Production and decays of a light ϕ 0 in the LRTH model under the LHC Higgs data
aa r X i v : . [ h e p - ph ] N ov Production and decays of a light φ in the LRTH model underthe LHC Higgs data Yao-Bei Liu , , Zhen-Jun Xiao ∗
1. Department of Physics and Institute of Theoretical Physics,Nanjing Normal University, Nanjing 210023, P.R.China2. Henan Institute of Science and Technology, Xinxiang 453003, P.R.China
Abstract
In this paper we study the production and decays of a light pseudoscalar boson φ with m φ ≤ m h / Br ( h → φ φ ) can be as large as 80% and can suppress significantly the visible γγ signal rate, but the latest LHC Higgs data put a strong constraint on it: Br ( h → φ φ ) ≤ σ level; (b) the p -value of the LRTH model is around 0 .
6, smaller than that of the SM in mostof the parameter space and approaches the SM value 0 . f parameter;(c) the neutral pseudoscalar φ dominantly decay into b ¯ b and the decay rate Br ( φ → b ¯ b ) canbe larger than 80% for m φ ≤
60 GeV, and the second main decay mode is φ → τ + τ − witha branching ratio about 14%; and (d) at the future e − e + collider with √ s = 250 GeV, theprocesses e + e − → Zh → Z ( φ φ ) → Z (4 b, b τ ) are promising for discovering such a lightpseudoscalar φ . PACS numbers: 12.60.Fr, 14.80.Ec ∗ Electronic address: [email protected] . INTRODUCTION The discovery of a neutral Higgs boson with a mass around 125 GeV at CERN’s LargeHadron Collider (LHC) has been confirmed by the ATLAS and CMS collaborations [1–6], which heralds the beginning of a new era of Higgs physics. So far the observedsignal strengths, albeit with large experimental uncertainties, consistent with the StandardModel (SM) predictions [5, 6]. However, the SM suffers from the so-called gauge hierarchyproblem and cannot provide a dark matter candidate.During past three decades, many new physics (NP) models beyond the SM have beenconstructed by extending the Higgs sector in the SM, such as the Supersymmetric (SUSY)models [7], large extra-dimensions [8], two-Higgs doublet models (2HDM) [9], and littleHiggs models [10–12] etc. Very recently, the twin Higgs models have been proposed [13–16] as a solution to the little hierarchy problem. Here we focus on the left-right twin Higgs(LRTH) model which is implemented with the discrete symmetry being identified withleft-right symmetry [17, 18]. In the LRTH model, several physical Higgs bosons are stillleft after the spontaneous symmetry breaking. Another additional discrete symmetry isintroduced under an odd SU (2) L doublet ˆ h while the other fields are even. The lightestparticle in the neutral components ˆ h is stable and can be a candidate for weakly inter-acting massive particle (WIMP) dark matter. Besides ˆ h , the LRTH model predicts theSM-like Higgs boson h and other three scalars: φ and φ ± .The neutral φ is a pseudoscalar and thus there are no φ W + W − and φ ZZ couplingsat the tree level., which makes the φ rather special. The particle spectrum and collider signatures ofthe LRTH model have been widely studied, for example, in Refs. [19–27].In a recent paper [28], we studied the properties of the SM-like Higgs boson h , calcu-lated the new physics contributions to the decays h → ( γγ, Zγ, τ τ, W W ∗ , ZZ ∗ , τ τ ) in theLRTH model, performed a globe fit to the current LHC Higgs data, and found that allthe signal rates are suppressed when NP contributions are taken into account, while theLRTH prediction for R γγ agrees well with the CMS measurement R γγ = 0 . ± .
