Table Of ContentHiggs boson decays to γγ and Zγ in models with Higgs extensions
Cheng-Wei Chiang1,2,3 and Kei Yagyu1
1Department of Physics, National Central University, Chungli, Taiwan 32001, ROC
2Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, ROC
3Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan 30013, ROC
The decays of a Higgs boson to the γγ and Zγ final states are purely quantum mechanical
phenomenathatareclosely related toeach other. Westudytheeffectsofan extendedHiggs sector
onthedecayratesofthetwomodes. Weproposethatasimultaneousdeterminationofthemandthe
ZZ modeisausefulwaytoseewhethertheHiggsbosonrecentlyobservedbytheLHCexperiments
is of the standard model typeor could be a memberof a larger Higgs sector.
PACSnumbers:
2
1
Introduction – The quest for the origin of elementary be realized by imposing a discrete Z symmetry, where
0 2
particle masses is arguably one of the most important the SMparticlesareZ -evenwhile the extrascalarfields
2 2
tasks in current high energy physics. According to the areZ2-odd. Inthiscase,thedominantproductionmech-
l
u standardmodel(SM),a scalarfieldisemployedtobreak anism of h at the LHC is the gluon fusion process, as in
J the electroweak (EW) symmetry down to the electro- the SM. We study how the decay rates of h γγ and
→
4 magnetic (EM) symmetry, SU(2)L U(1)Y U(1)EM, Zγ are modified (see also [9]).
× →
giving masses to the W and Z bosons that mediate Sincenoexcessisobservedintheh τ+τ− modeand
] weak interactions. This so-called Higgs mechanism [1] the Wh/Zh, h b¯b decay has only a→minor excess, it is
h
p is achieved when the scalar field spontaneously acquires stillunclearwhe→thertheobservedHiggsbosonisSM-like.
- a nonzero vacuum expectation value (VEV) due to the We therefore also analyze the scenario of a fermiophobic
p instability in its potential. As a consequence, the SM (FP) Higgs boson, in which the Yukawa couplings are
e
predicts the existence of a spin-0 Higgs boson. With the vanishinglysmall. Inthiscase,hisdominantlyproduced
h
[ introduction of Yukawa interactions, fermionic particles via the weak boson fusion process [10].
canobtaintheirmassesfromthesameHiggsfieldaswell. Models with a Higgs extension – In general, models
1 Therefore,thediscoveryoftheHiggsbosondoesnotonly
with an extended Higgs sector often contain charged
v
complete the particle spectrum of the SM, but also re-
5 Higgs bosons that, among other phenomena, can con-
veals the secrets of EW symmetry breaking and mass.
6 tribute to the h γγ and Zγ decays through the loop
0 Recently, both ATLAS and CMS Collaborations[2, 3] effect. Although→there are many possibilities for the ex-
1 oftheCERNLargeHadronCollider(LHC)havereported tendedHiggssector,wediscuss thosewith extraSU(2)
L
7. the observation of a Higgs boson at around 125 GeV singlets S (with Y = 1 and Y = 2), doublet D (with
0 at 5σ level through the combination of ZZ and γγ Y =1/2),andtripletsT (withY =0andY =1),whose
∼
2 channels. Minor excesses are observed in the WW and charge assignments are given in Table I [17].
1 Wh/Zh with h b¯b channels, while no excess is seen in
: the τ+τ− chann→el. Aroundthis massregion,anotherde- We consider three distinct classes of extended Higgs
v sectors: (I) models with one singly-charged scalar bo-
cay channel that is closely related to the diphoton mode
i son, (II) those with one singly-charged and one doubly-
X and clean in the LHC environment is the Zγ mode. At
charged scalar bosons, and (III) those with two singly-
r the leading order in the SM, both the γγ [4] and Zγ [5]
a charged scalar bosons. According to the representations
are loop processes mediated by the same particles. New
listedinTableI,therearethree,four,andsixpossibilities
particlesbeyondtheSMcanchangetheirrelativemagni-
for Class I, Class II and Class III, respectively, all listed
tudes. AlthoughtheZZ decayoccursattreelevelandis
in Table II. Examples of models in Class I (Models 1 to
less sensitive to new particle contributions, the rate de-
3)includethetwoHiggsdoubletmodel[11]andthemin-
pends on how the EWsymmetry is broken. Therefore,a
imal supersymmetric SM. Models in Class II (Models 4
simultaneous measurement of their production rates will
to 7) include the Higgs triplet model [12] and Zee-Babu
be helpful in diagnosing the observed Higgs boson.
