The New Compact 341 Model: Higgs Decay Modes
TThe New Compact 341 Model: Higgs Decay Modes
N.Mebarki, M.Djouala, J.Mimouni and H.Aissaoui
Laboratoire de Physique Mathmatique et SubatomiqueMentouri University, Constantine1, AlgeriaE-mail: [email protected]
Abstract.
New developments in the anomaly free compact 341 model are discussed and thehiggs bosons decay modes are studied taking into account the contributions of new fermions,gauge bosons and scalar bosons predicted by the model. It is shown from signal strengths andthe branching ratios of the various decay modes analysis and the LHC constraints that there isa room for this extended BSM model and it is viable.
1. Introduction
Despite all successes of the standard model, many questions remained unsolved and not wellunderstood like dark matter, neutrinos oscillation, matter anti-matter asymmetry etc... Tryingto find a solution to those problems, one needs to extend the standard model and go beyond(BSM). The most proposed model on the literature are the ones with two-Higgs doublets(THDM)[1], supersymmetry [2], 331, extra dimensions [3] and 341 gauge models [4, 11].Among those extensions, we focus on a model which is based on the SU (3) C ⊗ SU (4) L ⊗ U (1) N gauge symmetry (denoted by 341 model for a short hand). This model has new particles likeexotic quarks, new gauge bosons K , K (cid:48) , K ∓ , X ∓ , V ∓∓ , Y ∓ , Z (cid:48) and Z (cid:48)(cid:48) . Moreover, the 341model has a very specific arrangement of the fermions into generations; for leptons, one hasboth right and left handed helecities arranged in the same multiplet. In order to make themodel anomaly free, the second and (4) third quarks families has to belong to the conjugate 4 ∗ fundamental representation of the gauge group, while the first family transforms as a quadrupletin the fundamental representation. In this compact 341 model, we have a minimum of threescalars quartets[8] and after SSB which is achieved via three steps, one ends up with three CPeven neutral higgses h , h and h and eight CP odd massive higgses h ∓ , h ∓ and h ∓∓ .In this paper, we focus on the analysis of the neutral Higgs decays modes and discuss the signalstrengths and the branching ratios of the various decay modes as well as the LHC constraintsand show that there is a room for this extended BSM model and it is viable. In section 2,we present a brief review of the theoretical model. In section 3, we give the various analyticalexpressions of the partial decays width which we have derived using the new Feynman rules ofthe model. Finally, in section 4, we give our numerical results concerning the signal strengthof the various higgses branching ratios, after imposing the self consistency and compatibilityconstraints on the scalar potential of the model like triviality, unitarity, vacuum stability andnon-ghost conditions, make comparison with the signal strengths of the recent experimentaldata reported by ATLAS, CMS and combined ATLAS+CMS and draw our conclusions. a r X i v : . [ phy s i c s . g e n - ph ] S e p . The theoretical model The gauge group structure of the model is SU (3) C ⊗ SU (4) L ⊗ U (1) N and the electric chargeoperator (cid:98) Q is defined as [9]: (cid:98) Q/e = 12 (cid:18) T − √ T − √ γ (cid:19) + N (1)where: λ = diag (1 , − , , λ = 1 √ diag (1 , , − , λ = 1 √ diag (1 , , , − . (2)The fermions content of this model is as follows [4]: for the leptons (resp. quarks) denoted by L aL and Q L , Q iL respectively one has, f aL = ν a l a ν ca l ca ∼ (1 , , , Q L = u d U J ∼ (3 , ,
