New physics effect in advanced economical 3 - 3 - 1 models

28) gZ ′ V (f) = √ 1− 4s2WT8(fL) + √ 3s2W√ 1− 4s2W (X +Q)(fL), (2.29) gZ ′ A (f) = c2W√ 1− 4s2W T8(fL)− √ 3s2W√ 1− 4s2W T3(fL). (2.30) 2.2.2. Interactions of scalars with gauge bosons Derived from the Lagrangian ∑ S(D µS)†(DµS), with S = η, χ. the relevant interactions and couplings are resulted as in Tables 2.1 to 2.9. 2.2.3. Scalar self-interactions and Yukawa interactions Since we work in the unitary gauge, the scalar self-interactions include only those with physical scalar particles. Note that the interactions between the normal scalars and the inert scalars were given in [35]. Therefore, we necessarily calculate only self-interactions of the normal scalars, Self-interaction results of scalars are often presented in tables 2.10 and 2.11. The inert scalars do not have Yukawa interaction with fermions due to Z2 symmetry. Therefore, we turn to investigate the Yukawa interactions of the normal scalars, the relevant interactions and couplings are resulted as in Tables 2.12 to 2.14. 2.3. Phenomenology 2.3.1. The SM like Higgs particle The discovery of the Higgs particle marks the success of the LHC, and its couplings can be summarized via the combined best-fit signal strength µh = 1.1± 0.1, which deviates 10% from the standard model. Let us particularly investigate the Higgs coupling to two photons that substitutes in: µγγ = σ(pp→ h)Br(h→ γγ) σ(pp→ h)SMBr(h→ γγ)SM , (2.31) where the numerator is given by the considering model once measured by the experiments, while the denominator is the standard model prediction. The Higgs production dominantly comes from the gluon gluon fusion via top loops. The new physics effects are shown in the picture 2.1. Note that the (b) diagram was skipped in [42,74]. 8 GG h t cξ (a) G G h Ja −tθsξ (b) Figure 2.1: Contributions to the Higgs production due to gluon-gluon fusion. The main contributions to decaying the Higgs into two photons are shown in the diagram 2.2. γ γ h t cξ (a) γ γ h Ja−tθsξ (b) γ γ h W cξ (c) γ γ h X(Y ) sθ−ξ sθ ( −sξ tθ ) (d) γ γ h W cξ (e) γ γ h X(Y )sθ−ξ sθ ( −sξ tθ ) (f) γ γ h H±,φ (g) gH±,φ γ γ h H±,φ (h) gH±,φ Figure 2.2: Contributions to the decay h→ γγ. Our numerical study yields a maximal bound, 1 ≤ µγγ ≤ 1.06, in agreement with the data. 9 2.3.2. The Bs-B¯s mixing and rare Bs → µ+µ− decay The left graph of 2.3 for this mixing as explained by basic Z ′ boson. We have: [(V ∗dL)32(VdL)33] 2 w2 < 1 (100 TeV)2 . (2.32) The CKM factor is given by |(V ∗dL)32(VdL)33| ' 3.9× 10−2, which implies w > 3.9 TeV, slightly larger than the bound given in [35]. Correspondingly, the Z ′ mass is bounded by mZ′ > 4.67 TeV, provided that s 2 W ' 0.231 is at the low energy regime of the interested precesses. The new physics contribution is demonstrated by the right graph in 2.3 by basic Z ′ boson exchange. Generalizing the results in [88], we obtain the signal strength, µBs→µ+µ− = Br(Bs → µ+µ−) Br(Bs → µ+µ−)SM = 1 + r2 − 2r, (2.33) where r = ∆C10/C10 (C10 = −4.2453 is standard model Wilson coefficient) is real and bounded by 0 ≤ r ≤ 0.1. It leads to mZ′ ≥ 2.02 TeV. (2.34) Z ′ s b b s Z ′ µ− µ+ b s Figure 2.3: Contributions to the Bs-B¯s mixing and rare Bs → µ+µ− decay due to the tree-level flavor-changing coupling. 