model [13]. Finally, models in Class III (Models 8 to 13)
Inview ofthe 125GeVHiggsboson,denotedbyh, we
consider models that have only an extended Higgs sec-
tor for simplicity. There are some recent studies in the
literatureaboutthe h γγ decayin models withanex- S+ S++ D T0 T1
→
tended Higgs sector [6–8]. In this Letter, we investigate SU(2)L 1 1 2 3 3
both the h γγ and Zγ decays in models with Higgs
extensionsb→asedonvariousphysicsmotivations. Wefirst U(1)Y +1 +2 +1/2 0 +1
assume that h is SM-like, meaning that the couplings of
h with fermions (hf¯f) as well as the weak gauge bosons TABLE I: Charge assignments for extra scalar fields under
(hVV) are the same as the SM ones. This situation can theSU(2)L×U(1)Y gauge symmetry.
2
s =sinθ , c =cosθ withθ beingthe weakmix-
Model 1 2 3 4 5 6 7 8 9 10 11 12 13 W W W W W
ing angle. In Class II models, M for the singly-charged
i
S+ 1 0 0 1 0 0 0 2 0 0 1 1 1 scalar boson (i = 1) and for the doubly-charged scalar
S++ 0 0 0 1 0 1 1 0 0 0 0 0 0 boson (i=2) are generally independent parameters, ex-
cept for Model 5 where they are the same.
D 0 1 0 0 0 1 0 0 2 0 1 1 0
InClassIII models,onthe otherhand,the twosingly-
T0 0 0 1 0 0 0 1 0 0 2 0 0 1 chargedchargedscalar bosons S± and S± generally mix
1 2
T1 0 0 0 0 1 0 0 0 0 0 0 0 0 with each other, so that the expressions for gSijSZ and
λij can be quite different from those given in Eq. (3).
SSh
TABLE II: Models considered in this work and their extra In this case, the coupling gij are written in the mass
SSZ
scalar field contents. eigenbasis of the two charged scalar bosons (S±,S±) as
1 2
include those where tiny Majorana neutrino masses are g Iϕ1c2+Iϕ2s2 s2 (Iϕ2 Iϕ1)s c
genLeoroapt-eidndvuicaedhigdhibeors-loonopdepcraoycsesosefsH[1ig4g].s – The decay cW (cid:20) 3(I3ϕθ2 −I33ϕ1)θs−θcθW I3ϕ1s32θ+−I3ϕ32c2θ−θ sθ2W (cid:21), (4)
rates of h γγ and Zγ can be generally expressed as where θ is the mixing angle (c = cosθ, s = sinθ) con-
→ θ θ
necting between the weak eigenstates (ϕ±,ϕ±) and the
Γγγ = √2G2F56απ2e3mm3h mthaestsheiirgdenissotsaptiens:cϕom±1,2po=necnθSt1±o,f2ϕ∓±sθSa2±n,d1,Iwϕ1i2th2II3ϕϕ1,12.bNeointge
2 1,2 3 ≥ 3
that if Iϕ1 = Iϕ2, the off-diagonal couplings g21,21 are
(cid:12) 2Q2 vλii Ii + Q2NfI +I (cid:12) , (1) 3 6 3 SSZ
×(cid:12) Si hSS S f c f W(cid:12) nonzeroandcancontributetotheh Zγ decayaswell.