23 ) , Q iL = d i u i D i J i ∼ (3 , ∗ , −
13 )Where a=1,2,3 and i=2,3. Here U , J , D i and J i are exotic quarks with electric charges , , − and − respectively. Right-handed quarks transform as u R (3 , , ), d R (3 , , − ), U R (3 , , ), J R (3 , , ), u iR (3 , , ), d iR (3 , , − ), D iR (3 , , − ), J iR (3 , , − ). The most generalscalar potential with a Z discrete symmetry in the compact 341 model is given by [4]: V ( η, ρ, χ ) = µ η η † η + µ ρ ρ † ρ + µ χ χ † χ + λ ( η † η ) + λ ( ρ † ρ ) + λ ( χ † χ ) + λ ( η † η )( ρ † ρ ) + λ ( η † η )( χ † χ ) + λ ( ρ † ρ )( χ † χ ) + λ ( ρ † η )( η † ρ )+ λ ( χ † η )( η † χ ) + λ ( ρ † χ )( χ † ρ ) , (3)Where µ µρχ are the mass dimension parameters and λ S S=1 , η , ρ and χ (which are necessary to generate masses) aregiven by the following quartets: η = η η − η η , = √ ( R η + iI η ) η − √ ( v η + R η + iI η ) η +2 , ∼ (1 , , ,ρ = ρ +1 ρ ρ +2 ρ ++ , = ρ +11 √ ( v ρ + R ρ + iI ρ ) ρ +2 ρ ++ , ∼ (1 , , ,χ = χ − χ −− χ − χ χ − χ −− χ − √ ( v χ + R χ + iI χ ) , ∼ (1 , , − . The reason to choose the η quadruplet developing VeV only in the only in the 3 rd component isto avoid mixings between ordinary quarks and exotic ones. Imposing the tadpole conditions: µ + λ v η + 12 λ v ρ + 12 λ v χ = 0 , µ + λ v ρ + 12 λ v η + 12 λ v χ = 0 + λ v χ + 12 λ v η + 12 λ v ρ = 0 (4)helps to find the CP-even neutral scalars mass matrix in the basis ( R ρ , R χ , R η , whose eigenvaluesare [7]: M h = λ υ ρ + λ λ + λ ( λ λ − λ λ ) λ − λ λ υ ρ , M h = c υ χ + c υ ρ ≈ c υ χ , M h = c υ χ + c υ ρ ≈ c υ χ . (5)representing the masses of the physical scalars h , h and h respectively (the lightest neutralscalar h is identified as SM like Higgs boson) and eigenstates: h = R ρ , h = aR χ + bR η , h = cR χ + dR η (6)where a = λ − λ − (cid:113) ( λ − λ ) + λ λ + ( λ − λ − (cid:113) ( λ − λ ) + λ ) , b = λ λ + ( λ − λ − (cid:113) ( λ − λ ) + λ ) (7) c = λ − λ + (cid:113) ( λ − λ ) + λ λ + ( λ − λ + (cid:113) ( λ − λ ) + λ ) , d = λ λ + ( λ − λ + (cid:113) ( λ − λ ) + λ ) (8)The SSB steps are: SU (4) L ⊗ U (1) N −→ v χ SU (3) L ⊗ U (1) X , SU (3) L ⊗ U (1) X −→ v η SU (2) L ⊗ U (1) Y ,SU (2) L ⊗ U (1) Y −→ v ρ U (1) QED . Here stands for the weak isospin quantum number and the VeVs are such that ∼
246 GeV, v η ∼ O (TeV) and v χ ∼ O (TeV) ( v χ ∼ v η ) The masses of the charged gauge bosons in this modelare: M W ∓ = g L υ ρ , M K ,K (cid:48) = g L υ η , M K ∓ = g L υ η + υ ρ ) , M X ∓ = g L υ χ , M V ∓∓ = g L υ ρ + υ χ ) ,M Y ∓ = g L υ η + υ χ ) . (9)and of the neutral ones: M γ = 0 , M Z = g υ ρ c W , M Z (cid:48) = g c W υ η h W , M Z (cid:48)(cid:48) = g υ η (cid:18) (1 − s W ) + h W (cid:19) h W (1 − s W ) . (10)where W ∓ = ( W µ ∓ iW µ ) √ , K , K (cid:48) = ( W µ ∓ iW µ ) √ , K ∓ = ( W µ ∓ iW µ ) √ , (11)and X ∓ = ( W µ ∓ iW µ ) √ , V ∓∓ = ( W µ ∓ iW µ ) √ , Y ∓ = ( W µ − iW µ ) √ . (12)Here, cos θ = c w , sin θ = s w and h