Các hiệu ứng vật lý mới trong các mô hình 3 2 3 1 và 3 3 3 1 tt tiếng anh

MINISTRY OF EDUCATION VIETNAM ACADEMY AND TRAINING OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY - - - - - - - - *** - - - - - - - - NGUYEN THI NHUAN SOME NEW PHYSICAL EFFECTS IN THE − − − AND − − − MODELS Major: Code: Theoretical and Mathematical Physics 44 01 03 SUMMARY OF PHYSICS DOCTORAL THESIS Hanoi - 2019 INTRODUCTION The urgency of the thesis The standard model (SM )of particle physics is based on two principal theories including electroweak theory with the SU (2)L × U (1)Y gauge symmetry and QCD theory with SU (3)c gauge symmetry The SM describes elementary particles which create matter and their interactions which make the entire universe In the SM, three interactions of particles are described successfully: strong interactions, electromagnetic interactions and weak interactions Many predictions of the SM such as: the existence of W ± , Z boson, quark c, t, neutral currents have been verified with high fidelity by experiments W, Z found in 1981 with the masses measured as the model proposed There are many ways to expand SM such as introducing the spectral particles, extend gauge group,etc Therefore, we would suggest two expansion models: the − − − and the 3−3−3−1 models The 3−2−3−1 model is based on the gauge group SU (3)C ⊗ SU (2)L ⊗ SU (3)R ⊗ U (1)X The − − − model solves the neutrino masses problem, provides naturally candidate for dark matter, indicates the existence of FCNC at the approximate tree caused by the gauge bosons and Higgs, explains why are there three fermion generations The − − − model is based on the gauge group SU (3)C ⊗ SU (3)L ⊗ SU (3)R ⊗ U (1)X It unifies both the left-right and 3-3-1 symmetries, so it inherits all the good features of the two models Therefore, the − − − model solves problems of fermion generation numbers, neutrino masses problems, dark matter problems, parity symmetry in electroweak theory In particular, the model predicts lepton flavor violation of the charged lepton Especially, on 4/7/2012, a particel was discovered at the Large Hadron Collider (LHC) located at the European Nuclear Research Center using two independent detectors, A Toroidal LHC ApparatuS (ATLAS) and Compact Muon Solenoid (CMS), with a mass measured about 125 − 126 GeV This particel has characteristics identical to the boson Higgs predicted by SM that has not been found previously It was the last piece for the picture called "Standard Model" to be completed It can be stated that the SM of particle physics is very successful describing interactions in the Universe However, the SM model can not explain some observed figures in the Universe and recent experimental results Specifically: Why neutrinos have mass? SM does not identify the candidates for dark matter particles SM does not explain some abnormal decay channels of mesons, higgs SM also does not answer the questions: Why are there three fermion generations? Why is asymmetrical between matter and antimatter? Why is mass graded in the fermion spectrum? So, an expansion is necessary For the mentioned reasons, we choose the subject "Some new physics effects in the − − − and − − models" The objectives of the thesis • Resolve the neutrino mass problem Parameterize the parameters in the model − − − to seek for dark matter for each version of the model with q = and q = −1 Research for Z1 and Z1 at LEPII and LHC • Survey in detail the mass of gauge bosons, Higgs bosons, flavor-changing neutral current in the model − − − and calculate the branch ratio of the decay process mu → eγ, µ → 3e in the model The main contents of the thesis • Overview of SM, flavor-changing neutral current, neutrino masses and dark matter problems in SM • Investigate the − − − model with any charge of new leptons, neutrino masses, and identify dark matter candidates in the model and search for dark matter by the method direct search • Investigate the model − − − with any charge of new leptons, gauge boson masses, Higgs mass, FCNCs, cLFV in decay process µ → eγ, µ → 3e CHAPTER OVERVIEW 1.1 The Standard Model SM describes strong, electromagnetic and weak interactions based on the gauge symmetry group SU (3)C ⊗SU (2)L ⊗U (1)Y (3−2−1) In particular, the gauge group SU (3)C describes strong interaction, gauge group SU (2)L ⊗U (1)Y describes weak electrical interaction The electric charge operator: Q = T3 + Y /2 The particles in SM are arranged under the gauge group as follows: Leptons: νaL eaL ψaL = ∼ (1, 2, −1), eaR ∼ (1, 1, −2), a = 1, 2, (1.1) Quarks: QaL = uaR ∼ uaL daL 3, 1, ∼ , 3, 2, , daR ∼ 3, 1, − , (1.2) where a is the generation