27 at 1 σ level. In this paper, we will study the production and decays of the light pseudo-scalar φ and to draw the possible constraints from currently available LHC Higgs data. If thisneutral φ were lighter than half of the SM-like Higgs boson h , i.e. m φ < m h /
2, the newdecay channel h → φ φ will be opened with a sizable branching ratio. Because the 125GeV SM Higgs decay width is small ( the measured value is about 4 MeV), such an exoticdecay mode can suppress greatly the visible signals of h and would have important phe-nomenological consequences [29–32]. We know that the current bound on the branchingratios to exotic states is still weak: a branching fraction as large as ∼
60% is allowed atthe 2 σ C.L. [5, 6]. If SM couplings are assumed, the universal Higgs fits constrain theinvisible branching fraction to be less than 25% at 95% C.L. [33–35], which still leavesappreciable scope for such an exotic decay mode. Thus, we will investigate the constrainsof the latest LHC Higgs data on the properties of such a light pseudoscalar φ in theLRTH model. We will also study the possibility of detecting such a light boson φ at highenergy colliders.This paper is organized as follows. In the next section, we briefly review the LRTHmodel and study the possible decay modes for a light pseudoscalar boson φ . In Sec. III,we investigate the decay branching ratios of h → φ φ and perform a fit using the latest2HC Higgs data. We study the possibility of detecting such a light pseudoscalar at theLHC experiments in section IV. Finally, we present our conclusion in Sec.V. II. THE LEFT-RIGHT TWIN HIGGS MODELA. Outline of the LRTH model
This model is based on the global U (4) × U (4) symmetry with a locally gauged subgroup SU (2) L × SU (2) R × U (1) B − L [13–17]. The twin symmetry is identified as the left-rightsymmetry which interchanges L and R, implying that the gauge couplings of SU (2) L and SU (2) R are identical ( g L = g R = g ). Two Higgs fields, H and ˆ H , are introduced andeach transforms as (4 ,
1) and (1 , H = (cid:18) H L H R (cid:19) , ˆ H = (cid:18) ˆ H L ˆ H R (cid:19) , (1)where H L,R and ˆ H L,R are two component objects which are charged under the SU (2) L × SU (2) R × U (1) B − L as H L and ˆ H L : (2 , , , H R and ˆ H R : (1 , , . (2)The global U (4) ( U (4) ) symmetry is spontaneously broken down to its subgroup U (3) ( U (3) ) with non-zero vacuum expectation values(VEV): < H > = (0 , , , f ) T , < ˆ H > = (0 , , , ˆ f ) T . (3)Each spontaneously symmetry breaking yields seven Nambu-Goldstone bosons, which canbe parameterized as H = f e iπf , with π = − N/ h − N/ h − N/ Ch ∗ h ∗ C ∗ N/ , (4)where π are the corresponding Goldstone fields. N is a neutral real pseudoscalar, C and C ∗ are a pair of charged complex scalar fields. ( h , h ) is the SM SU (2) L Higgs doublet.Accordingly, ˆ H is parametrized in the same way by its own Goldstone boson matrix ˆ π ,which contains ˆ N , ˆ C and ˆ h = (ˆ h +1 , ˆ h ).The original gauge symmetry SU (2) L × SU (2) R × U (1) B − L is broken down to the SM U (1) Y , six out of the 14 Goldstone bosons are respectively eaten by the SM gauge bosons W ± and Z , and additional gauge bosons W ± H , and Z H with masses of TeV order. Thenwe are left with the SM-like physical Higgs boson h , one neutral pseudoscalar φ , a pairof charged scalar φ ± , and an odd SU (2) L doublet ˆ h = (ˆ h +1 , ˆ h ) which only couples to thegauge boson sector. The lightest particle in ˆ h is stable and thus can be a candidate forWIMP dark matter, which have been studied for example in Refs. [21, 22].The covariant kinetic terms of Higgs fields can be written as [19] L H = ( D µ H ) † D µ H + ( D µ ˆ H ) † D µ ˆ H, (5)3here the covariant derivative is D µ = ∂ µ − ig W µ − ig n B − L W µB − L , and W = 12 W L √ W + L √ W − L − W L W R √ W + R √ W − R − W R , W B − L = W , (6)where g and g are the gauge couplings for U(1) B − L and SU(2) L,R , n B − L = 1 is the chargeof the field under U(1) B − L .In the LRTH model, a pair of vector-like quarks ( U L , U R ) are introduced to cancelthe one-loop quadratic divergence of Higgs mass induced