM = Lkin + LY + L VH, (2.3)

where Lkin, LY , L and VH are the kinetic term, the Yukawa interaction between and the fermions, the neutrino Yukawa interaction between and the lepton doublets, and the

Higgs potential, respectively.The most general Higgs potential invariant under the SU(2)L SU(2)R U(1)Y sym

metry in terms of the elds dened in eq. (2.1) is

VH = m21tr( ) + m22tr( ) + 1tr( )2 + 2[tr( )]2 + 3tr[( )2]

+ 4tr( )tr( ) + 5tr

a2 b 2

JHEP01(2013)026

tr( ta tb)

ta tb (P P )ab, (2.4)

where a are the Pauli matrices, ta are the 3 3 matrix representation of the SU(2)

generators given by

t1 = 12

0 1 0 1 0 1 0 1 0

+ 1tr

a2 b 2

(P P )ab + 2tr

, t2 = 1

0 i 0

i 0 i

0 i 0

, t3 =

1 0 0 0 0 0 0 0 1

, (2.5)

and the matrix P is dened as

P =

1/2 i/2 0 0 0 1

1/2 i/2 0

. (2.6)

As in the HTM, the SM electroweak symmetry breaking can induce the triplet eld to develop a VEV v through the 1 term in the Higgs potential. To our knowledge, most of the previous analyses ignore both 1 and 2 interactions in their phenomenology studies. We will keep these terms in this work.

Using the tadpole conditions,

= 0, VH

= 0, (2.7)

the parameters m21 and m22 can be eliminated as

m21 = v2

2c2H1 + 3

8s2H4 +

3 16s2H5

+ 3

8s2HM21, (2.8a)

m22 = v2

4s2H2 +

14s2H3 + c2H4 +

2c2H5

+ 1

2c2HM21 +

14M22, (2.8b)

where v2 = v2 + 8v2 = 1/(2GF ) and tan H = 22v /v with sH = sin H and cH = cos H. In eq. (2.8), we introduce M21 and M22 as

M21 =

v2sH 1, M22 = 3

2sH v2. (2.9)

The second and third conditions in eq. (2.7) give the same constraint in eq. (2.8b) as long as v = v.

Before we discuss the mass matrices and the mass eigenstates for the Higgs bosons, it is convenient to classify the Higgs boson states according to the custodial SU(2)V symmetry.

The triplet eld , which can be understood as a 3 3 representation of the SU(2)V

multiplet, can be decomposed into the irreducible representations 5 3 1. Likewise, the

doublet eld being the 2 2 representation of the SU(2)V multiplet, can be decomposed

into 3 1. The 3 representation of can be identied as the Nambu-Goldstone (NG)

bosons of the SM as long as there is no mixing between the 3 representations of and . The 5-plet (H5, H5 and H05), the 3-plet (3 and03) and the singlet (01) originating from can be related to the original component elds as

H5 = , H5 = 1

2( ), H05 =

1 3(r

JHEP01(2013)026

2r),

3 = 1

2( + ),

03 = i,

2r). (2.10)

It is seen that H05 and1 are CP-even states, whereas03 is a CP-odd state. In eq. (2.10), the scalar elds with a tilde are not mass eigenstates in general. They can in principle mix with the corresponding scalar elds from the Higgs doublet eld.

The mass of the doubly-charged Higgs boson H5 is

m2H++

01 = 1

3(r +

5 = s2H3 32c2H5 v2 + c2HM21 + M22. (2.11)

The mass matrix for the CP-odd Higgs states in the basis of (i,03) and that for the singly-charged states in the basis of (+,+3, H+5) are given by

(M2)CP-odd =

25v2 M21

(M2)CP-odd

s2H cHsH

cHsH c2H

!, (M2) =

0 0 m2H++

The mass matrix for the CP-even Higgs states in the basis of (r,01,05) is

(M2)CP-even =

(M2)11 (M2)12 0

(M2)12 (M2)22 0

0 0 m2H++

where the elements of the 2 2 submatrix are

(M2)11 = 8c2H1v2, (2.12a)

(M2)22 = s2H(32 + 3)v2 + c2HM21

2M22, (2.12b)

(M2)12 =

(24 + 5)v2 M21 . (2.12c)

r3 2sHcH

The mass eigenstates are related to the above-mentioned states via the following unitary transformations

i 03

= UCP-odd G0 H03

3 H5

= U

r 01 H05

= UCP-even

h H01

H05

(2.13)

where G and G0 are the NG bosons for the longitudinal components of the W and Z bosons. The explicit forms of the unitary matrices are

UCP-odd = cH sH sH cH

!, U =

JHEP01(2013)026

UCP-odd

0 0 1

, UCP-even =

c s 0 s c 0

0 0 1

, (2.14)

where c = cos , s = sin and the mixing angle is dened by

tan 2 = 2(M2)12

(M2)11 (M2)22

. (2.15)

The masses of the singly-charged Higgs bosons (H5 and H3), the CP-odd Higgs boson (H03) and the CP-even Higgs bosons (H05, H01 and h) are then

m2H+

= m2H0

= m2H++

, m2H+

= m2H0

25v2 + M21,

m2h = (M2)11c2 + (M2)22s2 + 2(M2)12sc,

m2H0

1 = (M2)11s2 + (M2)22c2 2(M2)12sc. (2.16)

It is observed that H5, H5 and H05 are degenerate in mass and so are H3 and H03 because of the custodial invariance in the Higgs potential. Therefore, the Higgs boson masses can be conveniently written as

m2H5 m2H++5 = m2H+5 = m2H05 , m2H3 m2H+3 = m2H03 , m2H1 m2H01 . (2.17)

The ve dimensionless couplings in the potential, 1, . . . , 5, can be substituted by the ve physical parameters mH5, mH3, mH1, mh and as follows:

1 = 1

8v2c2H

(m2hc2 + m2H1s2),

2 = 1

6v2s2H

2m2H1c2 + 2m2hs2 + 3M22 2m2H5 + 6c2H(m2H3 M21) ,

3 = 1 v2s2H

c2H(2M21 3m2H3) + m2H5 M22

"62 s2(m2h m2H1) + 3sHcH(2m2H3 M21)#,

5 = 2v2 (M21 m2H3). (2.18)

4 = 1

6v2sHcH

The decoupling limit of this model can be obtained when we take the v 0 limit (or

equivalently sH 0). In this limit, the mass formulae of the Higgs bosons reduce to

m2H5 =

325v2 + M21 + M22, m2H3 =

25v2 + M21, m2H1 = M21

2M22, m2h = 81v2.

(2.19)

Notice that M22 is proportional to sH2, and thus it becomes zero in this limit for a xed value of 2. If one wants to x M22 at a nite value, 2 has to be taken to innity to compensate sH 0 and eventually violates perturbativity in this model. Therefore,

M22 = 0 is the natural choice in this limit. On the other hand, M21 is proportional to 1/sH. Even in the sH 0 limit, we can take a nite value for M21 as long as 1 0 at the same

rate as sH. Consequently, the triplet-like Higgs bosons decouple when M21 v2, and only

h remains at the electroweak scale and acts like the SM Higgs boson. In addition, in the decoupling region v 0, we nd a simple mass relation for the triplet-like Higgs bosons: m2H1 = 3

2m2H3

2m2H5. (2.20)

For the convenience in discussing interactions between leptons and the Higgs triplet eld, we reorganize the Higgs elds as follows:

= +

!, =+2 ++ 0 +

!, =02 + 0

JHEP01(2013)026

!. (2.21)

The relationship between the two representations in eqs. (2.1) and (2.21) are given in appendix A. With the introduction of the eld above, the Yukawa interactions between the lepton doublets and the Higgs triplet are

L = hijLicLi2LjL + h.c. (2.22)

If we assign two units of lepton number to , then the 5 and 1 terms in the Higgs potential violate the lepton number. If we then take 5 = 1 = 0, H03 becomes massless and corresponds to the NG boson for the spontaneous breakdown of the global U(1) lepton number symmetry. In fact, H3 are also massless in that case because of the custodial symmetry.

The Majorana mass of neutrinos is derived as

(m)ij = hijv = hij

22vsH. (2.23)

This mass matrix can be diagonalized by the Pontecorvo-Maki-Nakagawa-Sakata matrix VPMNS, and the Yukawa matrix hij can be rewritten as

hij = 22V TPMNSmdiagVPMNSvsH . (2.24)

The left-handed neutrino elds are then transformed as

L = V PMNSL. (2.25)

For simplicity, we hereafter assume that VPMNS is the unit matrix and the mass eigenvalues

of mdiag are degenerate: mdiag = diag(m, m, m). In terms of the scalar mass eigenstates, the interaction terms are

L = 22m

22m

sHv H+5 + cHH+3 + sHG+

sHv H++5eciPLei

ciPLei

+ 2m

sHv

1 3(H05 +

2sh + cH01) + i(G0sH + H03cH)

ciPLi + h.c. (2.26)

The Yukawa interaction between the fermions of one generation and the Higgs doublet is given by

LY = YuQL

uR YdQLdR YeLLeR + h.c., (2.27)

with ~

= i2. In terms of the fermion masses mf = vcH

2 Yf and the physical Higgs states,

the interaction terms are expressed as

LY =

JHEP01(2013)026

Xf=u,d,emf v

c cH

ffh

s cH

ffH01 + iSign(f) tan H f5fH03

tan H(muPL mdPR)dH+3 + 2mev tan H PReH+3 + h.c., (2.28)

where Vud is one element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, Sign(f = u) = +1 and Sign(f = d, e) = 1.

Finally, we discuss the kinetic terms for the Higgs elds

Lkin = 1 2tr(D )(D ) +

2tr(D )(D ), (2.29)

where the covariant derivatives are

D = + ig a

2 W a igB

2Vud

2 , (2.30)

D = + igtaW a igB t3. (2.31)

The masses of the gauge bosons are obtained under the condition of v = v v as

m2W = g2

4 v2, m2Z =

g24 cos2 W v2. (2.32)

Thus, the electroweak rho parameter = m2W /(m2Z cos2 W ) is unity at the tree level. One-loop corrections to have been calculated in ref. [33] for the GM model. The deviation of

from unity depends on the logarithm of the triplet-like Higgs boson masses and, therefore, the one-loop e ect is not important in this model.

The Gauge-Gauge-Scalar (Gauge-Scalar-Scalar) vertices are listed in table 3 (table 4) in appendix B. We note that there is the H5W Z vertex at the tree level in the GM model (see table 3). In the Higgs-extended models with = 1 at the tree level and having singly-charged Higgs bosons (e.g., the 2HDM), the HW Z vertex is absent at the tree level [34] and can only be induced at loop levels. Therefore, the magnitude of this vertex in such models is much smaller than that in the GM model. Thus, this vertex can be used to discriminate models with singly-charged Higgs bosons. The possibility of measuring the HW Z vertex has been discussed in ref. [35] for the LEPII, in ref. [36] for the Tevatron in refs. [3740] for the LHC and in ref. [41] for future linear colliders.

