We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to
Standard Model. We point out that for the case of maximal mixing between
singlet scalars and standard Higgs boson the Higgs boson production cross
section is smaller than the standard Higgs boson production by factor
$\frac{1}{N+1}$, where N is the number of singlet scalar scalars. For the case
of big mixing Higgs boson could be nonobservable at LHC. However, there is also
a possibility for the observation of scalar singlets at LHC. As a
quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$
electroweak model with an additional gauge singlet chiral superfield.Comment: 9 pages, latex, no figure

Krasnikov, N. V.

English

arXiv

We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to Standard Model. We point out that for the case of maximal mixing between singlet scalars and standard Higgs boson the Higgs boson production cross section is smaller than the standard Higgs boson production by factor of big mixing Higgs boson could be nonobservable at LHC. However, there is also a possibility for the observation of scalar singlets at LHC. As a quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$ electroweak model with an additional gauge singlet chiral superfield.We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to Standard Model. We point out that for the case of maximal mixing between singlet scalars and standard Higgs boson the Higgs boson production cross section is smaller than the standard Higgs boson production by factor $\frac{1}{N+1}$, where N is the number of singlet scalar scalars. For the case of big mixing Higgs boson could be nonobservable at LHC. However, there is also a possibility for the observation of scalar singlets at LHC. As a quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$ electroweak model with an additional gauge singlet chiral superfield.We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to Standard Model. We point out that for the case of maximal mixing between singlet scalars and standard Higgs boson the Higgs boson production cross section is smaller than the standard Higgs boson production by factor $\frac{1}{N+1}$, where N is the number of singlet scalar scalars. For the case of big mixing Higgs boson could be nonobservable at LHC. However, there is also a possibility for the observation of scalar singlets at LHC. As a quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$ electroweak model with an additional gauge singlet chiral superfield.We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to Standard Model. We point out that for the case of maximal mixing between singlet scalars and standard Higgs boson the Higgs boson production cross section is smaller than the standard Higgs boson production by factor $\frac{1}{N+1}$, where N is the number of singlet scalar scalars. For the case of big mixing Higgs boson could be nonobservable at LHC. However, there is also a possibility for the observation of scalar singlets at LHC. As a quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$ electroweak model with an additional gauge singlet chiral superfield.We investigate a model of $SU(2) \otimes U(1)$ singlet scalars coupled to Standard Model. We point out that for the case of maximal mixing between singlet scalars and standard Higgs boson the Higgs boson production cross section is smaller than the standard Higgs boson production by factor $\frac{1}{N+1}$, where N is the number of singlet scalar scalars. For the case of big mixing Higgs boson could be nonobservable at LHC. However, there is also a possibility for the observation of scalar singlets at LHC. As a quasirealistic example we discuss a supersymmetric $SU(2) \otimes U(1)$ electroweak model with an additional gauge singlet chiral superfield

Krasnikov, N.V.

