Discrimination of the light CP-odd scalars in the NMSSM and in the simplest little Higgs model

C. S. Kim*

Department of Physics and IPAP, Yonsei University, Seoul 120-749, Korea

Kang Young Lee†

Division of Quantum Phases & Devices, School of Physics, Konkuk University, Seoul 143-701, Korea

Jubin Park‡

Department of Physics, National Tsing Hua University, HsinChu 300, Taiwan(Received 1 January 2012; published 25 June 2012)

The presence of the light CP-odd scalar boson arising in the next-to-minimal supersymmetric model

and the simplest little Higgs model dramatically changes the phenomenology of the Higgs sector. We

suggest a practical strategy to discriminate the CP-odd scalar bosons between the two underlying models,

produced in decays of the standard-model-like Higgs boson. We define the decay rate of ‘‘the non

b-tagged jet pair,’’ with which we compute the ratio of decay rates into leptons and jets. The ratio shows

quite different behavior in the next-to-minimal supersymmetric model and the simplest little Higgs model.

DOI: 10.1103/PhysRevD.85.117702 PACS numbers: 14.80.Ec

I. INTRODUCTION

Discovery of Higgs bosons, which are essential forunderstanding electroweak symmetry breaking, is the prin-cipal goal of the CERN Large Hadron Collider (LHC). Inthe standard model (SM), there exists one scalar boson h ofwhich mass is constrained by the lower bound of 114 GeVfrom the direct search of e�eþ ! Zh ! Zb �b process atthe CERN Large Electron Positron Collider (LEP) [1]. Atthe LHC, a promising production channel is the gluonfusion process, pp ! gg ! h. The Higgs boson domi-nantly decays into WW=ZZ when mh > 140 GeV, andinto b �b in the low mass region. Since the h ! b �b channelsuffers from huge QCD backgrounds, the favored searchchannel is through h ! ��. The LHC has reported thataccumulated data of last year reached 5 fb�1, and morethan 10 fb�1 are expected soon [2]. If so, the SM-likeHiggs boson might be observed in the early LHC erawith the 7 TeV center-of-mass energy [3].

The observed 95% C.L. exclusion mass ranges for theSM-like Higgs boson are 131–238 GeVand 251–466 GeVby the ATLAS [4] and 127–600 GeV by the CMS [5]collaborations with data of about 5 fb�1 so far. Thereremains only a low mass window of 115 GeV<mh <127 GeV. As the LHC will run successfully to accumulate15 fb�1 by the end of this year [2], it is possible to examinethe whole region ofmh < 600 GeV. If the SMHiggs bosonis excluded at the LHC, it will be clear evidence of theexistence of new physics beyond the SM. We have todeliberate the implication of absence of the SM-likeHiggs boson at such stage.

There exist a few scenarios of new physics modelsbeyond the SM, where it is hard to detect the SM-likeHiggs boson due to a light CP-odd scalar, at least in theearly stage of the LHC. One of the examples of thisscenario is the next-to-minimal supersymmetric model(NMSSM) with an additional singlet superfield. In theNMSSM, the parameter space with a very light CP-oddscalar a is allowed such that the SM-like CP-even Higgsboson can decay into a pair of light CP-odd scalar bosonswith a large branching ratio [6]. Such a light CP-odd scalarsequentially decays into b �b, c �c, and ���þ pairs dependingon its mass. Then it would be much more difficult toidentify the Higgs boson with four final states and wemight miss the Higgs boson signal in the early LHC era.Moreover, in this case other channels for Higgs bosondecays are suppressed due to the large branching ratio ofh ! aa. On the other hand, the present Higgs mass boundfrom the LEP data can be lowered due to the reduction ofthe ZZh coupling and Brðh ! b �bÞ in this model [7]. Thesimplest little Higgs model (SLHM) with the � parameteris another example of models with the light CP-odd scalar[8]. The production and decays of the SM-like Higgs bosonin the SLHM are similar to those in the NMSSM, the Higgsboson dominantly decays into a pair of light CP-oddscalars � and the Higgs mass bound weakens [9–11].There are still other new physics models of this kind, e.g.the minimal two Higgs doublet model with a twistedcustodial symmetry can have the lightCP-odd scalar bosonas a result of the inverted hierarchy of neutral Higgs bosonmasses [12].In this paper we consider the light CP-odd scalar

boson of the NMSSM and the SLHM. In these scenariosthe promising channel to find the Higgs boson is h !aa=�� ! b �bb �b via Wh and Zh production, if ma;� >