W = 3 − s w . It is worth to mention that, the mostattractive phenomenological features of the model is that in addition to the reproduction of allphenomenological success of SM, it has only 03 families of quarks and leptons and computationof the of U(1) gauge group running coupling shows the presence of a Landau pole at a scalearound 5 TeV. This implies the existence of a natural cut off for the model around the TeVscale and therefore solving hierarchy problem. Moreover, this cutoff can be used to implementfermions masses that are not generated by Yukawa couplings including neutrinos masses andconsequently one has a natural Dark matter candidate. . Higgs decays modes in the compact 341 model To determine the different SM Higgs-like branching ratios, we have derived all the Feynman rulesof the various vertices within the compact 341 model [7, 8] and get explicit analytical expressionsof the various h partial decay widths channels. The main Feynman diagrams contributing tothe neutral Higgs (denoted by in fig.1) double photon production ( h −→ γγ )are displayed inFig.1. Figure 1. the one-Loop diagrams contributing to h −→ γγ decay modes.The partial decay width is shown to have the following form:Γ( h −→ γγ ) = α m H π | (cid:88) V g HV V m V Q V A ( τ V ) + (cid:88) f g Hff m f Q f N c,f A ( τ f )+ (cid:88) f g HSS m S Q S N c,S A ( τ S ) | (13)Straightforward but lengthy calculations using the new derived Feynman vertices leads also to:Γ ( h −→ ll ) = g π m l m W m h (cid:18) − m l m h (cid:19) , Γ ( h −→ bb ) = 3 g π m b m W m h (cid:18) − m b m h (cid:19) , Γ( h −→ γZ ) = α m h π (cid:18) − M Z M h (cid:19) (cid:12)(cid:12)(cid:12)(cid:12) υ A SM sin θ W + A (cid:12)(cid:12)(cid:12)(cid:12) , Γ ( h −→ W ∗ W ) = 3 g m h π F (cid:18) m W m h (cid:19) , Γ ( h −→ Z ∗ Z ) = g g h ZZ π C W m h F (cid:18) m Z m h (cid:19)(cid:18) (cid:88) j = quarks ( g jV + g jA ) + (cid:88) l = leptons ( g lV + g lA ) (cid:19) . (14)where τ i = 4 m i /m h , V,f and S refer to Spin1, Spin and Spin0 particles respectively. The loopfunctions are given by : ( x ) = − x (cid:18) x − + 3 x − + 3(2 x − − f ( x − ) (cid:19) , A ( x ) = 2 x (cid:18) x − + ( x − − f ( x − ) (cid:19) ,A ( x ) = − x (cid:18) x − − f ( x − ) (cid:19) . (15)with f ( x ) = arcsin √ x f or x ≥ , − (cid:18) ln( √ − x − −√ − x − ) − ıπ (cid:19) f or x < . (16)Similarly, A = g h V V m V g ZV V ˜ A ( τ V , λ V ) + (cid:101) N c,f N c Q f m f g h ff ( g LZff + g RZff ) ˜ A ( τ f , λ f ) − N c Q S m S g h SS g ZSS ˜ A ( τ S , λ S ) , (17)with ˜ A ( x, y ) = 4(3 − tan θ W ) I ( x, y ) + (cid:18) (1 + 2 x − ) tan θ W − (5 + 2 x − ) (cid:19) I ( x, y ) , ˜ A ( x, y ) = I ( x, y ) − I ( x, y ) , ˜ A ( x, y ) = I ( x, y ) , (18)where I ( x, y ) = xy x − y ) + x y x − y ) (cid:18) f ( x − ) − f ( y − ) (cid:19) + x y ( x − y ) (cid:18) g ( x − ) − g ( y − ) (cid:19) ,I ( x, y ) = − xy x − y ) (cid:18) f ( x − ) − f ( y − ) (cid:19) .g ( x ) = √ x − − √ x f or x ≥ , √ − x − (cid:18) ln( √ − x − −√ − x − ) − ıπ (cid:19) f or x < . and F ( x ) = −| − x | ( 472 x −
132 + 1 x ) −