CERN Document Server

arXiv:hep-ph/9709467v1  26 Sep 1997Influence of SU (2)⊗ U (1) singlet scalars on Higgsboson signal at LHCN.V.Krasnikov ∗CERN, Geneva 23, SwitzerlandSeptember,1997AbstractWe investigate a model of SU(2) ⊗ U(1) singlet scalars coupled to StandardModel. We point out that for the case of the maximal mixing between singlet scalarsand standard Higgs boson the Higgs boson production cross section is smaller thanthe standard Higgs boson production by factor 1N+1 , where N is the number of singletscalars. For the case of big mixing Higgs boson could be nonobservable at LHC.However, there is also a possibility for the observation of scalar singlets at LHC.As a quasirealistic example we discuss supersymmetric SU(2) ⊗ U(1) electroweakmodel with an additional singlet chiral superfield.∗On leave of absence from INR, Moscow 117312, Russia1One of the main tasks of existing and future collider experiments (LEP2, LHC, NLC,..)is the search for the Higgs boson. Its detection would be the confirmation of the sponta-neous symmetry breaking mechanism and an experimental ”proof” of the renormalizabilityof the electroweak interactions. For the two most popular models of electroweak physics,the Standard Model(SM) and its minimal supersymmetric generalization(MSSM) LEP2and LHC will be able to discover the Higgs boson with a mass from 77 GeV(current stan-dard Higgs boson mass limit [1]) up to 103 GeV(upper limit comes from requirement oftree level unitarity [2]). In the SM and MSSM the Higgs boson for mh ≤ 400 GeV (thisbound comes from an analysis of high precision LEP1 data [3]) is rather narrow that leadsto sharply peaked resonance. The signal to background ratio in the resonance region ismostly determined by the experimental energy resolution.In this paper we investigate the influence of SU(2)⊗ U(1) singlet scalar fields on thedetection of the Higgs boson at LHC. Namely, we investigate the influence of the mixingbetween SU(2)⊗U(1) scalar singlets and the Higgs boson. We find that in an extreme caseof maximal mixing between SU(2) ⊗ U(1) scalars and the Higgs boson the Higgs bosonproduction cross section drops by factor 1N+1(N is the number of scalar singlets) thatcould lead to nonobservability of the Higgs boson at LEP or LHC. For instance, for LHCfor N ≥ 2 it is possible to make Higgs signal nonobservable for an integrated luminosityL = 105pb−1. However, there is also possibility for the observation of the scalar singletsat LHC. As a quasirealistic example we discuss a supersymmetric electroweak model withsinglet chiral superfield. In the limit when the number of singlet scalar fields N →∞ wefind that the Higgs boson mass is continuously distributed. A model of the Higgs bosonwith continuously distributed mass has been proposed in ref. [4]. It should be noted thatthe models with additional light SU(2) ⊗ U(1) singlet scalar boson have been discussedin the literature [5]. In such models Higgs boson invisible decay modes into light singletscalars result in a modification of branching ratios that leads to slightly different strategyfor the Higgs boson search. In recent paper of T.Binoth and J.J. van der Bij [6] a modelof light scalar singlets strongly coupled to the standard Higgs boson has been discussed.In such model Higgs boson decays mainly into light singlet scalar bosons and its decaywidth is not small that considerably affects the signal to background ratio S/B makingHiggs signal diluted. We consider slightly different situation when big mixing of the Higgsboson with scalar singlets results in the appearance of many ”Higgs like” scalar bosonsin the spectrum and the production cross section of ”Higgs like” bosons is smaller thanthe standard Higgs boson cross section production that leads to the Higgs signal dilution.In considered model the Higgs bosons branching ratios are not modified compared to thestandard Higgs boson case.Let us start with the simplest modification of the SM model, namely, we add to theSM an additional real scalar singlet φ(x). Take the effective potential in the formV = λ(H+H − v22)2 + k(H+H − v22)φ+M2φ22. (1)After the spontaneous symmetry breaking < H >= v√2, < φ >= 0 we find that in theunitare gauge H(x) = (0, v+h(x)√2) the mass matrix for the Higgs field h(x) and singlet fieldsφ(x) takes the formMˆ = m2hh2(x) +M2φ2(x) + 2δm2h(x)φ(x), (2)where m2h = 2λv2 and δm2 = kv2. The eigenstates of the mass matrix (2 ) are the fieldsh1(x) = h(x) cos(δ)− φ(x) sin(δ), (3)φ1(x) = φ(x) cos(δ) + h(x) sin(δ) (4)with eigenvaluesMh1,φ1 =m2h +M22±√(m2h −M2)24+ (δm2)2 (5)and with mixing angletan(2δ) =2δm2M2 −m2h. (6)Original Higgs field h(x) is expressed in terms of the h1(x), φ1(x) fields ash(x) = h1(x) cos(δ) + φ1(x) sin(δ) (7)3The main production mechanisms of the Higgs boson at LEP and LHC are the Higgsbremsstrahlung of a real(LEP2) or