(cid:12)Xi Xf (cid:12) λij can be calculated for Models 8→, 9 and 10 as
(cid:12) (cid:12) SSh
ΓZγ =(cid:12)(cid:12)√2G1F28απ2e3mm3h (cid:18)1− mm2Z2h(cid:19)3 (cid:12)(cid:12) λS11S,h22 = v2(m2S1+,2 −M12,2c2θ−M22,1s2θ∓M32s2θ) ,
2 1
λ12 = (M2 M2)s 2M2c .
(cid:12) 2Q vλij gij Jij + Q NcJ +J (cid:12) , (2) SSh v 1 − 2 2θ− 3 2θ
×(cid:12) Si SSh SSZ S f f f W(cid:12) (cid:2) (cid:3)
(cid:12)(cid:12)Xi,j Xf (cid:12)(cid:12) Those for Models 11 and 12 are
(cid:12) (cid:12)
whe(cid:12)reG istheFermidecayconstant,v =1/(√2(cid:12)G )1/2 1
F F λ11, 22 = [m2 (1+c2 )+m2 s2 2M2 c2 2M2 s2] ,
istheHiggsVEV,mh istheHiggsbosonmass,mZ isthe SSh v S1+,2 2θ S2+,1 2θ− 1,2 θ− 2,1 θ
Z bosonmass,Q istheelectricchargeofparticleX,Nf s
X c λ12 = 2θ[(m2 m2 )(1 2c )+2M2 2M2] .
is the color factor of the fermion f. The loop functions SSh 2v S1+ − S2+ − 2θ 1 − 2
for the scalar contribution Ii and Jij are given by
S S For Model 13,
1
ISi = m2[1+2m2SiC0(0,0,m2h,mSi,mSi,mSi)] , λii = 2(m2 M2) , λ12 =0 with i=1,2 . (5)
h SSh v Si+ − i SSh
1+[m2 C (0,m2,m2,m ,m ,m )+(i j)]
JSij = Si 0 Ze(mh2h−Smi 2Z)Si Sj ↔ rInamtheteerasbMove expsrheoswsiounpsifnorthλeiSjSscha,ltahrepdoitmenetniasilonful pa-
B (m2,m ,m ) B (m2,m ,m ) 1,2,3
+m2 0 h Si Sj − 0 Z Si Sj ,
Z e(m2 m2)2 V +M2 ϕ 2+M2 ϕ 2+M2(ϕ†ϕ +h.c.),
h− Z ⊃ 1| 1| 2| 2| 3 1 2
in terms of the Passarino-Veltman functions B and C
0 0 where ϕ and ϕ are the scalar fields including ϕ± and
defined in [15], where m is the mass of the charged 1 2 1
Si ϕ±,respectively. InModels11and12,theparametercor-
scalar boson S . The loop functions for the W boson 2
i respondingtoM isabsent,whilethereisanotherdimen-
(I and J ) as well as the fermion f (I and J ) con- 3
W W f f sionful parameter µ defined in the terms µΦ†ϕ ϕ +h.c.
tributions are given in [16]. The couplings between the 1 2
that induce mixing between ϕ± and ϕ±, where Φ is the
charged scalar bosons S and the Z boson as well as h 1 2
i Higgsdoubletfieldassociatedwithh. InModel13,there
are derived from
arenoparameterscorrespondingtoM andµand,there-
3
= λij S S∗h+igij (∂ S S∗+S ∂ S∗)Zµ+h.c. fore, there is no mixing at tree level.
LS − SSh i j SSZ µ i j i µ j Wenoteinpassingthatthecouplingformulaeforλij
SSh
In models of Classes I and II, the couplings are derivedassuming anunbrokendiscrete Z symmetry
2
in eachmodel. If the Z symmetry is brokenor does not
g 2 2
gSiiSZ = c (I3i −s2WQSi), λiSiSh = v(m2Si −Mi2) , (3) existatall, λiSjSh aregenerallydifferentfromthose given
W above, even when we take the limit where h is SM-like.