32 (1 − x + 4 x ) ln( x ) + 3(1 − x + 20 x ) √ x − x − x ) . (19)Here A SM represents the SM contribution, λ i = 4 m i /m Z and g h V V , g ZV V , g h ff , g LZff , g RZff , g h SS , g ZSS , g h V V are couplings constants. Here, Q V , Q f , Q S are electric charges of the vectors,fermions and scalars and N c ; f ; N c ; S are the number of fermion and scalar colors respectively[12].It is Here very important to mention that the SM contribution of the diphoton decay channelcomes essentially from the one loop top quark and the gauge bosons W. However, in the 341Model, beside the W and the top quark, it includes the new heavy gauge bosons K ∓ and V ∓∓ ,nd the charged higgs bosons h ∓ , h ∓ and h ∓∓ (there is no direct coupling between the exoticquarks and the Higgs like-boson h ). Regarding h and h higgs bosons, the expressions of mostof the various decay widths are the same as the ones of the higgs h except that the couplingsare different and replace m h by m h or m h . Among the interesting new decay modes, one has h −→ h h , h −→ h h , h −→ h h and h −→ h h with the corresponding decay width:Γ ( h −→ h h ) = 116 πm h ( g h h h ) (cid:18) − m h m h (cid:19) , Γ ( h −→ h h ) = 116 πm h ( g h h h ) (cid:18) − m h m h (cid:19) , Γ ( h −→ h h ) = 116 πm h ( g h h h ) (cid:18) − m h m h (cid:19) , Γ ( h −→ h h ) = 116 πm h ( g h h h ) (cid:18) m h m h − m h m h m h − m h + m h m h − m h + m h (cid:19) , (20)where g h h h = v χ (cid:18) λ γ + λ v η v χ α (cid:19) , g h h h = v χ (cid:18) λ σ + λ v η v χ β (cid:19) .g h h h = λ (cid:18) υ χ ( α σ + 2 αβγ ) + υ η ( βγ + 2 αγσ ) (cid:19) , g h h h = λ υ ρ αβ + λ υ ρ γσ. (21)The parameters α , β , γ and σ are functions of the potential parameters λ ’s (see refs.[7, 8]).It is worth to mention that in the decay modes h −→ γγ and h −→ Zγ , one has additionalcontributions of exotic fermions , charged scalars and the new gauge bosons (for more detailssee refs.[7, 8]).
4. Numerical results and conclusions
We have calculated the signal strength for each individual decay channel in the context of thecompact 341 model, an in order to reproduce the experimental results (e.g. m h ∼
126 GeVetc...), one has to take as inputs v χ ∼ v η ∼ m exotic quarks ∼
750 GeV (from the LHC experimentaldata concerning the lower bounds on exotic quarks), m h ∼
700 GeV and for gauge bosons seetable 1. Moreover, other inputs are the scalar potential couplings λ i ’s selected from a randomnumber generator and a Monte Carlo simulation after putting the self consistency constraints.In fact, we have obtained a confidence band due to the variations of the couplings’s within theallowed parameter space region after imposing the noghost, perturbative unitarity, trivialityand stability conditions. Table 2, shows the results of the signal strength experimental data ofATLAS, CMS, combined ATLAS+CMS and the predictions of the compact 341 model. Figs.2and 3, display the signal strengths for various decay modes compared to the ATLAS, CMS andthe combined ATLAS+CMS run2 data [13, 14]. Notice that the predictions of the 341 modelare fairly good and compatible with the run2 experimental data. This is a confirmation and aproof of the viability of the 341 BSM model. able 1. Masses of gauge bosons in compact 341 model.Gauge boson Mass TeVZ 0.091 Z (cid:48) Z (cid:48)(cid:48) W ∓ K , K (cid:48) K ∓ X ∓ V ∓∓ Y ∓ Table 2.