3 Constraints

In this section, we discuss constraints on the parameter space of the GM model. First, we consider the theoretical constraints from perturbative unitarity and vacuum stability. Secondly, as experimental constraints, we consider the Zbb data and other B physics data.

3.1 Perturbative unitarity and vacuum stability bounds

The perturbative unitarity bound for the GM model has been studied in ref. [42] and can be directly applied to our analysis. Before doing so, we will make a change in the parameterization. This is because eqs. (2.18) suggest apparent divergences in 2,3,4 in the

limit v v. However, this is only an artefact that can be avoided by reparameterization.

We therefore select the following parameterization

m2H1 = 1

2 3m2H3 m2H5 + 3s2H

JHEP01(2013)026

, M21 = 1

2 3m2H3 m2H5 + M2

, M22 = M2, (3.1)

in terms of which all the dimensionless couplings can be rewritten for sin = 0 as

1 = m2h 8v2c2H

, 2 = m2H3 m2H5 + M2 +

M22v2 , 3 =

m2H5 M2 v2 ,

m2H3 m2H5 + M2v2 . (3.2)

It is seen that the v dependence drops out in 2,3,4 and no divergent s appear even when v v.

For the vacuum stability condition, we require that the potential is bounded from below in any direction with large scalar elds. This condition imposes constraints on the dimensionless coupling constants 1, . . . , 5. In the GM model, we then derive the following inequalities

1 > 0, 2 + 3 > 0, 2 + 123 > 0, |4| + 2

p1(2 + 3) > 0,

4 = m2H3 + m2H5 M24v2 , 5 =

1 4|5| +

p21(22 + 3) > 0. (3.3)

They have taken into account the positivity of all combinations of two non-zero scalar elds, as have been discussed in ref. [43] for the HTM.

Figure 1 shows the regions excluded by the unitarity and the vacuum stability constraints for the case of mH3 = 150 GeV and v = 1 MeV. The left, center and right plots show the cases for M=0, 300, 350 GeV, respectively. For the unitarity bound, we consider the S-wave amplitudes for elastic scatterings of two scalar boson states and require their absolute values of the eigenvalues to be less than 1. It is observed that the allowed regions by the unitarity bound for larger M is smaller than those for smaller M. This is because the 2 coupling increases as M becomes larger. In fact, the excluded regions are determined by the following unitarity condition [42];

121

q(121 222 143)2 + 14424 < 16. (3.4)

+ 222 + 143

M = 0, m = 150 GeV, v = 1 MeV, a = 0

Vacuum Stability

m < 0

M = 300 GeV, m = 150 GeV, v = 1 MeV, a = 0

Vacuum Stability

m < 0

400

M = 350 GeV, m = 150 GeV, v = 1 MeV, a = 0

Vacuum Stability

Unitarity m < 0

300

M [GeV]

200

M [GeV]

200

M [GeV]

200

100

Vacuum Stability

100 150 200 250 300

mH5 [GeV]

100 150 200 250 300

mH5 [GeV]

100 150 200 250 300

mH5 [GeV]

Figure 1. Constraints from the unitarity and vacuum stability in the M-mH5 plane. In all the plot, the uncolored regions are allowed, and the 3-plet Higgs mass is taken to be 150 GeV, v = 1 MeV

and = 0. Blue, gray and pink shaded regions are respectively excluded by the vacuum stability bound, unitarity bound and a negative singlet Higgs mass (mH1 < 0). The left, center and right plot show the case of M = 0, 300 GeV and 350 GeV, respectively.

100 150 200 250 300 350 400

mH5 [GeV]

JHEP01(2013)026

M = 0, m = 300 GeV, v = 1 MeV, a = 0

Vacuum Stability

M = 200 GeV, m = 300 GeV, v = 1 MeV, a = 0

Vacuum Stability

M = 230 GeV, m = 300 GeV, v = 1 MeV, a = 0

Vacuum Stability

500

400

300

M [GeV]

200

200 Unitarity

100

Vacuum Stability

Unitarity

100

Unitarity

100 150 200 250 300 350 400

mH5 [GeV]

100 150 200 250 300 350 400

mH5 [GeV]

Figure 2. Constraints from the unitarity and vacuum stability in the M-mH5 plane. In all the plot, the uncolored regions are allowed, and the 3-plet Higgs mass is taken to be 300 GeV, v = 1 MeV

and = 0. Blue and pink shaded regions are respectively excluded by the vacuum stability bound and the unitarity bound. The left, center and right plot show the case of M = 0, 200 GeV and 230 GeV, respectively.

On the other hand, the vacuum stability bound becomes milder as M is taken to be a larger value because of the increasing 2 coupling. For a xed value of mH5 and M, a larger M value is allowed (excluded) by the unitarity (vacuum stability) bound.

Figure 2 also shows the regions excluded by the unitarity and the vacuum stability conditions for the case of mH3 = 300 GeV and v = 1 MeV. The allowed regions are much smaller than those in the case of mH3 = 150 GeV. The excluded regions from the vacuum stability for smaller (larger) values of M are determined by the third (fourth) inequality in eq. (3.3).

In the case of larger v values (e.g., v [greaterorsimilar] 10 GeV), the regions excluded by the unitarity (vacuum stability) condition are larger (smaller) compared to the small v case. This is because the 1 coupling becomes larger. In addition, the singlet Higgs boson mass gets a larger value, so that the regions excluded due to mH1 < 0 are smaller in the larger v case.

3.2 Zbb data

The renormalized Zbb vertex is dened by [44]

LZbb =

esW cW Z

b(gLbPL + gRbPR)b,

where the renormalized coupling gL,Rb can be expressed as

gL,Rb = gL,Rb + gL,R (SM)b + gL,R (GM)b with

gLb = Ib s2W Qb, gRb = s2W Qb, (3.5)

where gL,R (SM)b (gL,R (GM)b) denote the one-loop corrections to the Zbb vertices from the SM (GM) contributions, where the W boson and the NG boson (H3) are running in the loop, If (Qf) is the third component of the isospin (the electric charge) for the eld f, and sW = sin W and c2W = 1 s2W . The analytic formulas for gL,R (SM)b is given in ref. [45],

and their numerical values are calculated as [46]

gL (SM)b = 0.4208, gR (SM)b = 0.0774. (3.6)

The one-loop correction gL(GM)b is given in terms of the Passarino-Veltman function [48] by

gL(GM)b =

e sW cW

JHEP01(2013)026

2 tan2 Hm2t v2

1 162

hc2W C24(m2b, m2Z, m2b, mt, mH3, mH3) + 2s2W QtC24(m2b, m2Z, m2b, mH3, mt, mt) 12s2W Qt

+ m2t(It s2W Qt)C0(m2b, m2Z, m2b, mH3, mt, mt) (Ib s2W Qb)B1(m2b, mt, mH3)i

. (3.7)

On the other hand, gR(GM)b can be neglected because the corrections are proportional to the bottom quark mass [see eq. (2.28)]. We can also neglect the contributions from H03 loop diagrams for the same reason. The renormalized couplings gL,Rb can be compared to the experimental value of Rexpb [47]

Rexpb = 0.21629 0.00066. (3.8)

In gure 3, we show the excluded parameter space in the mH3-v plane using the Rb data in eq. (3.8). Basically, the upper bound on v increases monotonically with mH3. The 2 bound is about 25 GeV more relaxed than the 1 bound over the considered range. We note in passing that the constraint of the b s data for the GM model is similar to

that in the Type-I 2HDM [49, 50] and is milder than the Rb constraint.

4 Higgs decays

In this section, we discuss the decay of the triplet-like Higgs bosons, namely the 5-plet Higgs bosons H5 (= H5, H5 or H05), 3-plet Higgs bosons H3 (= H3 or H03) and the singlet Higgs boson H01. Decay branching ratios of the Higgs bosons depend on the mass

100 200 300 400 500 600 700

mH3 [GeV]

Figure 3. Constraint from the Rb data given in eq. (3.8) on v as a function of mH3. The region above the black (red) line is excluded at 1 (2) level.

parameters mH5, mH3 and mH1, the VEV of the triplet eld v , and the mixing angle . The mass of the SM-like Higgs boson h is xed at 125 GeV. Using the mass relation given in eq. (2.20), we can treat mH1 as an dependent parameter determined by mH3 and mH5. Hereafter, we take m mH3 mH5, mH3 and v as the input parameters, and

assume = 0 for simplicity. Once we apply the mass relation, there are three di erent patterns of masses for the triplet-like Higgs bosons. In the case of m = 0, all the masses of the triplet-like Higgs bosons are degenerate: mH5 = mH3 = mH1, whereas in the case of m > 0 ( m < 0), the mass spectrum is then mH1 > mH3 > mH5 (mH5 > mH3 > mH1).

First, we consider the decays of the 5-plet Higgs bosons. In the case of m 0, the

5-plet Higgs bosons can decay into weak gauge boson pairs or lepton pairs depending on the magnitude of v . When m < 0, the 5-plet Higgs bosons can decay into a 3-plet Higgs boson and a gauge boson, such as H++5 W +H+3 and H+5 W +H03, in addition to the two decay modes allowed in the case of m 0.

In gure 4, the decay branching ratios of H++5, H+5 and H05 are shown as a function of v in the case of mH3 = 150 GeV. When m = 0 (upper row), the main decay modes of H++5, H+5 and H05 change from ++, +, and to W +W +, W +Z, and W +W or ZZ at around v = 103 GeV, respectively. Here H05 decays more dominantly into W +W

than ZZ because of the mass threshold e ect. When m = 50 GeV (lower row) and for

the wide range of 108 [lessorsimilar] v [lessorsimilar] 1 GeV, the main decay mode of H++5 is H+3W +, those of H+5 are H+3Z and H03W +, and those of H05 are H3W and H03Z.

Figure 5 shows the decay branching ratios of the 5-plet Higgs bosons for mH3 =

300 GeV. The general behavior here is roughly the same as the case with mH3 = 150 GeV. The crossing point for the main decay modes in each of the upper plots ( m = 0) slightly shifts to a smaller v ( 104 GeV).

Figure 6 shows the contour plots of the decay branching ratios of H++5, H+5 and H05 on the v -| m| plane (with m < 0) for the cases with mH3 = 150 GeV (upper plots) and

mH3 = 300 GeV (lower plots). There are always three distinct regions in this plane. In

Excluded

2 s

v D[GeV]

1 s

JHEP01(2013)026

m = 150 GeV, Dm = 0

l l W W

l n W Z

W W

++ )

+ )

0 )

BR(H 5

10 10 10

vD [GeV]

10 10 10

vD [GeV]

10 10 10

vD [GeV]

JHEP01(2013)026

m = 150 GeV, Dm = -50 GeV

H W

l l

W W

H Z

H W + c.c.

W W

l n H W

H Z

W Z

++ )

+ )

0 )

BR(H 5

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

Figure 4. The decay branching ratios of H++5 (left), H+5 (center) and H05 (right) as a function of v . We take mH3 = 150 GeV, mh=125 GeV and = 0 in all the plots. The mass di erence m is taken to be 0 for the upper three plots, and to be 50 GeV for the lower three plots.