2.3.3. Radiative β decay involving Z ′ as a source of CKM unitarity violation CKM unitarity states that ∑ k V ∗ ikVjk = δij and ∑ i V ∗ ikVil = δkl, where we relabel V = VCKM, i, j = u, c, t, and k, l = d, s, b. The standard model prediction is in good agreement with the above relations [1]. How- ever, a possible deviation would be the sign for the violation of CKM unitarity. Considering the first row, the experiments constrain [1] ∆CKM = 1− ∑ k=d,s,b |Vuk|2 < 10−3. (2.35) Since mW ' 80.4 GeV and mZ′ in the TeV range (in fact, mZ′ > 4.67 TeV), we have ∆CKM < 10 −5. The effect of CKM unitarity violation due to Z ′ is negligible and thus the model easily evades the experimental bound. This conclusion contradicts a study of the minimal 3-3-1 model in [83]. 10 2.3.4. LEPII search for Z ′ The effective Lagrangian: Leff ⊃ g 2[aZ ′ L (e)] 2 c2Wm 2 Z′ (e¯γµPLe)(µ¯γµPLµ) + (LR) + (RL) + (RR), (2.36) LEPII studied such chiral interactions and gave respective constraints on the chiral cou- plings, which are typically in a few TeV [101]. Choosing a typical bound derived for a new U(1) gauge boson like ours, it yields [102] g2[aZ ′ L (e)] 2 c2Wm 2 Z′ < 1 (6 TeV)2 . (2.37) This translates to m′Z > 6g cW aZ ′ L (e) TeV = g cW √ 3(1− 4s2W ) TeV ' 354 GeV. (2.38) In fact, the Z ′ mass is in the TeV range, it easily evades the LEPII searches. 2.3.5. LHC searches for new particle signatures Dilepton and dijet searches Because the neutral gauge boson Z ′ directly couples to quarks and leptons, the new physics process pp → ll¯ for l = e, µ happens, which is dominantly contributed by the s- channel exchange of Z ′. 2% width 4% width 8% width 16% width 32% width Model 1000 2000 3000 4000 5000 10-5 10-4 0.001 0.01 0.1 1 10 mZ¢ @GeVD Σ Hpp ® Z ¢ ® llL@ pb D Figure 2.4: Cross section σ(pp→ Z ′ → ll¯) as a function of Z ′ mass. We show the cross section for the process pp→ Z ′ → ll¯ in 2.4 where l lis either electron or muon which has the same Z ′ coupling. The experimental searches use 36.1 fb−1 of pp collision data at √ s = 13 TeV by the ATLAS collaboration [106], yielding negative signal. 11 for new high mass events in the dilepton final state. This translates to the lower bound on Z ′ mass, mZ′ > 2.75 TeV, for the considering model, in agreement with a highest invariant mass of dilepton measured by the ATLAS. Diboson and diphoton searches At LHC, the collision of proton beams pp will generate new particles , and then they decay to pair of boson or photon, or lose energy. The generation of the pair of boson or photon can be related to new particles , such as new neutral Higss and Z ′, cthese particles have already studied and in agreement with experiments Monojet and dijet dark matter The missing energy can be happened due to the generation of DM, according to the law of energy conservation. This missing energy is equivalent to monojet and dijet. 