2mb, at the LHC with 14 TeV [10]. If ma;� < 2mb, it

*cskim@yonsei.ac.kr†kylee14214@gmail.com‡honolo@phys.nthu.edu.tw

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may be produced in radiative heavy quarkonium decays[13] or in associated production [14]. The collider signa-tures of the CP-odd scalar boson at the LHC are quitesimilar in both models, the NMSSM and the SLHM. Thusit is not easy to determine the underlying theory even if weobserve a light CP-odd scalar boson at the LHC. Thereforeit is very important to clarify the underlying structure of thelight CP-odd scalar boson. We present a strategy todiscriminate the CP-odd scalar bosons between the twounderlying models, assuming that the CP-odd scalar bosonhas been already discovered and its mass measured. Sincethe production cross sections and the decay rates depend onmany model parameters as well as the final state masses,we cannot fix the model by the measured cross sectionsand branching ratios. However, if we accumulate a largeenough number of CP-odd scalars events to estimate theratio of decay rates, the dependence on most parameter iscanceled and the features of the underlying models arerevealed. Especially in the SLHM, the Yukawa couplingsare commonly expressed by the new scale f and tan� andthe ratios of decay rates are determined by the � mass andthe final states masses only.

We consider the ratio of the decay rate into tau leptonpairs to that into quark pairs. Since it is impossible toidentify the c-jet events and only partly possible to tagthe b-jet events, we define a new observable �ðj0j0Þ, thedecay width into ‘‘non b-tagged jet pair’’, by subtractingtagged b-jet from the total jet decay rates. We show that itis possible to discriminate the underlying models of theCP-odd scalars, by considering the ratio of the decay rateinto tau lepton pairs to that into non-b-tagged jet pairs withan allowed value of the b-tagging efficiency. If the SM-likeHiggs boson is not observed at the early stage of the LHC,the light CP-odd scalar scenario should be consideredseriously. Then it will be very important to find out theunderlying model of the CP-odd scalar.

II. TWO SCENARIOS FOR THE LIGHT CP-ODDSCALAR FROM THE NMSSM AND THE SLHM

In the NMSSM, the Higgs sector is described by thesuperpotential [15],

W ¼ QHuhuUc þ HdQhdD

c þ HdLheEc

þ �SðHuHdÞ þ 1

3�S3; (1)

where S is a singlet chiral superfield. The associated softtrilinear coupling terms for the singlet field are pickedup as

V ¼ �A�SHuHd þ 1

3�A�S

3 þ H:c:; (2)

from the superpotential. The effective �eff term is gener-ated by the vacuum expectation value (VEV) of the singlet

scalar s � hSi, yielding �eff ¼ �s. With an extra complex

singlet scalar field, the Higgs sector of the NMSSM con-sists of three CP-even Higgs bosons, two CP-odd Higgsbosons, and a pair of charged Higgs boson and is describedby six parameters �, �, A�, A�, tan�, and �eff , wheretan� ¼ hHui=hHdi ¼ v1=v2. The Lagrangian for CP-oddscalars and fermion couplings is given by

L ¼ ig

2mW

½md tan� �d�5dþmu cot� �u�5u�� ða cos�þ A sin�Þ: (3)

The light and heavy physical states of the CP-odd scalar, aand A, are given by

PS

� �¼ cos� � sin�

sin� cos�

� �aA

� �; (4)

with the mixing angle �. Omitting the massless Goldstonemode, the massive pseudoscalar state of the Higgs doubletsis given by P ¼ cos�HuI þ sin�HdI in terms of the weakbasis HuI and HdI, and S is the massive pseudoscalar stateof the scalar singlet. We concentrate only on a in this paper.The light CP-odd Higgs boson arises in the SLHM

with the � term, where the global symmetry is ½SUð3Þ �Uð1ÞX�2 with the gauge symmetry SUð3Þ �Uð1ÞX as itsdiagonal subgroup. The symmetries are broken to the SMgauge symmetry by the VEVs of the nonlinear SUð3Þtriplet scalar fields, h�1;2i ¼ ð0; 0; f1;2ÞT . We assume that

f1;2 are of order TeV. The remnant degrees of freedom in

the Goldstone boson sector are the SUð2ÞL doublet H andthe CP-odd scalar boson �. The Higgs potential is radia-tively generated via fermion and gauge boson loops and sois the SM-like Higgs boson mass. However, the � remainsmassless because it appears in the phase factor of�1;2. The

massless � has a trouble with constraints from the rare K,B decays, radiative � decays, and cosmology. Thus we

introduce ��2ð�y1�2 þ H:c:Þ term to generate the mass

of CP-odd scalar, even though it breaks the global sym-metry slightly. The fermion doublets of the SM are pro-moted to the SUð3Þ triplets in this model. In addition,heavy fermions are required in order to cancel quadraticdivergences of the SM top quark and remove the anomalyof the gauge group. The relevant Lagrangian with Yukawainteractions is [9–11]