10 10 10 10

vD [GeV]

m = 300 GeV, Dm = 0

l l W W

l n W Z

W W

++ )

+ )

0 )

BR(H 5

10 10 10 10

vD [GeV]

10 10

vD [GeV]

m = 300 GeV, Dm = -50 GeV

m = 300 GeV, Dm = - 50 GeV

H W

W W

l l

H Z

H W + c.c.

W W

l n

W Z

H W

H Z

++ )

+ )

0 )

BR(H 5

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

Figure 5. Same as gure 4, but for mH3 = 300 GeV.

m = 150 GeV, Dm < 0

|Dm| [GeV]

BR(H H V)

50 %

90 %

BR(H l l ) BR(H W W )

50 %

90 %

BR(H H V)

BR(H nn) BR(H VV)

BR(H H V)

BR(H l n)

50 %

90 %

BR(H W Z)

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

m = 300 GeV, Dm < 0

JHEP01(2013)026

BR(H H V)

BR(H W W )

BR(H l l )

50 %

90 %

50 %

90 %

BR(H nn)

BR(H H V)

BR(H VV)

BR(H H V)

50 %

90 %

BR(H l n)

BR(H W Z)

|Dm| [GeV]

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

10 10 10 10 10 10 10 10 10 10 10 10 10

vD [GeV]

Figure 6. Contour plots of the decay branching ratios of H++5 (left column), H+5 (center column) and H05 (right column) on the v -| m| plane (with m < 0). We take mh=125 GeV and = 0

in all the plots. The upper (lower) three plots show the case for mH3 = 150 GeV (300 GeV). Each solid (dashed) curve represents the branching ratio of 50% (90%) for the corresponding decay mode indicated by the arrow.

the region of small | m| and small (large) v , the main decay modes of the 5-plet Higgs

bosons are the a pair of leptons (weak bosons). In the region of large | m|, they are a

3-plet Higgs boson and a gauge boson, denoted by H3V in the plots (V = W or Z), where it is understood that all the possible channels of H3V should be summed over.

Secondly, we consider the decays of the 3-plet Higgs bosons. The 3-plet Higgs bosons can decay into a pair of fermions through the Yukawa interactions given in eq. (2.28) and a pair of leptons through the neutrino Yukawa interaction given in eq. (2.26), depending on the value of v in the case of m 0. In the region dominated by fermionic decays, the

main decay mode strongly depends on mH3. When mH3 is smaller than the top quark mass, H+3 (H03) mainly decays into + or cs (bb), whereas in the case of mt < mH3 < 2mt, H+3 (H03) decays into tb (bb). Furthermore, when mH3 is larger than 2mt, H03 decays dominantly into tt, and H+3 still mainly into tb. In addition, the 3-plet Higgs bosons can decay into the SM-like Higgs boson h and a gauge boson, e.g., H+3 hW + and H03 hZ if mH3 is

larger than mh. When m > 0 ( m < 0), the 3-plet Higgs bosons can decay into a gauge boson and a 5-plet (singlet) Higgs boson.

In gure 7, the decay branching ratios of H+3 and H03 are shown as a function of v for mH3 = 150 GeV. The mass di erence m is taken to be 0, 50 GeV and 50 GeV

in the top, middle and bottom plots, respectively. From the top two gures, it is seen that the dominant decay modes of H+3 (H03) change from + () to + or cs (bb) at

mH3 = 150 GeV, Dm = 0

100

mH3 = 150 GeV, Dm = 0

100

l+n

t+n

hW+

nn bb

t+t

+ )

0 )

BR(H 3

10-1

BR(H 3

10-1

10-2

10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-4 10-3 10-2

vD [GeV]

JHEP01(2013)026

mH3 = 150 GeV, Dm = 50 GeV

100

nn H5+W- + c.c.

H50Z

t+t

+ )

l+n H5++W

H5+Z

H50W+

t+n

0 )

BR(H 3

10-1

BR(H 3

10-1

10-2

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

mH3 = 150 GeV, Dm = -50 GeV

100

l+n H10W+

t+n

nn H10Z

t+t

+ )

0 )

BR(H 3

10-1

10-2

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

Figure 7. Decay branching ratios of H+3 (left column) and H03 (right column) as a function of v . We take mH3 = 150 GeV, mh = 125 GeV and = 0 in all the plots. The mass di erence m is xed to 0 (top plots), 50 GeV (middle plots) and 50 GeV (bottom plots), respectively.

around v = 103 GeV. In the case of m = 50 GeV (middle plots) and for a wide range 108 [lessorsimilar] v [lessorsimilar] 10 GeV, the 3-plet Higgs bosons mainly decay into a 5-plet Higgs boson and a weak gauge boson, i.e., H+3 H++5W , H+3 H+5Z and H+3 H05W + for H+3 decays

and H03 H5W and H03 H05Z for H03 decays. On the other hand, in the case of

m = 50 GeV (bottom plots), the main decay modes of H+3 (H03) are H01W + (H01Z) in

the range of 108 [lessorsimilar] v [lessorsimilar] 10 GeV.

Figure 8 shows the decay branching ratios of H+3 and H03 as a function of v for mH3 = 300 GeV. The mass di erence m is taken to be 0, 50 GeV and 50 GeV in the

mH3 = 300 GeV, Dm = 0

100

l+n

hW+

nn hZ

+ )

0 )

BR(H 3

10-1

0.1

10-5 10-4 10-3

vD [GeV]

10-4 10-3

vD [GeV]

JHEP01(2013)026

mH3 = 300 GeV, Dm = 50 GeV

100

H5+W- + c.c.

H50Z

l+n H5++W

H5+Z

H50W+

hW+

+ )

0 )

BR(H 3

10-1

BR(H 3

10-1

10-2

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

mH3 = 300 GeV, Dm = -50 GeV

100

l+n H10W+ tb

hW+

nn H10Z hZ

+ )

0 )

BR(H 3

10-1

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

Figure 8. Same as gure 7, but for mH3 = 300 GeV.

top, middle and bottom plots, respectively. When m = 0 (top plots), the main decay modes of H+3 (H03) change from + () to tb and hW + (hZ) at v 104 GeV. When

m = 50 GeV (middle plots) and m = 50 GeV (bottom plots), the main decay modes

are the same as in the case of mH3 = 150 GeV in the range of 107 [lessorsimilar] v [lessorsimilar] 1 GeV.

In gure 9, we give the contour plots of the decay branching ratios of H+3 and H03 for mH3 = 150 GeV. The mass di erence m is taken to be positive (negative) in the upper (lower) two gures. In this gure, BR(H+3 H5V ) and BR(H03 H5V ) denote the

sums of the decay branching ratios of the modes with a 5-plet Higgs boson and a gauge boson. BR(H+3 ff) and BR(H03 ff) denote the sum of the decay branching ratios

of H+3 + and H+3 cs and that of H03 b

b and H03 +, respectively. Similar

mH3 = 150 GeV, Dm > 0

101

Dm [GeV]

101

Dm [GeV]

50 %

90 %

BR(H3+ l+n)

BR(H3+ H5V)

BR(H3+ f f)

50 %

90 %

BR(H30 H5V)

BR(H30 nn) BR(H30 f f )

100

10-1

JHEP01(2013)026

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

mH3 = 150 GeV, Dm < 0

101

|Dm| [GeV]

BR(H30 H10Z)

BR(H30 nn) BR(H30 f f)

50 %

90 %

BR(H3+ H10W+)

BR(H3+ f f)

50 %

90 %

BR(H3+ l+n)

101

|Dm| [GeV]

100

10-1

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

Figure 9. Contour plots of the decay branching ratios of H+3 (left column) and H03 (right column) on the v - m plane. We take mH3 = 150 GeV, mh=125 GeV and = 0 in all the plots. The upper (lower) two plots show the case with m > 0 ( m < 0). Each solid (dashed) curve represents the branching ratio of 50% (90%) for the corresponding decay mode indicated by the arrow.

to gure 6, it is seen that there are three distinct regions in this plane. In the small m and small (large) v region, the main decay modes are + (+) for H+3 and (bb) for

H03. On the other hand, in the large m region, the decay modes associated with a 5-plet (singlet) Higgs boson dominate in the case of m > 0 ( m < 0). We notice that the regions where the H5V decay is dominant are wider than the corresponding one where the

H01V decay is dominant. This is because of a larger number of decay modes in H5V .

Figure 10 shows the contour plots of the branching ratios of the 3-plet Higgs bosons for mH3 = 300 GeV. In the plots of the left column, there is no dashed curve corresponding to the branching ratio of 90% for the H+3 t

b decay mode. This is because the H+3 hW + decay mode is also kinematically allowed at the same time when the H+3 t

b is open, and

the former amounts to around 30%.

mH3 = 300 GeV, Dm > 0

102

mH3 = 300 GeV, Dm > 0

102

50 %

90 %

BR(H3+ l+n)

BR(H3+ H5V)

BR(H3+ tb)

101

Dm [GeV]

50 %

90 %

BR(H30 nn)

BR(H30 H5V)

BR(H30 hZ)

Dm [GeV]

100

JHEP01(2013)026

10-1

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102

vD [GeV]

mH3 = 300 GeV, Dm < 0

102

BR(H3+ H10W+)

BR(H3+ tb)

BR(H3+ l+n)

50 %

90 %

101

|Dm| [GeV]

100

10-1

10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

vD [GeV]

Figure 10. Same as gure 9, but for mH3 = 300 GeV.

We here comment on the decays of the singlet Higgs boson H01. When we take = 0, the decay property of H01 is similar to that of H05. In the case of m 0, H01 can decay

into (W +W or ZZ) for smaller (larger) values of v . When m > 0, H01 can decay into a 3-plet Higgs boson and a weak gauge boson. If 6= 0, H01 can mix with h and can

thus decay into fermion pairs via the mixing in addition to the above-mentioned modes.