virtual(LEP1) Z-boson and gluon fusion correspond-ingly. As a consequence of the formula (7) we find that the production cross sectons ofthe h1 and φ1 bosons are the same as for the standard Higgs boson production with thecorresponding mass except multiplicative factors cos2(δ)(h1-boson) and sin2(δ)(φ1-boson).The branching ratios of the h1 and φ1 bosons into fermion-antifermion pairs, 2 gluons or2 photons are the same as for the SM Higgs boson. As a result of the additional factorscos2(δ), sin2(δ) the signal significance S = NS√NBwill be smaller than for the case of the SMHiggs boson provided the mass difference between the h1 and φ1 bosons is bigger than thedetector mass resolution. To be concrete consider the Higgs boson production at LHC 1.For the case 100 GeV ≤ mh ≤ 130 GeV the most promising signature for the search forthe Higgs boson ispp→ (h→ γγ) + ... (8)For low luminosity stage with an integral luminosity L = 3 · 104pb−1 CMS detector willbe able to discover the standard Higgs boson with the signal significance [8] 6 ≤ S ≤ 9.The ATLAS detector [9] will have the similar signal significance as the CMS. The massresolution of the diphoton pair invariant mass at low luminosity stage is assumed to beδmγγ ≈ 0.5 GeV. For the case of maximal mixing δ = pi4 and for Mh1 −Mφ1 ≥ 1 GeVas a result of nonzero mixing we shall have two resonances in the diphoton spectrum.For the case of maximal mixing the Higgs boson production cross section decreases byfactor 2 and the signal significance of each of two Higgs like resonances will be between3 and 4.5. According to standard convention Higgs boson is assumed to be discoveredprovided the signal significance is bigger than 5. So at low luminosity stage in the caseof maximal mixing the Higgs boson escapes from being discovered. At high luminositystage for an integral luminosity L = 105pb−1 the signal significance for CMS detector for110 GeV ≤ mh ≤ 140 GeV is estimated to be 11 ≤ S ≤ 13. At high luminosity stagetwo Higgs like resonances will be detected at S ≥ 5 significance level. Therefore there is1LEP1 data [7] lead to the bound sin2(δ) ≤ 0.1 for mφ1 ≤ 30 GeV4nonzero probability instead of the single Higgs boson to discover 2 Higgs bosons by themeasurement of the diphoton spectrum.For the Higgs boson mass interval 140 GeV ≤ mh ≤ 600 GeV the most promisingsignature for the Higgs boson detection is through the decayh→ ZZ∗(Z)→ 4leptons. (9)For the Higgs boson mass 200 GeV ≤ mh ≤ 400 GeV the signal significance for anintegrated luminosity L = 105pb−1 is estimated to be S = 16 − 18 [8]. For such massinterval the maximal mixing will be detected at S ≥ 5 significance level. Moreover forsuch mass interval it is possible to detect two Higgs like resonances at 5σ level providedthe mixing angle sin2(δ) ≥ 0.32.At LEP1 and LEP2 the effects of nonzero mixing are the same as at LHC provided themass difference between the scalars h1 and φ1 is bigger than the detector energy resolutionδE ∼ 4 GeV. Again instead of the single Higgs boson we shall have two Higgs like bosonswith production cross sections for the maximal mixing two times smaller the standardone. Therefore the signal significance S = NS√NBis decreased by factor two compared tothe standard case. An increase of an integral luminosity L by factor 4 just compensatesthe decrease of the Higgs boson production cross section.Consider now the case of N additional SU(2) ⊗ U(1) singlet scalar fields. Take theeffective potential in the formV = λ(H+H − v22)2 + ki(H+H − v22)φi +12m2ijφiφj, (10)where i, j = 2, 3, ...N +1. The equations for the determination of the nontrivial minimumof the effective potential (10) have solution < H >= v√2, < φi >= 0. In the unitare gaugeH = (0, v+h(x)√2) the mass matrix for the Higgs field φ1(x) ≡ h(x) and singlet fields φi(x)(i = 2, 3, ..N + 1) has the formMˆ2 = m2ijφi(x)φj(x), , (11)where i, j = 1, 2...N + 1, m211 = 2λv2, m21i = m2i1 =kiv2. After the diagonalization the5mass matrix (11) takes the formMˆ2 =M2i (φ′i)2, (12)where φ′i = Oijφj , φi = Ojiφ′j and OijOik = δjk. Parameters m2ij are arbitrary so ingeneral orthogonal matrix Oij can have arbitrary form. Consider as an extreme examplethe case of maximal mixing, i.e.O1,1 = O2,1 = ... = ON+1,1 =1√N + 1. (13)For the mixing matrix (13) the original Higgs field h(x) ≡ φ1(x) is a superposition of theof the fields φ′i(x) with definite massh(x) =1√N + 1N+1∑i=1φ′i (14)Again as in the case of N = 1 one can find that the branching ratios for the Higgs likebosons φ′i(x) are the same as for the standard Higgs boson but their production crosssection drops by factor 1N+1compared to the standard Higgs boson case. For the Higgsboson mass range interval 100 GeV ≤ mh ≤130 GeV and for an integrated luminosityL = 105pb−1 the signal significance in an extreme case of maximal mixing is 2.7 ≤ S ≤ 4.1for