L ¼ �iXf

mf

vy�f�

�f�5fþmt

vði� �TPRtþ H:cÞ; (5)

where the Yukawa couplings are

y�l ¼ y

�d;s;b ¼ �y

�u;c;t ¼

ffiffiffi2

pv

fcot2�;

y�Q ¼ �v

f½cos2�þ cos2�Q� csc2�;

(6)

with leptons l ¼ e, �, �, heavy quarks Q ¼ D, S, T. Inthis model, the new physics scale f2 ¼ f21 þ f22 and

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tan� ¼ f2=f1, and the mixing angles �T;S;D between

the heavy quarks T, S, D and the SM quarks t, s, d aredefined by

cos2�F ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 2f2

v2

m2q

m2Q

sin22�

vuut : (7)

III. DISCRIMINATORY SIGNATURES OF TWOLIGHT CP-ODD SCALARS

In our investigation, we assume that the light CP-oddscalar is produced by the SM-like Higgs boson decay, h !aa=��. Then the CP-odd scalar will decay into fermionpairs or gauge boson pairs, and the decay channels dependon its mass. The decay rates of � in the SLHM are given inRef. [11] and those of a in the NMSSM given in Ref. [15].Since the Yukawa couplings are proportional to the fer-mion masses, the dominant decay modes are b �b, c �c, and���þ when ma;� > 2mb. However, as it is not likely to

identify the c-quark jets at the LHC, we consider thedecays into two types of jet pairs instead. We define the‘‘non b-tagged jet pair,’’ j0j0, which is two-jet event nottagged as b-quark jets. If we define the efficiency b as theefficiency to identify the b �b pair, the decay rate of thenon-b-tagged two-jet event is obtained by subtractingb-tagged events from total two-jet events, i.e.

�ðj0j0Þ ¼ �ðb �bÞð1� bÞ þ �ðc �cÞ ¼ �ðjjÞ � b�ðb �bÞ;(8)

where �ðjjÞ is the total decay width of the CP-odd scalarinto two jets.

In the NMSSM, the decay width of a to a fermion pairf �f is given by

�ða ! f �fÞ ¼ NC

8

�mf

v

�2C2�cos

2�ma

�1� 4m2

f

m2a

�1=2

; (9)

where C� ¼ tan� for down-type quarks and leptons, and

C� ¼ cot� for up-type quarks.

If we consider the ratio of the decay widths of a into b �band ���þ, tan� dependence is canceled and the ratio isdetermined only by the final state masses and ma, as is thecase of the SLHM shown below. Thus we cannot discrimi-nate two models. Instead, we consider the ratio of ���þand non b-tagged two-jet events, which reveals tan� de-pendence, as given by

�ða ! ���þÞ�ða ! j0j0Þ ¼ m2

�faðm�Þ3m2

bfaðmbÞð1� bÞ þ 3m2ccot

4�faðmcÞ;

(10)

where faðmÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4m2=m2

a

p. We note that the additional

parameter cos� does not appear in this ratio of decay rates.Since the decay rate of � into fermion pairs is given by

�ð� ! f �fÞ ¼ NC

8

�mf

v

�2y�2f m�

�1� 4m2

f

m2�

�1=2

; (11)

in the SLHM, we now consider the ratio of their decaywidths, as in Eq. (10)

�ð� ! ���þÞ�ð� ! j0j0Þ ¼ m2

�f�ðm�Þ3m2

bf�ðmbÞð1� bÞ þ 3m2cf�ðmcÞ

;

(12)

where f�ðmÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4m2=m2

a

p. Note that this ratio is de-

termined only by the final-state fermion masses and scalarmass and does not depend on any model parameters, eventan�. We see that the ratio of Eq. (12) in the SLHM is

scalar mass (GeV)

Γ(a,

η→

τ-τ+

)/Γ(

a,η

→ jj

)