where M is a dimensionful parameter unrelated to the Numerical results – Toseethe correlationbetweenthe
i
Higgs VEV, Ii is the third isospin component of S , and decay rates of h Zγ and γγ, we further define the
3 i →
3
Observables Regular FP Classes I, II and III, respectively:
Γtot (MeV) 3.7 0.93
Bγγ (%) 0.28 1.8 mh < m2S −M2 <√π , (6)
BZγ (%) 0.18 0.79 − v √πv2
R=BZΓZZ(γ%/Γ)γγ 02..633 09..413 mh < m2S1,2 −M12,2 <√π , (7)
− √2v √πv2
TanAdBFLPEHIIiIg:gTsobtoaslodne,craeyspraetcetiavnedlyb,rinantchheinSgMra.tiosofaregular mh < m2S1,2c2θ+m2S2,1s2θ−M12,2 <√π . (8)
− √2v √πv2
We shall use them and neglect the slight changes among
Model 1 2 3
the models in each class due to some coupling constants
∆Bγγ (%) −9.9 (4.2) −9.9 (4.2) −9.9 (4.2) that are irrelevant to our analysis.
∆BZγ (%) 3.3 (−1.2) −3.8 (1.4) −11 (4.2) ThedeviationsfromtheSMpredictionsfortheh γγ
R 0.72 (0.60) 0.67 (0.61) 0.63 (0.63) →
and Zγ branching ratios can be parametrized as
Model 4 5 6 7
∆Bγγ (%) −45 (11) −45 (11) −45 (11) −45 (11) ∆ = NP SM / SM , (9)
∆BZγ (%) 17 (−3.4) −12 (2.5) 9.4 (−1.9) 2.2 (−0.50) Bγγ(Zγ) hBγγ(Zγ)−Bγγ(Zγ)i Bγγ(Zγ)
R 1.3 (0.55) 1.0 (0.58) 1.3 (0.56) 1.2 (0.56)
where NP ( NP) is the branchingratio ofh γγ (h
Bγγ BZγ → →
TABLE IV: Deviations of the h → γγ and Zγ branching Zγ)inaHiggs-extendedmodel,while SM ( SM)isthat
Bγγ BZγ
ratios from the SM expectations and the ratio R in models in the SM. In Table IV, the deviations and R are listed
of Classes I and II. All the charged scalar boson masses are in the case of m = 400 GeV for Class I models, and
S+
taken to be 400 GeV. The numbers without (with) paren- m = m = 400 GeV with M = M = M for
S+ S++ 1 2
theses correspond to the case with M = 0 (M = MMAX), Class II models. The parameter M is constrained by
whereMMAXdenotesthemaximumvalueallowedbythecon- Eqs.(6)and(7)tobe0<M .470(440)GeVforClassI
ditions in Eqs. (6) and (7). In Class I models MMAX = 470 (Class II). The results for the FP Higgs boson scenario
GeV, while in Class II models MMAX = 440 GeV assuming
using the same parameter set are given in Table V.
M1 =M2 =M.
For models in Class III, we consider as an example
the case where m = 400 GeV and m = 500 GeV.
S+ S+
1 2
Model (FP) 1 2 3 We assume that the three dimensionful parameters are
∆Bγγ (%) 500 (570) 500 (570) 500 (570) the same: M1 = M2 = M3 = M. The maximally al-
∆BZγ (%) 360 (340) 330 (350) 300 (360) lowedvalueofM dependsonthemixingangleθ,butthe
R 0.48 (0.41) 0.45 (0.42) 0.42 (0.43) strictest upper bound on M from Eq. (8) is found when
Model (FP) 4 5 6 7 θ = 0. In this case, the upper bound is 440 GeV, which
∆Bγγ (%) 320 (610) 320 (610) 320 (610) 320 (610) is used in the following numerical analysis.