Throughout this section, the decay properties of the 5-plet Higgs bosons and the 3-plet Higgs bosons can be separately considered for four di erent regions in the v - m plane, as schematically shown in gure 11. In Region I, all the triplet-like Higgs bosons mainly decay leptonically:

H++5 ++, H+5 +, H05 ,

H+3 +, H03 . (4.1) In this region, the mass of the 5-plet Higgs bosons is constrained to be mH5 [greaterorsimilar] 400 GeV by the search at the LHC for doubly-charged Higgs bosons decaying into same-sign dilep-tons [26, 27]. In Region II, the 5-plet Higgs bosons mainly decay into the weak gauge boson

Figure 11. Four regions are schematically shown on the v -| m| plane.

pairs, while the 3-plet Higgs bosons decay into the fermion pairs. When the mass of the 3-plet Higgs bosons is less than the top quark mass, the main decay modes are

H++5 W +W +, H+5 W +Z, H05 W +W /ZZ,H+3 +/cs, H03 b

b. (4.2)

For Region III and Region IV, one has to separately consider the cases whether the sign of m is positive or negative. In the case of m > 0, the 5-plet Higgs bosons mainly decay into the lepton pairs (weak gauge boson pairs) in Region III (Region IV). The 3-plet Higgs bosons mainly decay into a 5-plet Higgs boson and a weak gauge boson:

H++5 ++ (W +W +), H+5 + (W +Z), H05 (W +W /ZZ), H+3 H++5W /H+5Z/H05W +, H03 H5W /H05Z. (4.3)

In the case of m < 0, the main decay modes in both Region III and Region IV are

H++5 H+3W +, H+5 H+3Z/H03W +, H05 H3W /H03Z

H+3 H01W +, H03 H01Z. (4.4)

5 Phenomenology at the LHC

In this section, we discuss how the custodial symmetry of the GM model can be tested at the LHC. There are characteristic features of the triplet-like Higgs bosons that mainly originate from the triplet eld of the model. (1) The masses of the Higgs bosons belonging to the same SU(2)V multiplet are the same. (2) The 5-plet and the singlet Higgs bosons have the Gauge-Gauge-Scalar type of couplings as listed in table 3, but not the Yukawa couplings given in eq. (2.28), while the 3-plet Higgs bosons have the Yukawa couplings, but not the Gauge-Gauge-Scalar type of couplings. These features can be used to test the custodial symmetry of the GM model.

JHEP01(2013)026

As is discussed in the previous section, it is important to study the decay pattern of the triplet-like Higgs bosons. In particular, feature (2) mentioned above can be most clearly tested in Region II because the 5-plet (3-plet) Higgs bosons mainly decay into weak gauge boson pairs (fermion pairs) in this region. In the following discussion, we focus on Region II and the detectability of the 5-plet and 3-plet Higgs bosons.

5.1 Production modes

There are several production modes for the 5-plet Higgs bosons H5 and the 3-plet Higgs bosons H3, as listed below. Throughout this section, q, q, Q, Q and those with bars denote light quarks and anti-quarks.

1. The Drell-Yan process

H5 and H3 can be produced in pairs via and Z, e.g., pp H5H5 and pp H3H3.

The cross section is determined by the gauge coupling as well as the Higgs masses mH5 and mH3, independent of the value of v .

2. The mixed Drell-Yan (mDY) processH5 and H3 can be produced at the same time, e.g., pp H5H3, which we call the

mixed Drell-Yan (mDY) process to be separated from the usual Drell-Yan process mentioned above. The cross section is proportional to c2H, and is thus relatively suppressed in comparison with the Drell-Yan process, especially in the large v case.

3. The weak vector boson fusion (VBF) processThe single production of H5 occurs via the qQ H5 process. The cross section is

proportional to v2 , so that this mode can be important in the large v case.

4. The weak vector boson associated processIn addition to the VBF process, H5 can also be produced in association with a weak gauge boson, e.g., qq H5V . The cross sections of such modes are proportional to

v2 as for the VBF production mode. Thus, this mode can also become important

when the VBF process is important.

5. The Yukawa process

H3 can be produced through the Yukawa interactions given in eq. (2.28) as the gluon fusion process for the SM Higgs boson: gg H03. There are t-channel H3 and H03

production modes: gb tH3 and gb bH03. These production cross sections are

proportional to tan2 H.

6. The top quark decay

When mH3 is smaller than the top quark mass, H3 can be produced from the top quark decay. The decay rate of the t bH3 depends on tan2 H.

Among these production processes, channels 3 and 4 can be useful to discriminate the GM model from the others with doubly-charged Higgs bosons and to test the mass degeneracy of H5. In the HTM, for example, the doubly-charged Higgs boson can in

JHEP01(2013)026

H5++ productions, vD = 20 GeV, Dm = 0

H5+ productions, vD = 20 GeV, Dm = 0

8 TeV

103

14 TeV

8 TeV

14 TeV

102

s[fb]

101

s[fb]

101

H5 qq

100

H5 W

H5qq

H5V

H5 H3

H5 H30

100

10-1

JHEP01(2013)026

100 150 200 250 300 350 400

mH5 [GeV]

100 150 200 250 300 350 400

mH5 [GeV]

H50 productions, vD = 20 GeV, Dm = 0

14 TeV

102

8 TeV

s[fb]

101

100

H50qq

H50V

H50H30

H50H3

10-1

100 150 200 250 300 350 400

mH5 [GeV]

Figure 12. Production cross sections of the 5-plet Higgs bosons in various processes as a function of mH5. The upper-left, upper-right, and bottom plots show the production cross sections for H5,

H5, and H05, respectively. In all the plots, we take v = 20 GeV and m = 0. The LHC collision energy is assumed to be 8 TeV (dashed curves) and 14 TeV (solid curves).

principle be produced via the VBF and the vector boson associated processes. However, these cross sections are much suppressed due to the tiny triplet VEV required by the electroweak rho parameter. In the GM model, v can be of order 10 GeV, so that these production processes become useful. The mDY process is also a unique feature of the GM model because the Higgs bosons H5 and H3 having di erent decay properties are produced at the same time. In particular, when Region II is realized, the main decay modes of these two Higgs bosons are distinctly di erent. Thus, this process can be useful not only to test the mass degeneracy of H3 but also to distinguish the model from the others also having doubly-charged and/or singly-charged Higgs bosons.

In gure 12, production cross sections of the 5-plet Higgs bosons from channels 2, 3, and 4 are shown as a function of mH5 for the LHC running at 8 and 14 TeV. We take v = 20 GeV and m = 0 as an example in all the plots. It is noted that the dominant production mechanism is the VBF process for a su ciently large mH5.

5.2 Signal and background analysis

We will rst discuss the VBF process and the vector boson associated process to study the mass degeneracy among H5, H5 and H05. Then we turn to the mDY process.

Let us consider the case with mH3 = 150 GeV, m = 10 GeV (i.e., mH5 = 140 GeV) and v = 20 GeV as an example in Region II. In this case, the 5-plet Higgs bosons decay into gauge boson pairs almost 100% (the branching fractions of H05 W +W and H05 ZZ

being 67% and 33%, respectively). On the other hand, H3 decays to at 66% and cs at 29%, and H03 decays to bb at 89%. We note that the branching fraction of t H+3b here

is around 0.4%. The upper limit of the top quark decay into a charged Higgs boson and the bottom quark is 2-3% in the case where the charged Higgs boson mass is between 80 and 160 GeV, under the assumption that the charged Higgs boson decays to at 100% [51]. Thus, the selected parameter set is allowed by the constraint from the top quark decays. The signal events from the VBF production processes for the 5-plet Higgs bosons are given by

qQ H5qQ W W jj,qQ H5qQ W Zjj,qQ H05qQ W W jj/ZZjj. (5.1)

From the vector boson associated processes, we have the following events

qq H5W W W jjqq H5W W Zjj, qq H5Z W Zjj,

qq H05Z W +W jj/ZZjj, qq H05W W +W jj/ZZjj, (5.2) where the associated weak gauge bosons are assumed to decay hadronically so that they have the same nal states as the VBF process. Moreover, we consider the case where the weak gauge bosons produced from the decay of H5 decay leptonically. Then the nal states of the signal events have same-sign (SS) dileptons plus dijets and missing transverse energy (jj /

ET ) for the H5 production mode, where denotes collectively the light leptons e and hereafter. The nal state of the H5 production mode includes trileptons plus dijets and missing transverse energy (jj /

ET ), while that for the H05 production mode has opposite-sign (OS) dileptons plus dijets and missing transverse energy (jj /

ET ).

The corresponding background events for these signal events are from the W W jj for

the H5 production, W Zjj for the H5 production, and tt, W W jj and ZZjj for the H05 production.

We simulate the signal and the background event rates by using MadGraph 5 [52] at the parton level for the cases where the LHC operates at the center-of-mass (CM) energy s of 8 TeV and 14 TeV. We impose the following basic kinematic cuts

pjT > 20 GeV, pT > 10 GeV, |j| < 5, || < 2.5, Rjj > 0.4, (5.3) where pjT and pT are the transverse momenta of the jet and the lepton, respectively, j and are the pseudorapidities of the jet and the lepton, respectively, and Rjj is the distance

JHEP01(2013)026

jj /

between the two jets. The cross sections for the signal and background events are listed in table 1, where the signal cross section includes contributions from the VBF production and the vector boson associated production. An integrated luminosity of 100 fb1 is assumed in the simulations. In this table, the signal signicance is dened by

S = S/S + B, (5.4) where S and B are the numbers of the signal and background events, respectively. The signicance of the jj /

ET event from the H5 production process exceeds 5 even using simply the basic cuts. However, the signicances for the remaining two events from the

H5 and H05 production processes are less than 1. For the jj /

ET event, in particular, the background is larger than the signal by 3 to 4 orders of the magnitude because of the huge tt background.

To improve the signicance, we need to impose additional kinematic cuts. Figure 13 shows the distributions of the pseudorapidity gap jj for the dijet system and the trans-verse mass [5355] in the leptons plus missing transverse energy system for s = 8 TeV and the integrated luminosity of 100 fb1. Explicitly, these two kinematical quantities are dened by

M2T q

M2vis + (pvisT)2 + |/pT | 2 h

i2, (5.5)

jj |j1 j2|, (5.6)

where Mvis and pvisT are the invariant mass and the vector sum of the transverse momenta of the charged leptons, respectively, and /

pT is the missing transverse momentum determined

ET jj /

Cuts H5jj W W jj S H5jj W Zjj S H05jj tt/V V jj S

Basic 3.71 3.48 13.8 0.61 45.9 0.89 1.15 4.39103 0.17

(8.72) (8.13) (21.2) (1.60) (1.39102) (1.35) (2.76) (1.77104) (0.21) jj 1.82 0.20 12.8 0.33 4.42 1.51 0.51 30.7 0.91(5.68) (0.65) (22.6) (0.98) (15.6) (2.41) (1.42) (1.99102) (1.00) MT 1.80 0.05 13.2 0.33 0.07 5.22 0.48 11.4 1.39(5.58) (0.12) (23.4) (0.98) (0.46) (8.17) (1.36) (67.4) (1.64)

b-jet veto - - - - - - 0.48 1.82 3.16 - - - - - - (1.36) (10.8) (3.90)

Table 1. Signal and background cross sections in units of fb after each kinematic cut, along with the signicance S dened by eq. (5.4) based on an integrated luminosity of 100 fb1. The numbers

without (with) parentheses correspond to the case with a CM energy of 8 TeV (14 TeV). The signal cross section includes contributions from both the VBF production and the vactor boson associated production processes. For the jj /

ET events, we further impose the requirement of the b-jet veto for each jet to reduce the background, where the b-tagging e ciency is take to be 0.6 [56].