by the top quark. The relevantLagrangian can be written as [19] L t = y L ¯ Q L τ H ∗ L U R + y R ¯ Q R τ H ∗ R U L − M ¯ U L U R + h.c. (7)where Q L = − i ( u L , d L ) T and Q R = ( u R , d R ) T .The details of the LRTH model as well as the particle spectrum, Feynman rules, andsome phenomenology analysis have been given for example in Ref. [19]. Here we will focuson the properties of the light pseudoscalar φ . B. The mass and decay of the light scalar φ In the LRTH model, the soft left-right symmetry breaking terms, so called µ − term,can generate mass for the light φ : V µ = − µ r ( H † R ˆ H R + h.c. ) + ˆ µ H † L ˆ H L . (8)The mass of φ and new scalar self-interactions are given by [19] m φ = µ r f ˆ f ˆ f + f cos x · ( ˆ f (cid:2) cos x + sin xx (3 + x ) (cid:3) f (cid:0) cos x + sin xx (cid:1) + 2 cos x + f cos x (1 + cos x )2 ˆ f ) , (9) hφ φ : vm h f · "
11 + 15 − m φ m h ! , (10)where x = v/ ( √ f ) and v = 246 GeV is the electroweak scale. Once f is fixed, the scaleˆ f can be determined from the electroweak symmetry breaking condition. In general ˆ f islarger f about 5 times or more [19, 20] and here we set ˆ f = 5 f as a rough estimate.From the expression of m φ in Eq. (9), one can see that the value of m φ depend ontwo parameters µ r and f . The value of µ r cannot be too large, since the fine-tuning of theSM-like Higgs boson mass m h will become severe for larger µ r [19]. Assuming 4 ≤ µ r ≤ ≤ f ≤ m φ : m φ ≤ . h → φ φ can be opened in the parameter space ofthe LRTH model considered here. The lower limit of m φ , say m φ > GeV £ m Φ £
500 700 900 1100 1300 1500051015202530 f H GeV L Μ r H G e V L FIG. 1: The upper constraint m φ ≤ . the non-observation of the decay Υ → γ + X [36, 37]. As illustrated in Fig. 1, the upperlimit m φ ≤ . f, µ r ) are in the light-darkregion in the f − µ r plane. The rare decays of Z → f ¯ f φ and Z → φ γ have been studiedin Ref. [38].In the LRTH model, the decays φ → gg, γγ are mediated by the one loop Feynmandiagrams involving the top quark and the new heavy quark T . The leading order decaywidths can be written as [39]Γ( φ → gg ) = √ G F α s m φ π (cid:12)(cid:12)(cid:12)(cid:12) − F / ( τ t ) y t − F / ( τ T ) y T (cid:12)(cid:12)(cid:12)(cid:12) , (11)Γ( φ → γγ ) = √ G F α e m φ π (cid:12)(cid:12)(cid:12)(cid:12) F / ( τ t ) y t + 43 F / ( τ T ) y T (cid:12)(cid:12)(cid:12)(cid:12) , (12)where F / = − τ [1 + (1 − τ ) f ( τ )] with f ( τ ) = [sin − (1 / √ τ )] and τ t = 4 m t /m φ , τ T = 4 m T /m φ . The explicit expressions of the relevant couplings y t and y T are of theform y t = S L S R , y T = m t m T C L C R , (13)5here the mixing angles S L,R and C L,R are S L = 1 √ p − ( y f cos 2 x + M ) /N t , C L = q − S L , (14) S R = 1 √ p − ( y f cos 2 x − M ) /N t , C R = q − S R , (15)with N t = q ( M + y f ) − y f sin x, (16)where x = v/ ( √ f ). The mass of the top quark and new heavy T -quark are thereforecan also be written as [19] m t = 12 ( M + y f − N t ) , m T = 12 ( M + y f + N t ) . (17)The parameter y in Eqs. (14-17) denotes the top quark Yukawa coupling, and can bedetermined by fitting the measured value of m t according to Eq. (17) for given values ofthe new physics parameters f and M .For φ → f i ¯ f i decays with f i the leptons and/or light quarks, the decay width can bewritten as: Γ( φ → f i ¯ f i ) = N C G F v m i m φ √ πf (1 − x i ) / , (18)where x i = 4 m i /m φ , N c = 3(1) for f i being a quark (lepton). It is easy to see that thedecays of φ to those light final state fermions, such as f i = ( e, µ, u, d, s ), are stronglysuppressed due to the severe helicity suppression ( ∝ m i ), and therefore can be neglectedsafely.In the LRTH model, consequently, the five major decay modes of φ are φ → b ¯ b, c ¯ c , τ + τ − , gg and γγ . The m φ -dependence of the branching ratios, assuming f = 500 GeVand M = 150 GeV, are illustrated in Fig.2a. The Fig. 2b shows the M -dependence ofthe branching ratio of the dominant φ → b ¯ b decay for fixed f = 500 and 1500 GeV.For φ → f ¯ f decays, furthermore, their decay rates in the LRTH model are stronglysuppressed by a factor of v / (2 f ) ≤ .