∆BZγ (%) 410 (330) 290 (350) 380 (330) 350 (340) In Fig. 1, the deviation of the h γγ branching ratio
R 0.78 (0.38) 0.60 (0.40) 0.73 (0.39) 0.69 (0.39) is plotted against sinθ. Accordin→g to the left plot for
the scenario with a regular Higgs boson, Models 8 – 10
TABLE V: Same as Table IV, butfor theFP Higgs case. all have the same behavior of positive corrections, while
Models 11 and 12 share a common negative corrections.
ratio R Γ /Γ . First, we give the SM expectations Model13,ontheotherhand,isaconstantduetoEq.(5)
Zγ γγ
≡
of the two diboson decays of a regular and FP Higgs and has virtually no deviationfrom the SM expectation.
boson in Table III, where m = 125 GeV and m = InthescenariowithanFPHiggs,however,thedeviations
h t
173 GeV are used. Next, we show numerical results for are all shifted to around +550% or more.
the case with an extended Higgs sector. As mentioned
before, we assume that the observed Higgs boson is SM-
like in couplings with the gauge bosons and fermions in 6 mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV 580 mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV
our numerical studies. Moreover, we present the results
4 570
for the case where the charged scalar boson are at least %] Model 8 = Model 9 = Model 10 %] Model 8 = Model 9 = Model 10
400 GeV in mass. B [γγ 2 B [γγ560
∆ ∆ Model 13
Model 13
For meaningful discussions, we calculate parameter 0 550
Model 11 = Model 12
bounds by considering unitarity and vacuum stability Model 11 = Model 12
constraints. For unitarity, we impose the condition that -20 0.2 0.4sinθ0.6 0.8 1 5400 0.2 0.4sinθ0.6 0.8 1
themagnitudesofalldimensionlesscouplingconstantsdo
FIG. 1: Deviation of the branching ratio of h → γγ as a
not exceed2π. For vacuum stability, we require that the
scalar potential is bounded from below in the parame- function of sinθ. We take M1 =M2 =M3 =M =440 GeV,
ter space where the quartic terms dominate. Combining mS1+ =400GeVandmS2+ =500GeV.Theleft(right)figure
shows the case with theregular (FP) Higgs boson.
the two bounds, we obtain the following conditions for
4
8 mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV 380 mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV ation is between about 3% and 5% (330% and 360%).
Model 8 Model 11 Model 8 Model 11 −
6 Model 9 Model 12 370 Model 9 Model 12 Finally,weshowthe ratioR inFig.3 forthe twoscenar-
%] 4 Model 10 Model 13 %]360 Model 10 Model 13 ios as well, in contrast with the values for the SM.
B [γZ2 B [γZ350 We now briefly comment on the case with lighter
∆ 0 ∆ 340 charged scalar bosons. When we take all their masses
-2 330 to be 200 GeV and use the maximally allowed M, the
-40 0.2 0.4sinθ0.6 0.8 1 3200 0.2 0.4sinθ0.6 0.8 1 deviation in the branching ratio of h → γγ is predicted
to be 14 %, 59% and 22% in Classes I, II and III with
FIG. 2: Deviation of the branching ratio of h → Zγ as a θ =0, respectively, in the regular Higgs boson scenario.
function of sinθ. We take M1 =M2 =M3 =M =440 GeV,
Summary – With the observation of a Higgs boson h
mS1+ =400GeVandmS2+ =500GeV.Theleft (right)figure of mass 125 GeV by ATLAS and CMS, it would be in-
shows thecase with the regular (FP) Higgs boson.
teresting to diagnose whether h is standard model-like
(SM-like) or part of a larger Higgs sector. We thus con-
0.66 mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV mS1+ = 400 GeV, mS2+ = 500 GeV, M = 440 GeV sider and classify models with simple Higgs extensions.
Model 8 Model 11 Model 8 Model 11 Wehaveimposedtheunitarityandvacuumstabilitycon-
Model 9 Model 12 0.44 Model 9 Model 12
0.64 Model 10 Model 13 Model 10 Model 13 straints on the model parameters. We have studied the
SM SM (Fermiophobic)
neutral diboson decays of h, assuming that it has SM-
R R
0.62 0.42 likecouplingswiththeweakbosonsandfermions. Inour
framework,theZZ modeisvirtuallyunaffected,whereas
0.6
the γγ and Zγ modes can be modified by a few to a few
0 0.2 0.4sinθ0.6 0.8 1 0.40 0.2 0.4sinθ0.6 0.8 1 tens of percent. A simultaneous determination of their
branching ratios is thus useful in exploring the possibil-
FIG. 3: The ratio R as a function of sinθ. We take M1 = ity of an extended Higgs sector. As a comparison, we
M2 =M3 =M =440GeV,mS1+ =400GeVandmS2+ =500 have also considered the scenario where h is fermiopho-
GeV. The left (right) figure shows the case with the regular
bic and observed more dramatic changes in the diboson
(FP) Higgs boson. The SM case is indicated by the dashed
decay rates.
line for comparison.