NMSSM, tan β=10

NMSSM, tan β=1 / SLHM

NMSSM, tan β=0.5

εb=0.5

(a)

0

0.05

0.1

0.15

0.2

0.25

10 15 20 25 30 35 40 45 50 tan β

Γ(a,

η→

τ-τ+

)/Γ(

a,η

→ jj

)

NMSSM, ma=10 GeV

NMSSM, ma=20 GeV

NMSSM, ma=50 GeV

SLHM, mη=10 GeV

SLHM, mη=20 GeV

SLHM, mη=50 GeV

εb=0.5

(b)

0

0.05

0.1

0.15

0.2

0.25

10-1

1 10

FIG. 1 (color online). The ratio of the decay rate into ���þ to that into the non-b-tagged two-jet as a function of (a) the CP-oddscalar mass, and (b) tan�.

BRIEF REPORTS PHYSICAL REVIEW D 85, 117702 (2012)

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identical to that of the NMSSM given in Eq. (10) withtan� ¼ 1.

Figure 1(a) depicts the ratios �ða ! ���þÞ=�ða ! j0j0Þgiven in Eq. (10) as a function of tan� in the NMSSM andthe SLHM. Note that this ratio in the SLHM falls on thatwith the tan� ¼ 1 case in the NMSSM. Figure 1(b) depictsthe tan� dependence of the ratios of Eqs. (10) and (12) inboth models. If tan�> 1 in the NMSSM, the c �c contribu-tion becomes less important and the values of this ratio aresaturated. The predictions for the SLHM do not depend ontan�. Instead, the SLHM plots cross the NMSSM curves attan� ¼ 1 for all m�. We have to take care that the defini-

tions of tan� in the NMSSM and the SLHM are differentfrom each other.

We assume that we can observe a CP-odd scalar bosonoriginating from the SM-like Higgs decay, and collectenough data for determination of branching ratios. If theorigin of the CP-odd scalar is the SLHM, the ratio shouldbe fixed, e.g. �0:11 when m� > 20 GeV and b ¼ 0:5. If

the measured ratio is much different from that value, wecan exclude the SLHM, and the NMSSM is a strongcandidate. If ma;� ! 2mb, the kinematic factor for the

b �b channel vanishes and the ratios in Eqs. (10) and (12)tend to the ratios �ða=� ! ���þÞ=�ða=� ! c �cÞ.

In Fig. 1, we set b ¼ 0:5. If we cannot identify theb �b pair, i.e. b ¼ 0, the b-quark contribution dominatesin the denominator and the tan� dependence of the ratioof Eq. (10) is very weak when tan�> 1. Then it is hardto discriminate between the NMSSM and the SLHM inthis region. If b ¼ 1, we can tag all b �b jet pairs, and weobtain the ratio �ð��Þ=�ðc �cÞ, which allows us to dis-criminate between the two models clearly, which it is anideal case. We show the effects of b on the tan�dependence of the ratio in Fig. 2. We can see that thehigher the b, the easier it is to discriminate between thecurves. When we identify the resonance of the CP-oddscalar, b is strongly related to the b-tagging efficiency

at the LHC. The b-tagging is achieved by several algo-rithms at colliders, e.g. track counting, simple secondaryvertex, and their variants. The recent estimation of theCMS group tells us that the b-tagging efficiency canreach 0.562 [16]. We expect that b is close to this valueand find that it is conservatively possible to discriminatebetween the two models with the allowed values of theb-tagging efficiency.The a=� ! �� channel might be useful to find the

signal due to the relatively low background [17].However, the decay rates are too small to be measured�10�4, and even worse to involve many model parameters.Thus we do not consider this channel in this work.

IV. CONCLUDING REMARKS

The light CP-odd scalar boson a or �, produceddominantly in the decays h ! aa=��, provides a newphenomenology of the Higgs sector. We have to find theSM-like Higgs boson h through identifying a or� owing tothe large Brðh ! aa=��Þ. In this paper, assuming that wehave observed a CP-odd scalar boson, we present a strat-egy to determine it to be a or �, the CP-odd scalar in theNMSSM or in the SLHM. The signal cross section anddecay rates depend on many undetermined parameters.Since the Yukawa couplings in the SLHM involve commondependence on model parameters, the ratios of the decayrates are expressed by final state masses and ma only.However, in the NMSSM, the Yukawa couplings for theup-type quarks involve cot�, and those of down-typequarks and charged leptons involve tan� due to the super-symmetry. Therefore, the ratio of decay rates in theNMSSM can strongly depend on tan� and show muchdifference from that in the SLHM with fixed particlemasses. We define the decay width of non-b-tagged two-jet events, where the term with tan� dependence stillsurvives. In conclusion, if we measure the ratio of decayrate into � pairs to that into non-b-tagged two-jets, we can