12 when compared with those of the SM Higgsboson decays H → f ¯ f . From Fig. 2 one can see that:1. The dominant decay mode of the light pseudoscalar φ is φ → b ¯ b . In the consideredregion of 500 GeV ≤ f ≤ GeV , the value of the branching ratio Br ( φ → b ¯ b ) isabout 81% for m φ = 50 GeV, and has a rather weak dependence on the variationsof the parameters f and M .2. The partial width into c ¯ c is smaller than that into τ + τ − , this is because we usethe running mass of the quarks evaluated at the scale m φ to calculate the Yukawacoupling. In the allowed parameter spaces, Br ( φ → τ + τ − ) ≃ Br ( φ → gg ) becomes large along with the increase of m φ , which can reach 30%for m φ = 200 GeV. This is due to the enhancement from the contribution of heavy T -quark, which is non-decoupled in the triangle loops.6 -5 -4 -3 -2 -1 B r an c h i ng R a t i o m (GeV)bbcc ggf = 500 GeVM = 150 GeV (a) f = 500 GeV f = 1500 GeV B r( bb ) M (GeV) m = 50 GeV (b)
FIG. 2: (a) the branching ratios of the considered φ decays as a function of m φ for given valuesof f = 500 GeV and M = 150 GeV. (b) the branching ratio of the dominant φ → b ¯ b decayversus M for fixed m φ = 50 GeV and f = 500 ,
4. The values of Br ( φ → γγ ) is very small: at the level of 10 − to 10 − in most ofthe parameter space. This is due to the absence of the coupling between φ and thecharged gauge bosons. III. EFFECTS OF A LIGHT φ AND THE LHC HIGGS DATA
In our calculations, we take the SM-like Higgs mass as m h = 125 . f , M and m φ . Following Ref. [19], we here also assumethat the values of the free parameters f and M are in the ranges of500 ≤ f ≤ , ≤ M ≤ . (19)while 8 ≤ m φ ≤ . A. The h → φ φ decay For m h ≥ m φ , the new decay channel h → φ φ will open and the partial decaywidth is given by Γ( h → φ φ ) = g hφ φ πm h s − m φ m h , (20)where g hφ φ is the coupling of hφ φ vertex. The open of this new decay mode, conse-quently, can suppress greatly the visible signals of the boson h at the LHC. Thus, themajor decay modes of the SM-like Higgs boson h in the LRTH model become now: h → φ φ , and h → f ¯ f ( f = b, c, τ ) , V V ∗ ( V = W, Z ) , gg, γγ, (21)7here W ∗ /Z ∗ denoting the off-shell charged or neutral electroweak gauge bosons. Thebranching ratio of h → φ φ can be written as Br ( h → φ φ ) = Γ( h → φ φ )Γ LRTH ( h ) + Γ( h → φ φ ) , (22)where Γ LRTH ( h ) denotes the total decay width of SM-like Higgs boson h for m φ > m h /
500 700 900 1100 1300 15000369121518 m = 20 GeV m = 40 GeV m = 60 GeV ( h ) ( M e V ) f (GeV) (a)
500 700 900 1100 1300 15000.00.20.40.60.81.0 m = 20 GeV m = 40 GeV m = 60 GeV B r( h ) f (GeV) (b) FIG. 3: The f -dependence of Γ( h → φ φ ) (left) and Br ( h → φ φ ) (right) for M = 150 GeVand three typical values of m φ = 20 ,
40 and 60 GeV.