N = 2. So the Higgs boson will escape from being detected. However for totalluminosity L = 4 · 105pb−1 the signal significance is bigger than S ≥ 5.4 and 3 Higgslike bosons could be discovered. Similar analysis works for the Higgs boson mass rangeinterval 140 GeV ≤ mh ≤ 400 GeV, where the most promising signature is the use of theHiggs boson decay into 4 leptons (9). As it follows from the LEP1 data [7] it is possiblefor the Higgs like bosons with masses m ≤ 30 GeV to escape from the detection for themaximal mixing case provided N ≥ 10.As a toy example consider the following mass spectrum of the φ′i(x) fields:M2(i) = M20 +δ · iN + 1, (15)where i = 1,2...N+1. In the limit N →∞ we shall have the Higgs boson with continuouslydistributed mass M20 ≤ M2h ≤ M20 + δ. For δ ∼ M2 Higgs boson has big decay width6and escapes from the detection. Such Higgs boson with continuously distributed masslooks like broad resonance with decay width Γ =√M20 + δ −M0 and a mass M20 + δ2 .The branching ratios for such ”modified” Higgs boson coincide with the correspondingbranching ratios of the standard Higgs boson unlike to the model of ref. [6] where the bigdecay width of the Higgs boson is due to Higgs boson decays into invisible modes. Suchmodels with continuously distributed Higgs boson mass have been discussed in ref. [4].As a quasirealistic example consider NMSSM(NMSSM =MSSM + chiral SU(2)⊗U(1)singlet superfield) [10]. The superpotential of the NMSSM contains a term δW = λσH¯Hin the superpotential that relates the SU(2)⊗U(1) singlet chiral superfield σ with chiralsuperhiggs fields H and H¯ . For small coupling constant λ singlet superfield σ effectivelydecouples from the MSSM superfields and most of the NMSSM predictions(spectrum,branching ratios, cross sections...) coincide with the corresponding MSSM predictions.The general form of the soft breaking terms for complex scalar singlet field σ(x) =σ1(x)+iσ2(x)√2isVsoft,σ =m21σ212+m22σ222+m212σ1σ2 + (k1σ1 + k2σ2)H¯H + c1σ1 + c2σ2 + ... (16)The nondiagonal terms in (16) lead to nonzero mixing between the singlet fields σ1(x),σ2(x) and the lightest Higgs field h(x). It is possible to choose parameters of the modelsuch that the mixing is the maximal one, i.e.h(x) =1√3(φ1(x) + φ2(x) + φ3(x)), (17)where the fields φi(x) have masses Mi. As it has been discussed before for such case weshall have Higgs boson signal dilution compared to the standard case.To conclude, in this paper we have studied the influence of scalar singlets on the Higgsboson detection at LHC. We have found that big mixing of singlet fields with Higgs bosonfield can lead to the nonobservation of the Higgs boson at LHC or to the observation ofthe additional Higgs like states.I am indebted to the collaborators of the INR theoretical department for discussionsand critical comments. I thank CERN TH Depatment for the hospitality during my stay7at CERN where this paper has been finished. The research described in this publicationwas made possible in part by Award No RP1-187 of the U.S. Civilian Research andDevelopment Foundation for the Independent States of the Former Soviet Union(CRDF).Note added. After this paper has been finished I became aware of paper by AnnindyaDatta and Amitava Raychandhuty, hep-ph/9708444, where the effects of mixing betweensinglet and Higgs fields have been studied.8References[1] A.Sopczak. Talk given at the international conferenceNon-Accelerator searches for new physics, Dubna, 7-11 july 1997.[2] B.W.Lee, C.Quigg and C.B.Thacker, Phys.Rev. D10(1974)1145.[3] J.Ellis, Phenomenology of LEP2 physics, CERN-TH/97-131.[4] N.V.Krasnikov, Phys.Lett.B325(1994)430.[5] R.E.Schrock and M.Suzuki, Phys.Lett.B100(1982)250;L.F.Li, Y.Liu and L.Wolfenstein, Phys.Lett.B159(1985)45;D.Chang and W.Keung, Phys.Lett.B217(1989)238;N.V.Krasnikov, Phys.Lett.B291(1992)89;A.S. Joshipura and J.W.F.Valle, Nucl.Phys.B397(1993)105.[6] T.Binoth and J.J. van der Bij, Z.Phys.C75(1997)17.[7] O.Adriani et al.,, Phys.Lett.B294(1992)457;D.Buskulic et al., Phys.Lett.B313(1993)312.[8] CMS, Technical Proposal, CERN/LHCC/94-38 LHCCP1, 15 december 1994.[9] ATLAS, Technical Proposal. CERN/LHCC/94-43 LHCCP2, 15 december 1994.[10] J.Ellis et al., Phys.Rev.D39(1989)844;L.Durand and J.L.Lopez, Phys.Lett.B217(1989)463;S.F.King and P.L.White, Phys.Rev.D52(1995)4183;M.Drees, Int.J. Mod.Phys.A4(1989)3635;U.Ellwanger, M.Rausch de Traubenberg and C.A.Savoy, Phys.LettB315(1993)331;Z.Phys.C67(1995)665; Nucl.Phys.B492(1997)21.9

Influence of $SU(2) \otimes U(1)$ singlet scalars on Higgs boson signal at LHC

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Influence of SU(2)⊗U(1)SU(2) \otimes U(1)SU(2)⊗U(1) singlet scalars on Higgs boson signal at LHC

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Influence of $SU(2) \otimes U(1)$ singlet scalars on Higgs boson signal at LHC