JHEP01(2013)026

pvisT + /

SS dilepton + missing + 2 jets

mDY VBF + Associate

102

SS dilepton + missing + 2 jets

Total Signal

Total BG

Total Signal

# of Events / bin

VBF + Associate

# of Events / bin

101

mDY

JHEP01(2013)026

1 1 2 3 4 5 6 7 8 9

Dhjj

100

0 100 200 300 400 500 MT [GeV]

103

3 leptons + missing + 2 jets

Total BG

3 leptons + missing + 2 jets

Total BG

Total Signal

mDY

102

# of Events / bin

102

VBF + Associate

101

Total Signal

mDY

VBF + Associate

101

100

1 2 3 4 5 6 7 8

Dhjj

100

100 200 300 400 500MT [GeV]

OS dilepton + missing + 2 jets

Total BG

105

104

OS dilepton + missing + 2 jets

Total BG

Total Signal

VBF + Associate

mDY

104

# of Events / bin

103

# of Events / bin

103

102

Total Signal

mDY

VBF + Associate

101

100

1 2 3 4 5 6 7 8

Dhjj

100

0 100 200 300 400 MT [GeV]

Figure 13. jj and MT distributions for the signal and background events. The top, middle and bottom plots show these distributions for the jj /

ET , jj /

ET and jj /

ET events,

respectively. The distributions for the signal events are divided into those from the VBF process and vector boson associated process (green dashed curve), the mDY process (blue dashed curve) and the sum of them (red solid curve). The bin size for the jj (MT ) distribution is taken to be0.2 (5 GeV). The integrated luminosity and the CM energy are assumed to be 100 fb1 and 8 TeV, respectively.

by the negative sum of visible momenta in the transverse direction. In gure 13, the distributions of jj and MT for the signal events from the VBF process plus vector boson associated process and the mDY process are separately indicated by dotted lines. The latter production mode will be discussed in details later. A signicant feature of the VBF process is that the two external quark jets are almost along the beam direction and carry most of the energy of the collider protons. Therefore, they are mostly detected in the forward regions. This is seen in the jj distribution of gure 13. The end point in the MT distribution of signals rests at around 140 GeV, corresponding to the mass of the 5-plet

Higgs boson.

According to the above-mentioned observations, we nd the following additional kinematic cuts useful in further reducing the backgrounds:

jj > 3.5 (> 4.0 for jj /

ET ), 50 < MT < 150 GeV. (5.7)

The cross sections for the signals and backgrounds in each step of the kinematic cuts are listed in table 1. After making the rst two cuts, the signicances of the events from H5 and H5 achieve 13.2 and 5.2, respectively. However, the signicance of the events from H05 is around 1.4. We further require that events with at least one b-jet are tagged and rejected in order to reduce the tt background. The b-tagging e ciency is taken to be 0.6 [56]. By using this cut, the tt background events with the nal state of bb+ /

ET can be reduced to be 16%. Consequently, the signal signicance for the +jj /

ET event can reach 3.16 (3.90) with s = 8 TeV (14 TeV) after all the cuts discussed above are imposed.

Next, we focus on the mDY production mode discussed in the previous subsection. In order to reconstruct the masses of H3 Higgs bosons, we consider their hadronic decays, namely H3 cs and H03 b

b. The signal events are

pp H5H3 W W cs,pp H5H3 W Zcs, pp H5H03 W Zb

pp H05H3 W +W cs/ZZcs, pp H05H03 W +W b

b/ZZbb, (5.8)

where leptonic decays of the weak gauge bosons from the H5 decays are also assumed in this analysis. Thus, the nal states of the signal events from the mDY process are the same as those from the VBF process as well as the associated process. Its di erence from the VBF process is observed in the jj distribution of the dijet system. In the mDY process, the dijets in the nal state come from the decay of the 3-plet Higgs boson, not the external quark jets. According to the plots in the left column of gure 13, the events from the mDY process concentrates in the jj [lessorsimilar] 2.5 region for all the three cases. On the other hand, the MT distributions from the mDY process and the VBF plus associated process are almost the same. This is because the leptons plus missing transverse energy system come from the decays of H5 in both processes. Therefore, we apply the same MT cut given in eq. (5.7) to this analysis, but not the jj cut. In the analysis of the mDY process, the jj /

ET signal events are overwhelmed by the huge background from the tt production.

JHEP01(2013)026

jjET/ jjET/

Cuts H5jj H5H3 W W jj S H5jj H5H,03 W Zjj S

Basic 3.71 (8.72) 0.72 (1.63) 3.48 (8.13) 15.8 (24.1) 0.61 (1.60) 0.53 (1.21) 45.9 (1.39102) 1.66 (2.36) MT 3.65 (8.57) 0.71 (1.60) 1.02 (2.20) 18.8 (28.9) 0.61 (1.60) 0.53 (1.21) 1.16 (3.42) 7.52 (11.3)

Table 2. Signal and background cross sections in units of fb after each kinematic cut, along with the signicance based on an integrated luminosity of 100 fb1. The numbers without (with) parentheses correspond to the case with a CM energy of 8 TeV (14 TeV).

JHEP01(2013)026

SS dilepton + missing + 2 jets

3 leptons + missing + 2 jets

Total Signal

Total BG

102

VBF + Associate

# of Events / bin

101

Total Signal

101

VBF + Associate

mDY

Total BG

100

mDY

10-1

0 50 100 150 200 250 300 Mjj [GeV]

Figure 14. Invariant mass distribution for the dijets system. The bin size in this distribution is5 GeV. The distributions for the signal events are divided into those from the VBF process and vector boson associated process (green dashed curve), the mDY process (blue dashed curve) and the sum of them (red solid curve). The integrated luminosity and the CM energy are assumed to be 100 fb1 and 8 TeV, respectively.

Table 2 lists the cross sections of the signal and the background events after imposing the basic cut and MT cut. In addition, the signal signicance is given by assuming an integrated luminosity of 100 fb1. We nd that the signicances exceed 5 in both cases after imposing the MT cut.

Figure 14 show the dijet invariant mass Mjj distributions of the signal and the background events. These distributions are plotted after imposing the MT cut. We can see a peak at around 150 GeV, corresponding to the mass of the 3-plet Higgs bosons, in both the jj /

ET and jj /

ET events. This suggests that the mass degeneracy between H3 and H03 can be readily established from the mDY process. First, the jj /

ET event

comes from the H5H3 production. Thus, the peak at around 150 GeV in the Mjj distribution gives the mass of H3. Secondly, the jj /

ET event comes from the H5H3 and H5H03 production processes. These two production cross sections are almost the same as shown in gure 12. Nevertheless, the decay branching fractions of H3 cs and H03 b

are about 30% and 90%, respectively. Thus, the jj /

ET event mainly comes from the H5H03 production. Therefore, one can conclude that the peak at around 150 GeV in the

Mjj distribution is the mass of H03.

6 Higgs to and Z decays

In this section, we discuss the decays of the SM-like Higgs boson h to diphotons and the photon plus Z boson, both of which are loop-mediated processes in the SM. The Higgs to diphoton decay is one of the most important modes in the Higgs boson search at the LHC. According to the current data, the signal strength, dened by (the observed cross section)/(the expected cross section in the SM), of the diphoton mode is 1.6 0.4 at the

CMS [1] and 1.8 0.5 at the ATLAS [2]. It is consistent with the SM prediction at the

2 level. If the observed deviation persists, it may hint at contributions from new charged particles that can couple to the SM Higgs boson. The Higgs decay into the photon and Z boson is also important to determining the structure of the Higgs sector [59]. The decay rate of this mode is closely related to that of the Higgs to diphoton mode in the sense that particles contributing to the latter generally also contribute to the former. Yet the deviations do not follow the same pattern in general [5759]. In the GM model, the doubly-charged Higgs boson H5 as well as the singly-charged Higgs bosons H5 and H3 can contribute to these processes in addition to the W boson and the top quark at the one-loop level. The decay rates of these processes are calculated as

(h ) =

GF 2emm3h

12823

XSQ2ShSS I0(mS)+ c cH

XfQ2fNfcI1/2+(ccH + 2

3 ssH)I1

(6.1)

JHEP01(2013)026

1 m2Z m2h

(h Z) =

2GF 2emm3h 1283

XSQShSS gZSS J0(mS)+ c cH

XfQfNcfJ1/2+(ccH + 2

3 ssH)J1

(6.2)

where Nfc = 3 (1) for f = q (), and the loop functions I0,1/2,1 for h and J0,1/2,1

for h Z are given in appendix C. The summation over S includes H++5, H+5, and H+3. In eqs. (6.1) and (6.2), the couplings between h and the charged Higgs bosons hSS are

given by

hH++

5 H5 =

2 v2

(cHc(3m2H3 2M21)+r23s sH

h2m2H5 +m2h M22+3c2H(M212m2H3)i) ,

(6.3)

hH+

5 H5 = hH

++5 H5 (6.4)

hH+

3 H3 =

1 v2

ccH 2c2Hm2H3 + s2Hm2h

+ 26

ssH 2s2Hm2H3 + c2Hm2h M21

, (6.5)

and those between the Z boson and the charged Higgs bosons gZSS are given by

gZH++

5 H5 =

gcW (1 2s2W ), gZH

+5 H5 = gZH

+3 H3 =

2gZH

++5 H5. (6.6)

To illustrate how the event rates of h and h Z deviate from the SM predictions,

we dene the following ratios:

R = (gg h)GM BR(h )GM

(gg h)SM BR(h )SM

, RZ = (gg h)GM BR(h Z)GM

(gg h)SM BR(h Z)SM

(6.7)

where (gg h)SM [(gg h)GM] is the gluon fusion production cross section in the

SM (GM model), and BR(h X)SM [BR(h X)GM] is the branching fraction of the

h X decay mode in the SM (GM model) with X = or Z. In fact, the ratio in the

production cross sections, (gg h)GM/(gg h)SM, can be replaced by c2/c2H.

In the numerical calculation of R and RZ, we use the parameterization given in eq. (3.1). The mass of the singlet Higgs boson mH1 does not directly a ect the decay rates of h and h Z. Nevertheless, it a ects the parameter space as constrained by the

vacuum stability and unitarity conditions. In this parameterization, the couplings given in eq. (6.5) can be rewritten as

hH++

5 H5 =

JHEP01(2013)026

1cHv2 (2c2Hm2H3 + s2Hm2h). (6.8)

Figure 15 shows the contours of R (left plot) and RZ (right plot) on the M-mH5 plane. Here we take mH3 = 150 GeV, M = 300 GeV and = 0. The triplet VEV v is taken to be 20 GeV in the upper two plots and 60 GeV in the lower two plots. The blue, pink and gray shaded regions are excluded by the vacuum stability bound, unitarity bound and by having a negative value for mH1, respectively. For xed values of mH5, both R

and RZ increase with M. In other words, there is a correlation between the two ratios in this model. For the case with a larger v , R and RZ tend to have smaller values because the hW +W coupling gets smaller. Using mH5 = 150 GeV as an example, the maximally allowed values of R and RZ are about 1.8 (1.0) and 1.2 (0.8) in the case of v = 20 GeV (60 GeV), respectively.