In Fig. 3 we show the f -dependence of the decay width Γ( h → φ φ ) and the branchingratio Br ( h → φ φ ) for M = 150 GeV and three typical values of m φ : m φ = 40 ± h → φ φ decay becomessmaller rapidly along with the increase of the parameter f . This is because the couplingsof hφ φ is proportional to the suppression factor of ( v/f ) . For m φ = 40 GeV, we find2% ≤ Br ( h → φ φ ) ≤
70% for 500 ≤ f ≤ f = 500 GeV,the decay width Γ( h → φ φ ) can be as large as 16 MeV and thus can suppress greatlythe branching ratios for other decay modes of the SM-like Higgs boson h : such as thephenomenologically very interesting h → γγ decay. B. h → γγ decay in the LRTH model For the SM Higgs diphoton decay, the measured signal strength as reported by ATLAS[5] and CMS collaboration [6] are rather different, R γγ = σ ( H → γγ ) σ SM ( H → γγ ) = (cid:26) . +0 . − . , ATLAS;0 . ± . , CMS . (23)but these results are still consistent with the SM expectation within 2 σ level due to ratherlarge errors. If the excess (deficit) seen by ATLAS (CMS) were eventually confirmed by the8ear future LHC measurements, the extra NP contributions would be help to understandsuch excess or deficit [42–46].At the LHC, the Higgs single production is dominated by the gluon-gluon fusion (ggF)process. The hadronic production cross section σ ( gg → h ) has a strong correlation withthe decay width Γ( h → gg ). Other main production processes of the Higgs boson includevector-boson fusion (VBF), associated production with a W/Z boson (VH) and associatedproduction with a t ¯ t pair (ttH). For m h = 125 . h → γγ normalized to the SM values is generally definedas R γγ = [ σ ( pp → h ) × Br ( h → γγ )] LRT H [ σ ( pp → h ) × Br ( h → γγ )] SM . (24)
500 700 900 1100 1300 15000.00.30.60.91.21.5 CMS -1CMS +1ATLAS -2 R f (GeV) M = 0 M = 150 GeVATLAS -1 m = 50 GeV
FIG. 4: The f -dependence of R γγ in the LRTH model for m φ = 50 GeV and two typical valuesof parameters M as indicated. In Fig. 4 we plot R γγ versus f for m φ = 50 GeV and M = 0, 150 GeV, respectively.It can be seen from Fig. 4 that ratio R γγ in the LRTH model is always smaller than unit,and will approach one (the SM prediction) for a large f . On the other hand, one cansee that the ratio R γγ is insensitive to the variation of the mixing parameter M . Sincethe ATLAS diphoton data is above the SM value by about 2 σ , the predicted rate in theLRTH model is always outside the 2 σ range of the ATLAS data. But the theoreticalprediction for R γγ in the LRTH model is in good agreement with the current CMS datawithin 1 σ error for f ≥
600 GeV. The key point here is the large difference between thecentral values reported by ATLAS and CMS respectively. Further improvement of the R γγ measurements from both ATLAS and CMS collaboration are greatly welcome andwill play the key role in constraining the new physics models beyond the SM.In Fig. 5 we show the contours of R γγ in f - m φ plane and f - Br plane for R γγ ≥ . , . .
9, respectively. One can see that the assumption R γγ ≥ f ≥ ³ ³ ³
600 800 1000 1200 1400102030405060 f H GeV L m Φ H G e V L R ³ ³ ³
600 800 1000 1200 14000.00.10.20.30.40.5 f H GeV L B r H h ® Φ Φ L FIG. 5: The contours of R γγ in m φ − f plane (left) and Br ( h → φ φ ) − f plane (right) forthree typical values of R γγ ≥ . , . . GeV for m φ = 60 GeV, but leads to a limit f ≥
900 GeV for m φ = 30 GeV. FromFig. 5b, it is easy to see that one can draw strong constraint on the exotic decay rate Br ( h → φ φ ) from the measured Higgs diphoton rate. A limit of R γγ ≥ Br ( h → φ φ ) ≤ C. Global fit within LRTH model
Now we perform a global fit to the LRTH model with the method proposed in Refs. [48–56] by using the latest LHC Higgs data from both ATLAS [5, 57–62] and CMS collabo-ration [6, 63–67]. We use 20 sets of experimental data which include the measured signalstrengths for γγ , ZZ ∗ , W W ∗ , b ¯ b and τ + τ − channels, as listed explicitly in Table I.When fitting the various observable, we considered the correlation coefficients givenin Ref. [68] due to the independent data for different exclusive search channels by twocollaborations. The global χ function is defined as: χ = X i,j ( µ i − ˆ µ i )( σ ) ij ( µ j − ˆ µ j ) , (25)where σ ij = σ i ρ ij σ j , ˆ µ i and σ are the measured Higgs signal strengths and their 1 σ error, ρ ij is the correlation matrix, µ i is the corresponding theoretical predictions in terms of theLRTH parameters. The details about the statistical treatment are presented in AppendixA. In Fig. 6a we plot χ versus f for M = 150 GeV and m φ = 20 ,
40 and 60 GeV,respectively. One can see that the value of χ of the LRTH model is larger than that forSM for most of parameter space of f and approaches the SM value for a sufficiently large f . For a light pseudoscalar φ , for example setting m φ = 20 GeV, the Higgs data will10 ABLE I: The measured Higgs signal strengths ˆ µ i and the theoretical predictions µ i in theLRTH model. Here we set m φ =40 GeV, M =150 GeV and f = 800 , , and 1200 GeV.The following corrections are included in the fit: ρ γγ = − . ρ ZZ ∗ = − . ρ W W ∗ = − . ρ τ + τ − = − .