12 H ′1 H ′1 g g g H H ′1 H ′1 g g g H H ′1 H ′1 g g g H H ′1 H ′1 g g g H H ′1 H ′1 q qc g H H ′1 H ′1 q g q H A′1 H ′1 q qc g Z ′ A′1 H ′1 q qc g Z ′ A′1 H ′1 g q q Z ′ A′1 H ′1 g q q Z ′ Figure 2.5: Monojet production processes associated with a pair of dark matter. 13 CHAPTER 3. THE FLIPPED 3-3-1 MODEL The results of this chapter are based on the work published on JHEP bf 08 (2019) 051. 3.1. General flipped 3-3-1 model 3.1.1. Particle content The 3-3-1 gauge symmetry is given by SU(3)C ⊗ SU(3)L ⊗ U(1)X , (3.1) The electric charge and hypercharge are embedded as Q = T3 + βT8 +X, Y = βT8 +X, (3.2) he fermion content is written as ψ1L =  ξ+ 1√ 2 ξ0 1√ 2 ν1 1√ 2 ξ0 ξ− 1√ 2 e1 1√ 2 ν1 1√ 2 e1 E1  L ∼ ( 1, 6,−1 3 ) , (3.3) ψαL =  να eα Eα  L ∼ ( 1, 3,−2 3 ) , (3.4) eaR ∼ (1, 1,−1), EaR ∼ (1, 1,−1), (3.5) QaL =  da −ua Ua  L ∼ ( 3, 3∗, 1 3 ) , (3.6) uaR ∼ (3, 1, 2/3), daR ∼ (3, 1,−1/3), UaR ∼ (3, 1, 2/3), (3.7) The scalar content responsible for symmetry breaking and mass generation is given by η =  η01 η−2 η−3  ∼ (1, 3,−2/3), ρ =  ρ+1 ρ02 ρ03  ∼ (1, 3, 1/3), (3.8) 14 χ =  χ+1 χ02 χ03  ∼ (1, 3, 1/3), (3.9) S =  S++11 1√ 2 S+12 1√ 2 S+13 1√ 2 S+12 S 0 22 1√ 2 S023 1√ 2 S+13 1√ 2 S023 S 0 33  ∼ (1, 6, 2/3). (3.10) Note that ρ and χ are identical under the gauge symmetry, but distinct under the B−L charge, as shown below. 3.1.2. Dark matter The imprint at low energy is only the 3-3-1 model, conserving the matter parity as residual gauge symmetry WP = (−1)3(B−L)+2s = (−1)2 √ 3T8+3N+2s, (3.11) Because the matter parity is conserved, the lightest W - particle (LWP) is stabilized, responsible for dark matter. The dark matter candidates include a fermion ξ0, a vector Y 0, and a combination of ρ03 va` S 0 23. Due to the gauge interaction, Y 0 annihilates completely into the standard model particles. The The realistic candidates that have correct anbundance are only the fermion or scalar, as shown below. 3.1.3. Lagrangian The total Lagrangian consists of L = Lkinetic + LYukawa − V, (3.12) LYukawa = heαaψ¯αLρeaR + hEαaψ¯αLχEaR + hE1aψ¯1LSEaR + hξψ¯c1Lψ1LS +huabQ¯aLρ ∗ubR + hdabQ¯aLη ∗dbR + hUabQ¯aLχ ∗UbR +H.c. (3.13) The last part is the scalar potential, V = µ2ηη †η + µ2ρρ †ρ+ µ2χχ †χ+ µ2STr(S †S) +λη(η †η)2 + λρ(ρ†ρ)2 + λχ ( χ†χ )2 + λ1STr 2(S†S) + λ2STr(S†S)2 +ληρ(η †η)(ρ†ρ) + λχη(χ†χ)(η†η) + λχρ(χ†χ)(ρ†ρ) +ληS(η †η)Tr(S†S) + λρS(ρ†ρ)Tr(S†S) + λχS(χ†χ)Tr(S†S) +λ′ηρ(η †ρ)(ρ†η) + λ′χη(χ †η)(η†χ) + λ′χρ(χ †ρ)(ρ†χ) +λ′χS(χ †S)(S†χ) + λ′ηS(η †S)(S†η) + λ′ρS(ρ †S)(S†ρ) + ( µηρχ+ µ′χTS∗χ+H.c. ) (3.14) 15 3.1.4. Neutrino mass Substituting the VEVs into the Yukawa Lagrangian, the quark and exotic leptons gain suitable masses as follows [mu]ab = huab√ 2 v, [md]ab = −h d ab√ 2 u, [mU ]ab = −h U ab√ 2 w, (3.15) mξ = − √ 2hξΛ, [mE ]1b = −h E 1b√ 2 Λ, [mE ]αb = −h E αb√ 2 w. (3.16) The ordinary leptons obtain masses [me]αb = −h e αb√ 2 v, [mν ]11 = √ 2κhξ. (3.17) The heavy φ, νR are present and can imply neutrino masses via: Lν = hναbψ¯αLηνbR + 1 2 hRabν¯ c aRνbRφ+H.c. (3.18) We achieve Dirac masses [mDν ]αb = −hναbu/ √ 2 anh Majorana masses [mRν ]ab = −hRab〈φ〉. Because of u 〈φ〉, the observed neutrinos ∼ νL gain masses via a type I seasaw, by [mν ]αβ ' −[mDν (mRν )−1(mDν )T ]αβ = hναa(hR)−1ab (hν)Tbβ u2 2〈φ〉 ∼ u2 〈φ〉 . (3.19) Fitting the data mν ∼ 0.1 eV, we obtain: 〈φ〉 ∼ [(hν)2/hR]1014 GeV, since u is proportional to the weak scale. Given that hν , hR ∼ 1, one has 〈φ〉 ∼ 1014 GeV, close to the grand unification scale. It is clear that two neutrino ν2,3L achieve masses via the type I seasaw with the corre- sponding mixing angle θ23 comparable to the data, while the neutrino ν1L has a mass (which one sets hξκ ∼ 0.1 eV) via the type II seasaw and does not mix with ν2,3L. The mixing angles θ12 and θ13 can be induced by an effective interaction, such as Lmix = hν1β M2 ψ¯c1LψβLρη ∗φ+H.c., (3.20) where M is the new physics scale which can be fixed at M = 〈φ〉. The mass matrix of observed neutrino is corrected by [mν ]1β = −hν1β uv 〈φ〉 ∼ uv 〈φ〉 . (3.21) 3.1.5. Gauge sector The mass Lagrangian of gauge bosons is given by L ⊃ ∑ Φ=η,ρ,χ,S (Dµ〈Φ〉)† (Dµ〈Φ〉) , (3.22) The standard bosons has a mass of, m2W ' g2 4 (u2 + v2), m2X = g2 4 (u2 + w2 + 2Λ2), m2Y ' g2 4 (v2 + w2 + 2Λ2). (3.23) 16 The neutral gauge bosons has a mass of: m2Z1 ' g2 4c2W ( u2 + v2 ) , (3.24) m2Z2 ' g2 4(3− t2W ) [ (1 + t2W ) 2u2 + (1− t2W )2v2 + 4(w2 + 4Λ2) ] , (3.25) and the mixing angle t2ϕ ' √ 3− 4s2W 2c4W u2 − c2W v2 w2 + 4Λ2 . (3.26) Since κ is tiny, its contribution to the ρ parameter is neglected. The deviation of the ρ parameter from the standard model prediction is due to the Z-Z ′ mixing, obtained by ∆ρ ' (u 2 − c2W v2)2 4c4W (u 2 + v2)(w2 + 4Λ2) . (3.27) From the W mass, we derive u2 + v2 = (246 GeV)2. From the global fit, the PDG Collaboration extracts the ρ deviation as ∆ρ = 0.00039 ± 0.00019, which is 2σ above the standard model prediction [1]. Generally for the whole u range, the new physics scale are bounded by √ w2 + 4Λ2 ∼ 5–7 TeV [34]. 3.2. FCNC The Lagrangian that sums over six-dimensional interaction relevant to the standard model fermion at the tree-level: − Γ lZ′ αβ Γ lZ′ γδ m2Z′ ( l¯αγ µPLlβ ) ( l¯γγµPLlδ ) , (3.28) − Γ lZ′ αβ m2Z′ ( gs2W cW √ 1 + 2c2W )( l¯αγ µPLlβ ) ( l¯δγµPRlδ ) , (3.29) − Γ lZ′ αβ Γ νZ′ γδ m2Z′ (ν¯γγµPLνδ) ( l¯αγ µPLlβ ) , (3.30) − Γ νZ′ αβ m2Z′ ( gs2W cW √ 1 + 2c2W ) (ν¯αγµPLνβ) ( l¯δγ µPRlδ ) , (3.31) + ΓνZ ′ αβ m2Z′ g(2 + c2W ) 6cW √ 1 + 2c2W (ν¯αγ µPLνβ) (q¯γµPLq) , (3.32) + ΓνZ ′ αβ m2Z′ gs2W 3cW √ 1 + 2c2W (ν¯αγ µPLνβ) (η q q¯γµPRq) , (3.33) + ΓlZ ′ αβ m2Z′ g(2 + c2W ) 6cW √ 1 + 2c2W ( l¯αγ µPLlβ ) (q¯γµPLq) , (3.34) + ΓlZ ′ αβ m2Z′ gs2W 3cW √ 1 + 2c2W ( l¯αγ µPLlβ ) (ηq q¯γµPRq) , (3.35) − 1 m2Z′ ( g(2 + c2W ) 6cW √ 1 + 2c2W )2 (q¯γµPLq) (q¯γµPLq) , (3.36) 17 0 100 200 300 400 500 600 700 10 −18 10 −16 10 −14 10 −12 10 −10 10 −8 10 −6 10 −4 M (TeV) B ra n c h in g r a ti o Br (µ−>3 e) Br (τ−>3 e) Br (τ−>3 µ) 0 20 40 60 80 100 10 −18 10 −16 10 −14 10 −12 10 −10 10 −8 10 −6 M (TeV) B ra n c h in g r a ti o Br (µ−>3 e) Br (τ−>3 e) Br (τ−>3 µ) Figure 3.1: Branching ratios Br(µ → 3e), Br(τ → 3e), and Br(τ → 3µ) as functions of the new neutral gauge boson mass mz′ ≡ M , respectively. The left-panel is created θ`12 = pi/3, θ`13 = pi/6, θ ` 23 = pi/4, va` δ ` = 0, whereas the right-panel is produced according to sin θ`12 = 0.9936, sin θ`13 = 0.9953, sin θ ` 23 = 0.2324, and δ ` = 1.10pi. − 1 m2Z′ ( gs2W 3cW √ 1 + 2c2W )2 (ηq q¯γµPRq) (η q q¯γµPRq) . (3.37) The first two terms (3.28) and (3.29) provide charged lepton flavor violating processes like µ→ 3e, τ → 3e, τ → 3µ, τ → 2eµ, τ → 2µe, and µ−e. The next four tems (3.30), (3.31), (3.32), and (3.33) present wrong muon and tau decays as well as the nonstandard neutrino interactions that concern both co´ntrains from oscillation and non-oscillation experiments. The last four terms (3.34), (3.35), (3.36), and (3.37) describe semileptonic conversion in nuclei as well as the signals for new physics (dilepton, diject,...) at low energy such as the Tevatron. 3.3. Phenomenology 3.3.1. Leptonic three-body decays a. τ+ → µ+µ+µ−, τ+ → e+e+e−, µ+ → e+e+e− From the graph 3.1, we obtain the lower limit mZ′ ≥ 3.8, 20.6, 36.5 TeV. b. τ+ → µ+e+e−, τ+ → e+µ+µ− From the graph 3.2, we obtain the lower limit mZ′ ≥ 65.3 GeV. c. τ+ → µ+µ+e−, τ+ → e+e+µ− The current experimental constraints for the branching ratio of following channel τ+ → µ+µ+e− and τ+ → e+e+µ− are very small, so the lower bound of new gauge boson mass mz′ 18 0 5 10 15 20 10 −12 10 −10 10 −8 10 −6 10 −4 10 −2 M (TeV) B ra nc hi ng r at io Br (τ+−>µ+e+e−) Br (τ+−>e+µ+µ−) Figure 3.2: Dependence of the branching ratios Br(τ → eµµ) and Br(τ → µee) on the new neutral gauge boson mass, mz′ ≡M . received by the two channels is smaller than other channels, specifically µ → 3e. The figure of the branching ratio τ+ → µ+µ+e− and τ+ → e+e+µ− is 3.3. d. Comment on wrong µ and τ decays It is not hard to point out that the wrong muon and tau decays, e.g. µ → eνeν¯µ and τ → µνµν¯τ , take the same rate as of those in the previous section, respectively. take the same rate as of those in the previous section, respectively. Hence, such decays are far below the experimental limits Br ∼ 0.1 [1]. 3.3.2. Semileptonic τ → µ and τ → e decays The next topic we discuss in this paper is the semileptonic decays of τ , say Br(τ+ → `+P ) (3.38) Br(τ+ → `+V ) (3.39) in the graph 3.4 the lower limit obtained for the new neutral gauge boson mass mZ′ is about 3 TeV, which is the same limit set by the searches of the LHC dilepton and dijet signals. Similar conclusions are also obtained for the case of τ+ → `+V decay. The detail behaviors of the braching ratios Br(τ+ → `+V ) are depicted in Fig. 3.5. Comparing to the experimental bounds yields a Z ′ mass around 3 TeV. 19 0 5 10 15 20 10 −12 10 −10 10 −8 10 −6 10 −4 10 −2 M (TeV) B ra nc hi ng r at io Br (τ+−>µ+µ+e−) Br (τ+−>e+e+µ−) Figure 3.3: Dependence of the branching ratios Br(τ → µµe) and Br(τ → eµµ) on the new neutral gauge boson mass, mz′ ≡M . 