Figure 16 also shows the corresponding contour plots for the case of mH3 = 300 GeV, M = 200 GeV and = 0. The parameter space allowed by the unitarity and the vacuum stability constraints is much smaller than the previous case. Again, using mH5 = 150 GeV, the maximally allowed values of R and RZ are almost the same as the case of mH3 = 150 GeV, but the minimum values of both R and RZ are around 1.0 in the case of v = 20 GeV.

7 Conclusions

We have discussed how to test the custodial symmetry in the Higgs sector of the GM model at the LHC. This can be done by experimentally verifying three characteristic features. First, there are several Higgs bosons in addition to the SM-like Higgs boson h; namely, a pair of doubly-charged Higgs bosons, two pairs of singly-charged Higgs bosons, a CP-odd Higgs boson and three CP-even Higgs bosons. These Higgs bosons can be classied into the 5-plet Higgs bosons (H5, H5, H05), the 3-plet Higgs bosons (H3, H03), and the singlet Higgs

2v2 (m2H5 M2), hH

+3 H3 =

M = 300 GeV, mH3 = 150 GeV, vD = 20 GeV, a = 0

0.8

M = 300 GeV, mH3 = 150 GeV, vD = 20 GeV, a = 0

0.92

400

400 Vacuum

2.0

Vacuum Stability

Stability

3.0

1.8

300

1.6

300

1.4

M [GeV]

1.2

200

1.0

mH1 < 0

0.95

100

0.90

mH1 < 0

0.75

JHEP01(2013)026

100 150 200 250 300

mH5 [GeV]

100 150 200 250 300

mH5 [GeV]

M = 300 GeV, mH3 = 150 GeV, vD = 60 GeV, a = 0

2.01.51.00.8

0.6

0.4

0.3

Vacuum Stability

Unitarity

M = 300 GeV, mH3 = 150 GeV, vD = 60 GeV, a = 0

1.2

1.0

0.8

0.6

Vacuum Stability

Unitarity

500

400

M [GeV]

300

200

100

0.55

100 150 200 250 300 350 400

mH5 [GeV]

100 150 200 250 300 350 400

mH5 [GeV]

Figure 15. Contour plots of R (left) and RZ (right) on the M-mH5 plane in the case of mH3 = 150 GeV, M = 300 GeV and = 0. In the upper (lower) two plots, v is taken to be20 GeV (60 GeV). The blue, pink and gray shaded regions are respectively excluded by the vacuum stability bound, unitarity bound and by having a negative mass for H1.

boson H01 under the custodial SU(2)V symmetry. The Higgs bosons belonging to the same SU(2)V multiplet have the same mass, subject to small electromagnetic corrections at the order of a few hundred MeV. Secondly, the 5-plet and the singlet Higgs bosons can couple to weak gauge boson pairs, but not fermion pairs via the usual (not neutrino) Yukawa interaction at the tree level. On the other hand, the 3-plet Higgs bosons can couple to fermion pairs, but not weak gauge boson pairs. As discussed in the main text, such a feature leads to specic nal states for detecting these Higgs bosons and measuring their masses. Thirdly, the VEV of the isospin triplet Higgs elds can be taken to be of order 10 GeV while keeping = 1 at the tree level. This is not possible in models with triplet elds in general.

The decay properties of the triplet-like Higgs bosons have been discussed in details. They depend on the mass splitting m, dened by mH3 mH5, and the triplet VEV v .

We nd that the parameter space in the v - m plane can be divided into four regions, among which the main decay modes of the triplet-like Higgs bosons are quite distinct.

M = 200 GeV, mH3 = 300 GeV, vD = 20 GeV, a = 0

3.0 2.0

1.6 1.4 1.2

1.0

M = 200 GeV, mH3 = 300 GeV, vD = 20 GeV, a = 0

1.6 1.41.2

1.0

0.9

500

500 Vacuum Stability

Vacuum Stability

400

1.1

M [GeV]

300

200

0.9

Unitarity

100

JHEP01(2013)026

100 150 200 250 300 350 400

mH5 [GeV]

100 150 200 250 300 350 400

mH5 [GeV]

M = 200 GeV, mH3 = 300 GeV, vD = 60 GeV, a = 0

2.0 1.5 1.0 0.80.6

0.4

0.3

Vacuum Stability

M = 200 GeV, mH3 = 300 GeV, vD = 60 GeV, a = 0

1.2 1.0 0.8

0.6

0.55

Vacuum Stability

500

400

M [GeV]

300

200

Unitarity

100

100 150 200 250 300 350 400

mH5 [GeV]

100 150 200 250 300 350 400

mH5 [GeV]

Figure 16. Contour plots of R (left) and RZ (right) on the M-mH5 plane in the case of mH3 = 300 GeV, M = 200 GeV and = 0. In the upper (lower) two plots, v is taken to be 20 GeV (60 GeV). The blue and pink shaded regions are respectively excluded by the vacuum stability bound and unitarity bound.

We have discussed the collider phenomenology of the GM model at the LHC in Region II where the 5-plet Higgs bosons mainly decay to weak gauge boson pairs, whereas the main decay modes of H3 are and cs and that of H03 is bb when the mass of the 3-plet

Higgs bosons is less than mt. We focus on the VBF, the vector boson associated and the mDY production processes in order to verify the custodial symmetric nature of the model. We nd that H5 and H5 can be detected at more than 5 level by using the forward jet tagging for the VBF process and the transverse mass cut on the charged leptons and missing transverse energy system if the center-of-mass energy and the luminosity are 8 TeV and 100 fb1, respectively. The signicance of the H05 Higgs boson can be reached at 3

level by further imposing the b-jet veto.

We also nd that the 3-plet Higgs bosons can be detected via the mDY production process. After the MT cut, the masses of H3 and H03 can be measured from the peak in the invariant mass distribution of the dijet system. Therefore, the respective mass degeneracy in the 5-plet Higgs bosons and the 3-plet Higgs bosons can be tested.

We have also investigated the h and h Z processes in the GM model. In

this model, the H5, H5 and H3 bosons can contribute to these processes in addition to the SM top quark and the W boson at one-loop level. We nd that in the parameter space consistent with the unitarity and the vacuum stability, the maximally allowed value of R is around 1.8 (1.0) for the parameter choice of mH3 = 150 GeV, mH5 = 150 GeV and v = 20 GeV (60 GeV). Deviations in the rates of h Z and h processes

from the SM predictions can be used to distinguish models with various extended Higgs sectors. In the GM model, the maximally allowed value of RZ is around 1.2 (0.8) for mH3 = 150 GeV, mH5 = 150 GeV and v = 20 GeV (60 GeV). For the cases of larger mH3 (e.g., mH3 = 300 GeV), the maximally allowed values of R and RZ are not so di erent from the case of mH3 = 150 GeV. But, the minimum values of both R and RZ are about 1.0 when mH5 = 150 GeV and v =20 GeV.

Acknowledgments

The authors would like to thank Takaaki Nomura for useful technical help. This research was supported in part by the National Science Council of R.O.C. under Grants Nos. NSC-100-2628-M-008-003-MY4 and NSC-101-2811-M-008-014.

A Relationships among di erent representations of the Higgs elds

The Higgs elds expressed in eqs. (2.1) and (2.21) are related as follows:

tr( ) = 2, (A.1) tr( ) = 2tr( + ), (A.2) tr[( )2] = 6[tr()]2 4tr[()2] + 2tr(4) + 4tr()tr(), (A.3)

tr a2 b 2

tr( ta tb) = 2[()( ~) + h.c.] + 2()() ()tr(), (A.4)

(P P )ab = 12 +12(~ + h.c.), (A.5)

tr( ta tb)(P P )ab = 62tr(). (A.6)

B Coupling constants between the triplet-like Higgs bosons and the weak gauge bosons

The Gauge-Gauge-Scalar vertices and the corresponding coe cients are listed in table 3. The Gauge-Scalar-Scalar vertices are listed in table 4, where p1 and p2 are respectively the four-momenta of the rst and second particles in the vertex column into the vertex.

JHEP01(2013)026

a2 b 2

Vertex Coe cient Vertex Coe cient

H5W W

g222 sHvg H01ZZ g

12 (3scH 26csH)vg

H5W Z ggZ2 sHvg hW +W

2 Z

6 (3ccH + 26ssH)vg

H05W +W g

23 sHvg hZZ

g2Z

12 (3ccH + 26ssH)vg

H05ZZ

g2Z

23 sHvg GW A emW g

H01W +W g

6 (3scH 26csH)vg GW Z esW mZg Table 3. Gauge-Gauge-Scalar vertices and the associated coe cients.

Vertex Coe cient Vertex Coe cient

H++5H5A 2e(p1 p2) H5H5W g2 (p1 p2)

H+5H5A e(p1 p2) H5H05W

2 g(p1 p2)

H+3H3A e(p1 p2) H5H3W g2 cH(p1 p2)

G+GA e(p1 p2) H5H03W ig2cH(p1 p2)

H++5H5Z

g cW

(1 2s2W )(p1 p2) H3H05W

6 gcH(p1 p2)

JHEP01(2013)026

H+5H5Z

g2cW (1 2s2W )(p1 p2) H3H03W ig2(p1 p2)

H+3H3Z

g2cW (1 2s2W )(p1 p2) H3H01W

g6 (26cH c + 3sHs)(p1 p2)

H5H3Z gZ2 cH(p1 p2) H3hW

g6 (26cH s 3sHc)(p1 p2)

g6 (3ccH + 26ssH)

H03H01Z igZ6 (26cH c + 3sHs)(p1 p2) H03hZ igZ6 (26cH s 3sHc)(p1 p2)

Table 4. Gauge-Scalar-Scalar vertices and the associated coe cients.

H05H03Z i gZ

3 cH(p1 p2) GhW

C Loop functions in the h ! and Z decay rates

The loop functions appearing in the calculations of the SM-like Higgs boson decay to diphotons are given in terms of the Passarino-Veltman functions [48] as

I0(m) = 2v2 m2h

[1 + 2m2C0(0, 0, m2h, m, m, m)], (C.1)

I1/2 = 4m2f "

2m2h

4m2f

m2h

!C0(0, 0, m2h, mf, mf, mf)#, (C.2)

I1 = 2m2W

6 m2h

+ 1

2m2Wm2h 1

C0(0, 0, m2h, mW , mW , mW ) . (C.3)

m2W

+ 6

Those for the h Z process are given by

J0(m) = 2e(m2h m2Z)"

1 + 2m2C0(0, m2Z, m2h, m, m, m) + m2Z

m2h m2Z

B0(m2h, m, m)

B0(m2Z, m, m) #

, (C.4)

J1/2 =

4m2f(12If s2W Qf) sW cW (m2h m2Z) "

2 + (4m2f m2h + m2Z)C0(0, m2Z, m2h, mf, mf, mf)

+ 2m2Zm2h m2Z

JHEP01(2013)026

B0(m2h, mf, mf) B0(m2Z, mf, mf) #

, (C.5)

J1 = 2m2WsW cW (m2h m2Z)(

c2W

5 + m2h 2m2W

s2W

1 + m2h 2m2W

1 + 2m2W C0(0, m2Z, m2h, mW , mW , mW ) + m2Zm2h m2W

B0(m2h, mW , mW )

B0(m2Z, mW , mW )

6c2W (m2h m2Z)C0(0, m2Z, m2h, mW , mW , mW )

+ 2s2W (m2h m2Z)C0(0, m2Z, m2h, mW , mW , mW ))

. (C.6)

References

[1] CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, http://dx.doi.org/10.1016/j.physletb.2012.08.021

Web End =Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B716,30

Web End =INSPIRE ].