49 for ATLAS, and ρ γγ = − . ρ ZZ = − .
73 for CMS.Channel Signal strength ˆ µ i LRTH predictions µ i f=800 f=1000 f=1200ATLAS [5, 57–62]ggF+ttH, γγ . ± .
41 0.635 0.794 0.876VBF+VH, γγ . ± .
82 0.726 0.856 0.928ggF+ttH, ZZ ∗ . ± .
52 0.639 0.798 0.879VBF+VH, ZZ ∗ . ± .
12 0.732 0.861 0.931ggF+ttH,
W W ∗ . ± .
35 0.639 0.798 0.879VBF+VH,
W W ∗ . ± .
76 0.732 0.861 0.931VH tag, b ¯ b . +0 . − . τ + τ − . ± .
61 0.639 0.798 0.879VBF+VH, τ + τ − − . ± .
06 0.732 0.861 0.931CMS [6, 63–67]ggF+ttH, γγ . ± .
39 0.635 0.794 0.876VBF+VH, γγ . ± .
87 0.726 0.856 0.928ggF+ttH, ZZ ∗ . ± .
46 0.639 0.798 0.879VBF+VH, ZZ ∗ . ± .
38 0.732 0.861 0.9320/1 jet,
W W ∗ . ± .
21 0.621 0.798 0.853 Z ( ν ¯ ν ) h , b ¯ b . ± .
77 0.720 0.861 0.925 Z ( l + l − ) h , b ¯ b . ± .
97 0.720 0.861 0.925 W ( lν ) h , b ¯ b . ± .
87 0.720 0.861 0.9250/1 jet, τ + τ − . +0 . − . τ + τ − . +0 . − . τ + τ − . +1 . − . χ p − value 0.80 0.21 0.63 0.75 lead to effective constraint on the value of the parameter f : f ≥ σ (3 σ ) level.In Fig. 6b we plot the p -values versus m φ for M = 150 GeV and f = 800 , p − value, is about 0 .