0 2 4 6 8 10 10 −14 10 −12 10 −10 10 −8 10 −6 10 −4 10 −2 10 0 M (TeV) B r( τ− > e (µ ) P ) Br(τ−>e π) Br(τ−>e η) Br(τ−>e η/) Br(τ−>µ π) Br(τ−>µ η) Br(τ−>µ η/) Figure 3.4: Dependence of the branching ratios Br(τ+ → `+P ) on the new neutral gauge boson mass, mZ′ ≡M , with ` = e, µ and P = pi, η, η′. Here, lepton mixing angles and phase θ`12 = pi/3, θ ` 13 = pi/6, θ ` 23 = pi/4, and δ ` = 0 have been used. 3.3.3. µ− e conversion in nuclei In Fig. 3.6, the µ − e conversion ratios in the nuclei of Titanium, Aluminum and Gold as functions of the new gauge boson mass mz′ for the same sets of parameter values, θ`12 = pi/3, θ ` 13 = pi/6, θ ` 23 = pi/4, and δ ` = 0 used before. The present upper limits give stronger constraints on the new neutral gauge boson mass with the experimental results yields mz′ ≥ 116.7 TeV carried with Titanium target and, and mz′ ≥ 204.5 TeV with Gold target. 3.3.4. Constraining nonstandard neutrino interactions The latest constraints on the NSIs from the global analysis of oscillation data can be found, uαβ bounded in the range [−0.013, 0.014] or [−0.012, 0.009]. while dαβ bounded in the 20 0 2 4 6 8 10 10 −12 10 −10 10 −8 10 −6 10 −4 10 −2 10 0 M (TeV) B r( τ− > e (µ ) V ) Br(τ−>e ρ) Br(τ−>e ω) Br(τ−>e φ) Br(τ−>µ ρ) Br(τ−>µ ω) Br(τ−>µ φ) Figure 3.5: Dependence of the branching ratios Br(τ+ → `+V ) on the new neutral gauge boson mass mZ′ ≡M . range [−0.012, 0.009] and [−0.011, 0.009]. For the flipped 3-3-1 model, we have∣∣∣fCαβ ∣∣∣ ∼ 12√2GFm2z′ ' 3.0× 10−2 [ 1TeV mz′ ]2 , (3.40) which is at order 10−2, 10−4 and 10−6 for mz′ = 1; 10; 100 TeV. Comparing to the uαβ and dαβ , bounds, it is hard to probe the nonstandard neutrino interactions in the model for mz′ ≥ 3 TeV. 3.3.5. LHC dilepton and dijet searches The cross-section for producing a dilepton or diquark final state can be computed with the aid of the narrow width approximation [174], σ(pp→ Z ′ → ff¯) = 1 3 ∑ q dLqq¯ dm2Z′ σˆ(qq¯ → Z ′)Br(Z ′ → ff¯), (3.41) 21 0 500 1000 1500 2000 10 −18 10 −16 10 −14 10 −12 10 −10 10 −8 10 −6 10 −4 10 −2 M (TeV) C r( µ N − > e N ) Cr(µ Ti−>e Ti) Cr(µ Au−>e Au) Cr(µ Al−>e Al) 0 20 40 60 80 100 120 10 −18 10 −16 10 −14 10 −12 10 −10 10 −8 10 −6 M (TeV) C r( µ N − > e N ) Cr(µ Ti−>e Ti) Cr(µ Au−>e Au) Cr(µ Al−>e Al) Figure 3.6: The µ→ e conversing ratio Br(µ N → e N) versus the new neutral gauge boson mass mz′ ≡M , for different nuclei: i) 4822Ti (red line), ii) 2712Al (magenta line), and iii) 19779 Au (green line). 