Γ(a,

η→

τ-τ+

)/Γ(

a,η

→ jj

)

scalar mass (GeV)

εb=0.1

0

0.05

0.1

0.15

0.2

0.25

10 15 20 25 30 35 40 45 50

Γ(a,

η→

τ-τ+

)/Γ (

a,η

→ jj

)

scalar mass (GeV)

εb=0.5

0

0.05

0.1

0.15

0.2

0.25

Γ(a,

η→

τ-τ+

)/Γ(

a,η

→ jj

)

scalar mass (GeV)

εb=0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

10 15 20 25 30 35 40 45 50 10 15 20 25 30 35 40 45 50

FIG. 2 (color online). The ratio of the decay rate into ���þ to that into the non-b-tagged two-jet as a function of the CP-odd scalarmass for three different b-tagging efficiency values, b ¼ 0:1, 0.5, 0.9. The upper curves (blue) denote the NMSSM with tan� ¼ 10,the middle curves (black) the NMSSM with tan� ¼ 1 and the SLHM, and the lower curves (red) the NMSSM with tan� ¼ 0:5 in eachplot.

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easily discriminate between the two models in the case oftan� far from 1.

ACKNOWLEDGMENTS

C. S.K. was supported by the National ResearchFoundation of Korea (NRF) grant funded by the KoreanMinistry of Education, Science and Technology (MEST)

(No. 2011-0027275), (No. 2012-0005690) and (No. 2011-0020333). K.Y. L. was supported by WCU programthrough the KOSEF funded by the MEST (R31-2008-000-10057-0) and the Basic Science Research Programthrough the NRF funded by MEST (2010-0010916). J. P.was supported by the Taiwan NSC under Grant No. 100-2811-M-007-030 and 099-2811-M-007-077.

[1] R. Barate et al. (LEP Working Group for Higgs BosonSearches and ALEPH Collaboration), Phys. Lett. B 565,61 (2003); http://lepewwg.web.cern.ch.

[2] D. Fournier, The Hadron Collider Physics Symposium2011 (HCP2011) (Paris, France, 2011).

[3] ATLAS Collaboration, Eur. Phys. J. C 71, 1728 (2011);CMS Collaboration, Acta Phys. Pol. B 42, 1409 (2011).

[4] ATLAS Collaboration, Phys. Lett. B 710, 49 (2012).[5] CMS Collaboration, Phys. Lett. B 710, 26 (2012).[6] R. Dermisek, J. F. Gunion, and B. McElrath, Phys. Rev. D

76, 051105 (2007); R. Dermisek and J. F. Gunion, Phys.Rev. D 75, 075019 (2007).

[7] R. Dermisek and J. F. Gunion, Phys. Rev. D 73, 111701(R)(2006); C. S. Kim, S. C. Park, K. Wang, and G. Zhu, Phys.Rev. D 81, 054004 (2010).

[8] M. Schmaltz, J. High Energy Phys. 08 (2004) 056.[9] K. Cheung and J. Song, Phys. Rev. D 76, 035007 (2007).

[10] K. Cheung, J. Song, and Q.-S. Yan, Phys. Rev. Lett. 99,031801 (2007).

[11] K. Cheung, J. Song, P. Tseng, and Q.-S. Yan, Phys. Rev. D78, 055015 (2008).

[12] S. de Visscher et al., J. High Energy Phys. 08 (2009) 042;J.-M. Gerard and M. Herquet, Phys. Rev. Lett. 98, 251802(2007).

[13] F. Domingo, J. High Energy Phys. 04 (2011) 016; F.Domingo et al., J. High Energy Phys. 01 (2009) 061.

[14] K. Y. Lee and C. Yu, J. Korean Phys. Soc. 52, 36(2008).

[15] For review, see U. Ellwanger, C. Hugonie, and A.M.Teixeira, Phys. Rep. 496, 1 (2010).

[16] CMS Collaboration, CMS Physics Analysis Summary,Report No. BTV-10-001, 2010.

[17] S. Chang, P. J. Fox, and N. Weiner, Phys. Rev. Lett. 98,111802 (2007).

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