80, which means that the SM has a chance of 80% to be the trueinterpretation of the data. One can see that the p -value become smaller for the LRTHmodel in large part of its parameter space, and approaches the SM value for a sufficientlylarge f . For m φ = 40 GeV and f = 1000(1200) GeV, its p -value is about 0 . . χ for Br ( h → φ φ ) against the parameter f . One11
00 700 900 1100 1300 1500020406080 m = 20 GeV m = 40 GeV m = 60 GeV f (GeV)SM, = 14.60 (a)
10 20 30 40 50 600.00.20.40.60.81.0 f = 800 GeV f = 1000 GeV f = 1200 GeV p - v a l ue m (GeV) SM (b) FIG. 6: (a) the values of χ versus f for M = 150 GeV and m φ = 20 ,
40 and 60 GeV; (b) the p -values versus m φ for M = 150 GeV and f = 800 , Σ Σ Σ
600 800 1000 1200 14000.000.050.100.150.200.250.300.35 f H GeV L B r H h -> Φ Φ L FIG. 7: The contours of χ of the branching ratio Br ( h → φ φ ) at the 1 σ , 2 σ and 3 σ level. can see that the current LHC Higgs data can put strict constraint on the exotic decay h → φ φ : for example, Br ( h → φ φ ) should be less than 30% at 3 σ level. IV. PHENOMENOLOGY OF A LIGHT φ When the decay h → φ φ is open, the decays h → φ φ → b , 2 b τ or 4 τ are themajor promising channels to detect such a light pseudoscalar at the LHC experiments.As demonstrated in Ref. [69], the process pp → W/Zh → l + 4 b + X ( l denotes one leptonand X denotes anything) may provide a clean signature out of the backgrounds for a light12iggs boson. Following the suitable cuts, the signal rate depends on an overall scalingfactor C b = (cid:18) g NPVVh g SMVVh (cid:19) × Br ( h → φ φ ) × Br ( φ → b ¯ b ) , (26)which determines the cross section of the process V h → V b at the LHC [69, 70]. In theLRTH model, y V = g LRTHVVh /g SMVVh = 1 − v / (6 f ) [19]. The DELPHI Collaboration [71] hasmade model-independent searches for the process e + e − → Zh → ZAA → Z + 4 b with A a pseudoscalar particle. However, the experimental upper bound on C b is relaxed forthis model ( C b ≥ m h = 110 GeV and m A = 12 GeV), and it is the same case in thesimplest little Higgs (SLH) model [72].
500 700 900 1100 1300 15000.00.10.20.30.40.5 m = 20 GeV m = 40 GeV m = 60 GeV C f (GeV)
3 level of global fit
FIG. 8: The value of C b versus f for three values of m φ . In Fig. 8 we plot the factor C b versus the parameter f in the LRTH model. One can seethat, for f = 500 GeV and m φ = 20 GeV, the value of C b can be as large as 0.5. However,it is smaller than 0.2 after considering the bound of global fit at 3 σ level. Noticing thatthe value of C b is directly proportional to the factor y V = (1 − v / (6 f )) in the LRTHmodel and thus becomes larger for a large f . For the process pp → W/Zh → l + 4 b + X ,the authors of Refs.[69, 70] have shown that the cut on invariant mass of the four bottomquarks can suppress efficiently the relevant backgrounds. It is worth of mentioning thatCheung et al. studied the h → ηη decay [69], calculated the total signal and backgroundcross sections at parton level in the SLH model with C b = 0 .
16 [69], and found asignificance S/ √ B = 3 . − . Of course, a much higher luminosityis needed to discover such a light scalar. For example, even for C b = 0 .
11 in the SLHmodel, the significance S/ √ B can be increased from 1.4 to 4.4 for a luminosity of 300fb − . Considering the LHC Higgs data bound at 3 σ level, we estimate the value of C b is approximately 0.19 in the LRTH model ( C b ≃ . × . ). Therefore, we hope thatby using the suitable cuts, the possible signatures of the light scalar in the LRTH modelmay be detected via the process pp → V h → V b at the LHC with a high luminosity of1300 fb − . Certainly, detailed confirmation of the observability of the signals would requireMonte-Carlo simulations of the signals and backgrounds, which is beyond the scope ofthis paper.
10 20 30 40 50 6010 -4 -3 -2 f = 500 GeV f = 800 GeV ( e + e - - h ) ( f b ) m (GeV) FIG. 9: The cross section of e + e − → hφ at an electron-positron collider with √ s = 250 GeVfor f = 500 ,