2% Width 4% Width 8% Width 16%Width 32% Width pp pp ® ® ΜΜ, ΤΤ ee 1000 2000 3000 4000 5000 10-4 0.001 0.01 0.1 1 10 m Z' @GeVD Σ Hpp ® Z ' ® llL@p b D Figure 3.7: Dilepton production cross-section as a function of the neutral gauge bosson mass. In Fig. 3.7,we show the cross-section for dilepton final states l = e, µ, τ . The experimen- tal searches by the ATLAS [193] yield negative signals for new events of high mass, which transform to the lower limit for Z ′, mZ′ > 2.25 and 2.8 TeV, according to ee and µµ(ττ) channels, respectively. The last bound agrees with the highest invariant mass of dilepton hinted by the ATLAS. It is noteworthy that the ee and µµ(ττ) signal strengths are separated, which can be used to approve or rule out the flipped 3-3-1 model. 22 3.3.6. Dark matter The model contains two kinds of dark matter candidates: (i) the fermion triplet ξ which is unified with the standard model lepton doublet (ν1L e1L) in the SU(3)L sextet and (ii) the scalar that is either ρ3 or a combination (called D) of χ2 and S23, whereas the remaining combination of χ2 and S23 is the Goldstone boson of the Y gauge boson. The candidate D transforms as a standard model doublet, which interacts with Z. This gives rise to a large direct dark matter detection cross-section that is already ruled out [176]. The singlet candidate ρ3 can fit the relic density and detection experiments, which has been studied extensively [177,178]. The fermion candidate ξ is a new observation of this work. Generalizing the result in [179], we obtain the annihilation cross-section, 〈σv〉 ' 37g 4 96pim2ξ ' ( α 150 GeV )2(2.86 TeV mξ )2 , (3.42) With (α/150 GeV)2 ' 1 pb. Comparing to experimental observations, we have Ωξh 2 ' 0.1 pb/〈σv〉 ' 0.11 [1],, it leads to mξ ' 2.86 TeV. 23 NEW RESULTS 1. We have shown that the simple 3-3-1 model and the flipped 3-3-1 model contain the appropriate particle spectra of fermions, gauge and Higgs bosons and consistent cur- rents, in which all the standard model particles and interactions have been properly identified. 2. The 3-3-1 model with inert scalars: The inert scalars are essentially included to explain the experimental ρ-parameter, besides providing dark matter. The neutrino masses are induced due to approximate B − L violating effective interactions. All the standard model interactions and Higgs particle in this model have been determined. The quark flavor violating processes that contribute to the neutral meson mixings and decays have been examined. The CKM unitarity is satisfied when including the contribution of Z ′ boson. The effects of new particles including dark matter at the LEPII and LHC have been studied, yielding the new physics scale in TeV regime below the Landau pole. 3. The flipped 3-3-1 model: The model natually provides dark matter through the matter parity as a residual gauge symmetry. The dark matter candidates can be a neutral lepton or scalar. This model provides neutrino masses via the type I+II seesaw mecha- nism. The lepton flavor violating processes are governed by the interactions of Z ′ and are systematically studied in the model. 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