[2] ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, http://dx.doi.org/10.1016/j.physletb.2012.08.020

Web End =Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B716,1

Web End =INSPIRE ].

[3] T. Lee, A Theory of Spontaneous T Violation, http://dx.doi.org/10.1103/PhysRevD.8.1226

Web End =Phys. Rev. D 8 (1973) 1226 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D8,1226

Web End =INSPIRE ].

[4] J.C. Pati and A. Salam, Lepton Number as the Fourth Color, http://dx.doi.org/10.1103/PhysRevD.10.275

Web End =Phys. Rev. D 10 (1974) 275 [Erratum ibid. D 11 (1975) 703] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D10,275

Web End =INSPIRE ].

[5] R. Mohapatra and J.C. Pati, A Natural Left-Right Symmetry, http://dx.doi.org/10.1103/PhysRevD.11.2558

Web End =Phys. Rev. D 11 (1975) 2558 [ http://inspirehep.net/search?p=find+J+Phys.Rev.,D11,2558

Web End =INSPIRE ].

[6] G. Senjanovi and R.N. Mohapatra, Exact Left-Right Symmetry and Spontaneous Violation of Parity, http://dx.doi.org/10.1103/PhysRevD.12.1502

Web End =Phys. Rev. D 12 (1975) 1502 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D12,1502

Web End =INSPIRE ].

[7] N. Arkani-Hamed, A. Cohen, E. Katz and A. Nelson, The Littlest Higgs, http://dx.doi.org/10.1088/1126-6708/2002/07/034

Web End =JHEP 07 (2002) 034 [http://arxiv.org/abs/hep-ph/0206021

Web End =hep-ph/0206021 ] [http://inspirehep.net/search?p=find+J+JHEP,0207,034

Web End =INSPIRE ].

[8] T. Han, H.E. Logan, B. McElrath and L.-T. Wang, Phenomenology of the little Higgs model, http://dx.doi.org/10.1103/PhysRevD.67.095004

Web End =Phys. Rev. D 67 (2003) 095004 [http://arxiv.org/abs/hep-ph/0301040

Web End =hep-ph/0301040 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D67,095004

Web End =INSPIRE ].

[9] H. Georgi and M. Machacek, Doubly charged Higgs bosons, http://dx.doi.org/10.1016/0550-3213(85)90325-6

Web End =Nucl. Phys. B 262 (1985) 463 [ http://inspirehep.net/search?p=find+J+Nucl.Phys.,B262,463

Web End =INSPIRE ].

[10] T. Cheng and L.-F. Li, Neutrino Masses, Mixings and Oscillations in SU(2) U(1) Models

of Electroweak Interactions, http://dx.doi.org/10.1103/PhysRevD.22.2860

Web End =Phys. Rev. D 22 (1980) 2860 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D22,2860

Web End =INSPIRE ].

[11] J. Schechter and J. Valle, Neutrino Masses in SU(2) U(1) Theories,

http://dx.doi.org/10.1103/PhysRevD.22.2227

Web End =Phys. Rev. D 22 (1980) 2227 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D22,2227

Web End =INSPIRE ].

[12] G. Lazarides, Q. Sha and C. Wetterich, Proton Lifetime and Fermion Masses in an SO(10) Model, http://dx.doi.org/10.1016/0550-3213(81)90354-0

Web End =Nucl. Phys. B 181 (1981) 287 [http://inspirehep.net/search?p=find+J+Nucl.Phys.,B181,287

Web End =INSPIRE ].

[13] R.N. Mohapatra and G. Senjanovi, Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, http://dx.doi.org/10.1103/PhysRevD.23.165

Web End =Phys. Rev. D 23 (1981) 165 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D23,165

Web End =INSPIRE ].

[14] M. Magg and C. Wetterich, Neutrino mass problem and gauge hierarchy, http://dx.doi.org/10.1016/0370-2693(80)90825-4

Web End =Phys. Lett. B 94 (1980) 61 [http://inspirehep.net/search?p=find+J+Phys.Lett.,B94,61

Web End =INSPIRE ].

[15] M.S. Chanowitz and M. Golden, Higgs Boson triplets with M(W ) = M(Z) cos , http://dx.doi.org/10.1016/0370-2693(85)90700-2

Web End =Phys. Lett. B 165 (1985) 105 [http://inspirehep.net/search?p=find+J+Phys.Lett.,B165,105

Web End =INSPIRE ].

[16] T. Han, B. Mukhopadhyaya, Z. Si and K. Wang, Pair production of doubly-charged scalars: Neutrino mass constraints and signals at the LHC, http://dx.doi.org/10.1103/PhysRevD.76.075013

Web End =Phys. Rev. D 76 (2007) 075013 [arXiv:0706.0441] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D76,075013

Web End =INSPIRE ].

[17] A. Akeroyd, M. Aoki and H. Sugiyama, Probing Majorana Phases and Neutrino Mass Spectrum in the Higgs Triplet Model at the CERN LHC, http://dx.doi.org/10.1103/PhysRevD.77.075010

Web End =Phys. Rev. D 77 (2008) 075010 [arXiv:0712.4019] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D77,075010

Web End =INSPIRE ].

[18] P. Fileviez Perez, T. Han, G.-y. Huang, T. Li and K. Wang, Neutrino Masses and the CERN LHC: Testing Type II Seesaw, http://dx.doi.org/10.1103/PhysRevD.78.015018

Web End =Phys. Rev. D 78 (2008) 015018 [arXiv:0805.3536] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D78,015018

Web End =INSPIRE ].

[19] A. Akeroyd and C.-W. Chiang, Doubly charged Higgs bosons and three-lepton signatures in the Higgs Triplet Model, http://dx.doi.org/10.1103/PhysRevD.80.113010

Web End =Phys. Rev. D 80 (2009) 113010 [arXiv:0909.4419] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D80,113010

Web End =INSPIRE ].

[20] A. Akeroyd and C.-W. Chiang, Phenomenology of Large Mixing for the CP-even Neutral Scalars of the Higgs Triplet Model, http://dx.doi.org/10.1103/PhysRevD.81.115007

Web End =Phys. Rev. D 81 (2010) 115007 [arXiv:1003.3724] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D81,115007

Web End =INSPIRE ].

[21] A. Akeroyd, C.-W. Chiang and N. Gaur, Leptonic signatures of doubly charged Higgs boson production at the LHC, http://dx.doi.org/10.1007/JHEP11(2010)005

Web End =JHEP 11 (2010) 005 [arXiv:1009.2780] [http://inspirehep.net/search?p=find+J+JHEP,1011,005

Web End =INSPIRE ].

[22] CDF collaboration, D. Acosta et al., Search for doubly-charged Higgs bosons decaying to dileptons in pp collisions at s = 1.96 TeV, http://dx.doi.org/10.1103/PhysRevLett.93.221802

Web End =Phys. Rev. Lett. 93 (2004) 221802 [http://arxiv.org/abs/hep-ex/0406073

Web End =hep-ex/0406073 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,93,221802

Web End =INSPIRE ].

[23] D0 collaboration, V. Abazov et al., Search for doubly-charged Higgs boson pair production in the decay to ++ in pp collisions at s = 1.96 TeV,http://dx.doi.org/10.1103/PhysRevLett.93.141801

Web End =Phys. Rev. Lett. 93 (2004) 141801 [http://arxiv.org/abs/hep-ex/0404015

Web End =hep-ex/0404015 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,93,141801

Web End =INSPIRE ].

[24] D0 collaboration, V. Abazov et al., Search for pair production of doubly-charged Higgs bosons in the H++H ++ nal state at D0, http://dx.doi.org/10.1103/PhysRevLett.101.071803

Web End =Phys. Rev. Lett. 101 (2008) 071803

[arXiv:0803.1534] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,101,071803

Web End =INSPIRE ].

[25] CDF collaboration, T. Aaltonen et al., Search for Doubly Charged Higgs Bosons with Lepton-Flavor-Violating Decays involving Tau Leptons, http://dx.doi.org/10.1103/PhysRevLett.101.121801

Web End =Phys. Rev. Lett. 101 (2008) 121801 [arXiv:0808.2161] [http://inspirehep.net/search?p=find+J+Phys.Rev.Lett.,101,121801

Web End =INSPIRE ].

[26] ATLAS collaboration, Search for anomalous production of prompt like-sign muon pairs and constraints on physics beyond the Standard Model with the ATLAS detector,http://dx.doi.org/10.1103/PhysRevD.85.032004

Web End =Phys. Rev. D 85 (2012) 032004 [arXiv:1201.1091] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D85,032004

Web End =INSPIRE ].

JHEP01(2013)026

[27] CMS collaboration, A search for a doubly-charged Higgs boson in pp collisions at s = 7 TeV, http://dx.doi.org/10.1140/epjc/s10052-012-2189-5

Web End =Eur. Phys. J. C 72 (2012) 2189 [arXiv:1207.2666] [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.2666

Web End =INSPIRE ].

[28] J. Gunion, R. Vega and J. Wudka, Higgs triplets in the standard model, http://dx.doi.org/10.1103/PhysRevD.42.1673

Web End =Phys. Rev. D 42 (1990) 1673 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D42,1673

Web End =INSPIRE ].

[29] C.-W. Chiang, T. Nomura and K. Tsumura, Search for doubly charged Higgs bosons using the same-sign diboson mode at the LHC, http://dx.doi.org/10.1103/PhysRevD.85.095023

Web End =Phys. Rev. D 85 (2012) 095023 [arXiv:1202.2014] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D85,095023

Web End =INSPIRE ].

[30] S. Chakrabarti, D. Choudhury, R.M. Godbole and B. Mukhopadhyaya, Observing doubly charged Higgs bosons in photon-photon collisions, http://dx.doi.org/10.1016/S0370-2693(98)00743-6

Web End =Phys. Lett. B 434 (1998) 347 [http://arxiv.org/abs/hep-ph/9804297

Web End =hep-ph/9804297 ] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B434,347

Web End =INSPIRE ].

[31] A. Melfo, M. Nemevek, F. Nesti, G. Senjanovi and Y. Zhang, Type II Seesaw at LHC: The Roadmap, http://dx.doi.org/10.1103/PhysRevD.85.055018

Web End =Phys. Rev. D 85 (2012) 055018 [arXiv:1108.4416] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D85,055018

Web End =INSPIRE ].