800 GeV.
500 700 900 1100 1300 1500020406080100120 ( e + e - - h Z -) Z -( ) Z ) ( f b ) m = 20 GeV m = 40 GeV m = 60 GeV f (GeV) (a)
3 levle of global fit
500 700 900 1100 1300 150005101520 m = 20 GeV m = 40 GeV m = 60 GeV ( e + e - - h Z -) Z -( ) Z ) ( f b ) f (GeV) (b)
3 level of global fit
FIG. 10: The cross sections at an electron-positron collider with √ s = 250 GeV and m φ =(40 ±
20) GeV; (a) e + e − → Zh → Z ( φ φ ) → Z (4 b ), (b) e + e − → Zh → Z ( φ φ ) → Z (2 b τ ). The light scalar φ can also be produced associated with the SM-like Higgs h at theInternational Linear Collider (ILC), which has been studied in Ref. [73]. The numericalresults show that the resonance production cross section can be significantly enhancedat the high energy linear collider with √ s ≃ m Z H . On the other hand, the properties of14M-like Higgs h can be precisely measured through the Zh associated production at thelinear collider [74–76]. Here we calculate the cross sections of the process e + e − → hφ and e + e − → Zh → Z ( φ φ ) → Z (4 b, b τ ) at an electron-positron collider with √ s =250 GeV, as shown in the Fig. 10. As shown in Fig. 9, the associated production rate Br ( e + e − → hφ ) is smaller than the order of 10 − fb at √ s =250 GeV, which can hardlybe utilized to search for the light scalar h . However, the production cross sections ofprocesses e + e − → Zh → Z b and e + e − → Zh → Z ( φ φ ) → Z (2 b τ ) can reach 120fb and 20 fb respectively, as illustrated in Fig. 10. Certainly, the cross sections wouldbecome smaller when we consider the global fit bound at 3 σ level (reduced about twothirds). Since these signals are free of the SM background, such production process maycontribute the light scalar discovery at an electron-positron collider. V. CONCLUSIONS
The LRTH model predicts one neutral pseudoscalar particle φ , which may be lighterthan half of the Higgs boson mass. In this work we focus on the case of m φ < m h / h → φ φ can be open. In this work, we firstly calculated the decaywidths and the branching ratios of the h → φ φ decay , as well as the major decay modesof the φ itself: such as φ → ( b ¯ b, c ¯ c, τ + τ − ) and φ → ( gg, γγ ) decays. We then examinedthe f , M and m φ -dependence of the decay widths and corresponding branching ratios,and checked the possible constraints on the LRTH model from the latest LHC Higgs dataon such a possibility. We performed a global fit by using 20 sets of the measured Higgssignal strengths as reported by ATLAS and CMS collaboration for γγ , ZZ ∗ , W W ∗ , b ¯ b and τ + τ − channels. We also studied the detection of φ at future electron-positron colliderexperiments.From our numerical calculations and the phenomenological analysis we found the fol-lowing points:1. Without the LHC constrains, the branching ratio of the decay h → φ φ can beas large as 80% and it can suppress significantly the visible γγ signal rate. Thecurrent LHC Higgs data for the γγ channel can place strong limit on such a decay:for example, Br ( h → φ φ ) ≤
26% for R γγ ≥ . p -value of the SM Higgs boson is 0 .
80, which means that the SM is a reasonablygood fit to the Higgs data. In the LRTH model, its p -value is smaller than that of theSM in most of the parameter space and approaches the SM value for a sufficientlylarge f parameter.3. The latest LHC Higgs data constrain the branching ratio Br ( h → φ φ ) to be lessthan 30% at 3 σ level.4. The neutral scalar φ dominantly decay into b ¯ b and the decay rate Br ( φ → b ¯ b ) canbe larger than 80% for m φ ≤
60 GeV. The second main decay mode is φ → τ + τ − with a branching ratio about 14%. At the future e − − e + collider with √ s = 250 GeV,the processes e + e − → Zh → Z ( φ φ ) → Z (4 b, b τ ) are promising for discoveringsuch a light pseudoscalar φ . 15 cknowledgments We thank Shufang Su for providing the Calchep Model Code. This work is supportedby the National Natural Science Foundation of China under the Grant No. 11235005 andthe Joint Funds of the National Natural Science Foundation of China (U1304112).
Appendix A: The statistical treatment and data
Take the h → γγ for instance, the Higgs signal strength µ γγ can be defined as µ γγ = ǫ ggF σ ggF + ǫ V BF σ V BF + ǫ V H σ V H ǫ ggF σ SMggF + ǫ V BF σ SMV BF + ǫ V H σ SMV H × Br ( h → γγ ) Br ( h → γγ ) SM , (A1)where the coefficients ǫ accounting for the relative weight of each production channel givenin [5, 6, 50]. The SM production cross sections and decay widths are taken from [47].The errors on the reported Higgs signal strengths ˆ µ i are symmetrized by δ ˆ µ i = r ( δ ˆ µ + ) + ( δ ˆ µ − ) , (A2)where δ ˆ µ ± are the one-sided errors given by the experimental collaborations [5, 6]. Forplotting distributions of a function of one (two) parameter, the 68% (1 σ ), 95% (2 σ ) and99 .
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