The deviation of the h Zγ branching ratio varies a Acknowledgments The authors thanks C. M. Kuo for
→
lot among the Class III models, as shown in Fig. 2. For useful discussions. This research was supported in part
the scenario with a regular (FP) Higgs boson, the devi- by the National Science Council of Taiwan, R. O. C.
[1] F.EnglertandR.Brout,Phys.Rev.Lett.13,321(1964); and C. P. Yuan,Phys.Rev.D 64, 053007 (2001).
P.W. Higgs, Phys.Rev.Lett. 13, 508 (1964); G. S. Gu- [9] M.Carena,I.LowandC.E.M.Wagner,arXiv:1206.1082
ralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. [hep-ph].
Lett.13, 585 (1964). [10] E. Gabrielli, B. Mele and M. Raidal, arXiv:1202.1796
[2] F. Gianotti, talk presented at the CERN seminar, [hep-ph].
Geneva, Switzerland, July 4, 2012. [11] M. Sher, Phys. Rept. 179, 273 (1989); G. C. Branco,
[3] J. Incandela, talk presented at the CERN seminar, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher and
Geneva, Switzerland, July 4, 2012. J. P. Silva, Phys.Rept.516, 1 (2012).
[4] J. R. Ellis, M. K. Gaillard and D. V. Nanopoulos, Nucl. [12] T.P.ChengandL.F.Li,Phys.Rev.D22,2860(1980);
Phys. B 106, 292 (1976); B. L. Ioffe and V. A. Khoze, J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227
Sov.J.Part.Nucl.9,50(1978)[Fiz.Elem.Chast.Atom. (1980).
Yadra 9, 118 (1978)]; M. A. Shifman, A. I. Vainshtein, [13] A.Zee,Nucl.Phys.B264, 99(1986); K.S.Babu,Phys.
M. B. Voloshin and V. I. Zakharov, Sov. J. Nucl. Phys. Lett. B 203, 132 (1988).
30, 711 (1979) [Yad.Fiz. 30, 1368 (1979)]. [14] A.Zee,Phys.Lett.B93,389(1980);A.Zee,Phys.Lett.
[5] R. N. Cahn, M. S. Chanowitz and N. Fleishon, Phys. B 161,141 (1985); L.M. Krauss,S.Nasriand M.Trod-
Lett.B82,113(1979);L.BergstromandG.Hulth,Nucl. den,Phys.Rev.D67,085002 (2003); M.Aoki,S.Kane-
Phys.B 259, 137 (1985). muraand O.Seto, Phys.Rev.Lett.102, 051805 (2009).
[6] P. Posch, Phys. Lett. B 696, 447 (2011); A. Arhrib, [15] G. Passarino and M. J. G. Veltman, Nucl.Phys. B 160,
R.BenbrikandN.Gaur,Phys.Rev.D85,095021(2012); 151 (1979).
P.M.Ferreira, R.Santos, M.SherandJ.P.Silva,Phys. [16] A. Djouadi, Phys. Rept.457, 1 (2008).
Rev.D 85, 035020 (2012). [17] ThescalardoubletfieldwithY =3/2doesnotcontaina
[7] A. Arhrib, R. Benbrik, M. Chabab, G. Moultaka and neutral component, and cannot couple to the other SM
L. Rahili, JHEP 1204, 136 (2012); S. Kanemura and particlesattreelevelifnootherparticlesareintroduced.
K.Yagyu,Phys. Rev.D 85, 115009 (2012). Therefore, we do not consider such a case.
[8] S.Kanemura,T.Kasai,G.-L.Lin,Y.Okada,J.-J.Tseng