[32] M. Aoki, S. Kanemura and K. Yagyu, Testing the Higgs triplet model with the mass di erence at the LHC, http://dx.doi.org/10.1103/PhysRevD.85.055007

Web End =Phys. Rev. D 85 (2012) 055007 [arXiv:1110.4625] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D85,055007

Web End =INSPIRE ].

[33] J. Gunion, R. Vega and J. Wudka, Naturalness problems for = 1 and other large one loop e ects for a standard model Higgs sector containing triplet elds,http://dx.doi.org/10.1103/PhysRevD.43.2322

Web End =Phys. Rev. D 43 (1991) 2322 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D43,2322

Web End =INSPIRE ].

[34] J. Grifols and A. Mendez, The W ZH coupling in SU(2) |rmU(1) gauge models,

http://dx.doi.org/10.1103/PhysRevD.22.1725

Web End =Phys. Rev. D 22 (1980) 1725 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D22,1725

Web End =INSPIRE ].

[35] D.K. Ghosh, R.M. Godbole and B. Mukhopadhyaya, Unusual charged Higgs signals at LEP-2, http://dx.doi.org/10.1103/PhysRevD.55.3150

Web End =Phys. Rev. D 55 (1997) 3150 [http://arxiv.org/abs/hep-ph/9605407

Web End =hep-ph/9605407 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/9605407

Web End =INSPIRE ].

[36] K. Cheung and D.K. Ghosh, Triplet Higgs boson at hadron colliders, http://dx.doi.org/10.1088/1126-6708/2002/11/048

Web End =JHEP 11 (2002) 048 [http://arxiv.org/abs/hep-ph/0208254

Web End =hep-ph/0208254 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ph/0208254

Web End =INSPIRE ].

[37] E. Asakawa and S. Kanemura, The HW Z0 vertex and single charged Higgs boson production via W Z fusion at the large hadron collider, http://dx.doi.org/10.1016/j.physletb.2005.08.091

Web End =Phys. Lett. B 626 (2005) 111 [http://arxiv.org/abs/hep-ph/0506310

Web End =hep-ph/0506310 ] [http://inspirehep.net/search?p=find+J+Phys.Lett.,B626,111

Web End =INSPIRE ].

[38] E. Asakawa, S. Kanemura and J. Kanzaki, Potential for measuring the HW Z0 vertex

from WZ fusion at the Large Hadron Collider, http://dx.doi.org/10.1103/PhysRevD.75.075022

Web End =Phys. Rev. D 75 (2007) 075022 [http://arxiv.org/abs/hep-ph/0612271

Web End =hep-ph/0612271 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D75,075022

Web End =INSPIRE ].

[39] M. Battaglia, A. Ferrari, A. Kiiskinen and T. Maki, Pair production of charged Higgs bosons at future linear e+e colliders, eConf C 010630 (2001) E3017 [http://arxiv.org/abs/hep-ex/0112015

Web End =hep-ex/0112015 ] [http://inspirehep.net/search?p=find+EPRINT+hep-ex/0112015

Web End =INSPIRE ].

[40] S. Godfrey and K. Moats, Exploring Higgs Triplet Models via Vector Boson Scattering at the LHC, http://dx.doi.org/10.1103/PhysRevD.81.075026

Web End =Phys. Rev. D 81 (2010) 075026 [arXiv:1003.3033] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D81,075026

Web End =INSPIRE ].

[41] S. Kanemura, K. Yagyu and K. Yanase, Testing Higgs models via the HW Z vertex by a recoil method at the International Linear Collider, http://dx.doi.org/10.1103/PhysRevD.83.075018

Web End =Phys. Rev. D 83 (2011) 075018 [arXiv:1103.0493] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D83,075018

Web End =INSPIRE ].

[42] M. Aoki and S. Kanemura, Unitarity bounds in the Higgs model including triplet elds with custodial symmetry, http://dx.doi.org/10.1103/PhysRevD.77.095009

Web End =Phys. Rev. D 77 (2008) 095009 [arXiv:0712.4053] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D77,095009

Web End =INSPIRE ].

[43] A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka, M. Peyranere, L. Rahili and J. Ramadan, The Higgs Potential in the Type II Seesaw Model, http://dx.doi.org/10.1103/PhysRevD.84.095005

Web End =Phys. Rev. D 84 (2011) 095005 [arXiv:1105.1925] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D84,095005

Web End =INSPIRE ].

JHEP01(2013)026

[44] H.E. Haber and H.E. Logan, Radiative corrections to the Zbb vertex and constraints on extended Higgs sectors, http://dx.doi.org/10.1103/PhysRevD.62.015011

Web End =Phys. Rev. D 62 (2000) 015011 [http://arxiv.org/abs/hep-ph/9909335

Web End =hep-ph/9909335 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D62,015011

Web End =INSPIRE ].

[45] B.W. Lynn and R.G. Stuart, Electroweak radiative corrections to b quark production, http://dx.doi.org/10.1016/0370-2693(90)90505-Z

Web End =Phys. Lett. B 252 (1990) 676 [http://inspirehep.net/search?p=find+J+Phys.Lett.,B252,676

Web End =INSPIRE ].

[46] J. Field, Indications for an anomalous right-handed coupling of the b quark from a model independent analysis of LEP and SLD data on Z decays, http://dx.doi.org/10.1142/S0217732398002059

Web End =Mod. Phys. Lett. A 13 (1998) 1937 [http://arxiv.org/abs/hep-ph/9801355

Web End =hep-ph/9801355 ] [http://inspirehep.net/search?p=find+J+Mod.Phys.Lett.,A13,1937

Web End =INSPIRE ].

[47] Particle Data Group collaboration, K. Nakamura et al., Review of particle physics,http://dx.doi.org/10.1088/0954-3899/37/7A/075021

Web End =J. Phys. G 37 (2010) 075021 [http://inspirehep.net/search?p=find+J+J.Phys.,G37,075021

Web End =INSPIRE ].

[48] G. Passarino and M. Veltman, One Loop Corrections for e+e Annihilation Into + in the Weinberg Model, http://dx.doi.org/10.1016/0550-3213(79)90234-7

Web End =Nucl. Phys. B 160 (1979) 151 [http://inspirehep.net/search?p=find+J+Nucl.Phys.,B160,151

Web End =INSPIRE ].

[49] V.D. Barger, J. Hewett and R. Phillips, New constraints on the charged Higgs sector in two Higgs doublet models, http://dx.doi.org/10.1103/PhysRevD.41.3421

Web End =Phys. Rev. D 41 (1990) 3421 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D41,3421

Web End =INSPIRE ].

[50] M. Aoki, S. Kanemura, K. Tsumura and K. Yagyu, Models of Yukawa interaction in the two Higgs doublet model and their collider phenomenology, http://dx.doi.org/10.1103/PhysRevD.80.015017

Web End =Phys. Rev. D 80 (2009) 015017 [arXiv:0902.4665] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D80,015017

Web End =INSPIRE ].

[51] CMS collaboration, Search for a light charged Higgs boson in top quark decays in pp collisions at s = 7 TeV, http://dx.doi.org/10.1007/JHEP07(2012)143

Web End =JHEP 07 (2012) 143 [arXiv:1205.5736] [http://inspirehep.net/search?p=find+J+JHEP,1207,143

Web End =INSPIRE ].

[52] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, MadGraph 5: Going Beyond, http://dx.doi.org/10.1007/JHEP06(2011)128

Web End =JHEP 06 (2011) 128 [arXiv:1106.0522] [http://inspirehep.net/search?p=find+J+JHEP,1106,128

Web End =INSPIRE ].

[53] V.D. Barger, A.D. Martin and R. Phillips, Evidence for the t Quark in pp Collider Data, http://dx.doi.org/10.1016/0370-2693(83)91297-2

Web End =Phys. Lett. B 125 (1983) 339 [http://inspirehep.net/search?p=find+J+Phys.Lett.,B125,339

Web End =INSPIRE ].

[54] V.D. Barger, T. Han and J. Ohnemus, Heavy leptons at hadron supercolliders, http://dx.doi.org/10.1103/PhysRevD.37.1174

Web End =Phys. Rev. D 37 (1988) 1174 [http://inspirehep.net/search?p=find+J+Phys.Rev.,D37,1174

Web End =INSPIRE ].

[55] J. Bagger et al., CERN LHC analysis of the strongly interacting W W system: Gold plated modes, http://dx.doi.org/10.1103/PhysRevD.52.3878

Web End =Phys. Rev. D 52 (1995) 3878 [http://arxiv.org/abs/hep-ph/9504426

Web End =hep-ph/9504426 ] [http://inspirehep.net/search?p=find+J+Phys.Rev.,D52,3878

Web End =INSPIRE ].

[56] ATLAS collaboration, Calibrating the b-Tag E ciency and Mistag Rate in 35 pb1 of Data

with the ATLAS Detector, http://cds.cern.ch/record/1356198

Web End =ATLAS-CONF-2011-089 (2011).

[57] J.S. Gainer, W.-Y. Keung, I. Low and P. Schwaller, Looking for a light Higgs boson in the Z channel, http://dx.doi.org/10.1103/PhysRevD.86.033010

Web End =Phys. Rev. D 86 (2012) 033010 [arXiv:1112.1405] [

http://inspirehep.net/search?p=find+J+Phys.Rev.,D86,033010

Web End =INSPIRE ].

[58] M. Carena, I. Low and C.E. Wagner, Implications of a Modied Higgs to Diphoton Decay Width, http://dx.doi.org/10.1007/JHEP08(2012)060

Web End =JHEP 08 (2012) 060 [arXiv:1206.1082] [http://inspirehep.net/search?p=find+J+JHEP,1208,060

Web End =INSPIRE ].

[59] C.-W. Chiang and K. Yagyu, Higgs boson decays to and Z in models with Higgs extensions, arXiv:1207.1065 [http://inspirehep.net/search?p=find+EPRINT+arXiv:1207.1065

Web End =INSPIRE ].

JHEP01(2013)026

Word count: 15872

Show less

SISSA, Trieste, Italy 2013

Abstract

Translate

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 ^sub 5^), 3-plet (H ^sub 3^) and singlet (H ^sub 1^) Higgs bosons under the classification of the custodial SU(2)^sub 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)^sub V^ multiplet are degenerate; and (2) H ^sub 5^ and H ^sub 1^ couple to the electroweak gauge bosons but not SM quarks, whereas H ^sub 3^ couples to the quarks but not the gauge bosons. We find that the H ^sub 5^ production from the weak vector boson fusion process and the Drell-Yan process associated with H ^sub 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 [arrow right] γγ as well as h [arrow right] Zγ decays.

Details

Title

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

Author

Chiang, Cheng-wei; Yagyu, Kei

Pages

1-37

Publication year

2013

Publication date

Jan 2013

Publisher

Springer Nature B.V.

e-ISSN

10298479

Source type

Scholarly Journal

Language of publication

English

DOI

https://doi.org/10.1007/JHEP01(2013)026

ProQuest document ID

1652941983

SISSA, Trieste, Italy 2013

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

Jump to:

Full text

Abstract

Details

Suggested sources