Signal strength data of ATLAS,CMS, ATLAS+ CMS and compact 341 model.Decay channel ATLAS CMS ATLAS+CMS The compact 341 model µ γγ . +0 . − . . +0 . − . . +0 . − . µ ZZ . +0 . − . . +0 . − . . +0 . − . µ W W . +0 . − . . +0 . − . . +0 . − . µ ττ . +0 . − . . +0 . − . . +0 . − . µ bb . +0 . − . . +0 . − . . +0 . − . Z*Z h W*W h h γγ h ττ bb h ATLAS
Z*Z h h γγ W*Wh h ττ bbh CMS
Figure 2.
Signal Strengths for various decay modes compared to the ATLAS and CMS run2data.
Z*Z h h γγ W*W h h ττ bb h ATLAS+CMS
Figure 3.
Signal Strengths for various SM like higgs decay modes compared to the combinedATLAS-CMS run2 dataRegarding the heavy higgses h and h , the branching ratios (BR) for the various modechannels are shown in figs.4 and 5. We have used a Monte Carlo simulation taking intoaccount the theoretical constraints mentioned before. We have checked that there is no bigeffect regarding the ambiguity in the choice of the renormalization parameter. For the higgs h , the dominant decay mode is h −→ h h where the branching ratio BR( h h ) is ∼ bτ + τ − , b ¯ bW + W − , ¯ bbγγ , ¯ bb ¯ bb etc..and reconstruct it from them although the background isvery important. To do so and minimize the background, we use some searches strategies like jetsubstructure techniques , unboosted and Boosted searches like exploiting the event kinematicdifferences between signal and background ,generalize transverse mass cuts to pair productionandincrease luminosity etc..in order to gain sensitivity in the main higgs decay channels then,reconstruct the semi-invisible particle decays and so on. What are the implications of the di-higgs beyond the standard model physics (BSM) and its relevance to it? how can BSM physicsalter SM di-higgs phenomenology?. It is worth to mention that important resonant and nonresonant enhancements are possible in a large varieties of BSM models. In the compact 341model, one can have non resonant enhancement at large transverse momentum due to new loopcontributions of exotic quarks and extra heavy gauge bosons or scalars and/or new (on-shell)resonances like the CP even higgs h where its decay to h h is the dominant channel (newstates induce large deviations in igure 4. The various h -decay channels in the 341 model Figure 5.
The various h -decay channels in the 341 modelinclusive cross section and differential distributions). In this case, one can separate the SMand BSM contributions using cuts on the invariant mass of the h h besides allowing to boundand reconstruct tan β = v η /v χ . For the decay mode h −→ Zγ , one gets a BR(Z γ ) ∼ h −→ ZZ , the branching ratio BR(ZZ) is very small ∼ − and has a big slope as afunction of m h ∈ [0.7,1.0] TeV (see fig.4). For the Higgs h and contrary to h the dominantdecay modes are h −→ ZZ , h −→ X + X − and h −→ V ++ V −− where BR(ZZ) ∈ [0.12,0.45],BR( X − X + ) ∈ [0.257,0.261] and BR( V ++ V −− ) ∈ [0.24,0.245] respectively when m h ∈ [0.45,1.8]eV . However, for the decay modes h −→ h h , h −→ J ¯ J the branching ratios are ∼ O (10 − ).Finally, for the h −→ γγ and 3 −→ b ¯ b , the branching ratios are very small ∼ O (10 − ) (formore details see refs.[7]-[8])
5. Acknowlegments
We are very grateful to the Algerian Ministry of education and research and DGRSDT for thefinancial support.
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