index The SU (3)C ⊗ SU (2)L ⊗ U (1)Y gauge group is broken spontaneously via a single scalar field, φ= ϕ+ ϕ0 = ϕ+ v+h+iG Z √ ∼ (1, 2, 1) (1.3) After SSB, the received gauge bosons are: Aµ = sW A3µ + cW Bµ , Zµ = cW A3µ − sW Bµ , Wµ± = √ (A1µ ∓ iA2µ ), gv gv mA = 0, mZ = , mW ± = (1.4) 2cW The Yukawa interaction: i ¯ iL φdj + huij Q ¯ iL (iσ2 φ∗ )uj + H.c., − LY = heij ψ¯L φejR + hdij Q R R (1.5) for fermion mass matrices: Meij = heij √v2 , Mdij = hdij √v2 , Muij = huij √v2 Diagonalization of these mass matrices will determine the physical fermion states and their masses 1.2 GIM mechanism and CKM matrix 1.2.1 GIM mechanism If only three quarks exist: u, d, s with left-handed quarks arranged to doublet of SU (2)L group: Q1L = u dθc = L uL cosθc dL + sinθc sL , (1.6) and right-handed quarks arranged to singlet of SU (2)L group: uR , dθcR , sθcR (θ is flavor mixing angle, called Cabibbo angle), hence we have high flavor changing neutral current This contradicts experiment In 1970, Glashow, Iliopuolos and Maiani (GIM) proposed a new mechanism to solve this problem by introducing the two quark doublet which includes the four quark, which is now called the charm quark c, Q1L = uL cosθc dL + sinθc sL uR , , Q2L = cR , uL cosθc sL − sinθc dL dθc R , , sθc R (1.7) and then we have no flavor changing neutral current at the tree level Thus, the GIM mechanism came to the conclusion: to have a small FCNCs, there must be at least two quarks generations 1.2.2 CKM matrix In SM, if there were only two quark generations, scientists have no CP violation To solve the CP symmetry violating problem, scientists supposed the existence of the third quark generation The expansion of the model to three generations schemd, in order to accommodate the observed violation in KL decay, was first proposed by Kobayashi and Maskawa in 1973 The CP violation via a phase in quark mixing matrix The quark mixing matrix has three angles and one phase and is generalized from the Cabibbo mixing matrix into six quarks with three quark generations represented through the × matrix called the Cabibobo-Kobayashi-Maskawa matrix (CKM ) In 1977, the quark b was officially discovered, confirming the hypothesis of scientists has accurated It also mark proposal of Kobayashi-Maskawa that is success befor finding the quark c of the second generation By using three generations with a mixing angles: θ1 , θ2 , θ3 and CP violation phase, δ introduced by Kobayashi and Maskawa, the quark mixing matrix is as follows: V = R1 (θ2 )R3 (θ1 )C(0, 0, δ)R1 (θ3 ), (1.8) Another parameterization of V is the so-called standard parameterization which is is characterized in terms of three angles θ12 , θ23 , θ13 and a phase δ13 as:   −iδ13 c12 c13 V =  −s12 c23 − c12 s23 s13 eiδ13 s12 s23 − c12 c23 s13 eiδ13 s12 c13 c12 c23 − s12 s23 s13 eiδ13 −c12 s23 − s12 c23 s13 eiδ13 s13 e s23 c13 c23 c13  , (1.9) where, cij = cosθij , sij = sinθij , i, j = (1, 2, 3) ¯ mixing in SM 1.2.3 K − K Since neutral kaons are the bound states of s and d quarks and their antin¯ s), this mixing occur because there is a moving ¯ ∼ dγ quarks, (K ∼ s¯γ5 d, K ¯ In the FCNC processes of kaons, the strangeness changes process s¯d ↔ sd | S| = 2, while charge not Their mass diference: ∆mK ≡ mKL − mKS 2M12 , (1.10) According to Feynman rule, effective Lagrangian: |∆S|=2 Lef f αGF = √ 2πsin2 θW ∗ (Vis∗ Vid )(Vjs Vjd )E(xi , yj )(¯ sγµ PL d)(¯ sγ µ PL d, (1.11) i,j=c,t 5 where, PL = 1−γ , Vis are CKM matrix elements and confficient function E(xi , yj ) express the contributtions of two internal quarks with masses mi , mj m2 and xi ≡ M i2 he confficient function E(xi , xj ): w xi ) lnxi − xi [ − − ].(1.12) E(xi ) ≡ E(xi , xi ) = − ( xi − 4 xi − (xi − 1)2 To get M1 2, we need to evaluate the matrix element of respect to kaons states: ¯ = f m2 B, K |(¯ sγ µ Ld)|K K K (1.13) where, fk = 160 MeV is decay constant, mK is the mass of K-meson (mK M ) and B is the "bag-parameter", which parameterizes the ambiguity due ¯0 to the non-perturbative QCD effects to form the bound states K and K Hamiltonian is the mass-squared matrix reads as: H= δm2 2M M2 δm2 2M M , (1.14) δm this means M12 2M In the case of restricted two generatiob model, noting E(xc ) −xc với xc O(1) TeV LHC The LEPII at CERN searched for new neutral gauge boson signals that mediate the processes such as pp → Z1 → f f¯., where f is ordinary fermion in the final state The cross-section for dilepton final states f f¯:   dLqq¯ σ(pp → Z1 → f f¯) =  σ ˆ (q q¯ → Z1 ) × Br(Z1 → f f¯) (2.17) dmZ1 q=u,d 10 10 2% Width Width 8% Width 0.1 16% Width 32%Width Model: Β=-1/ + ll Model : Β Σ pp 0.01 0.001 10 10 1000 2000 3000 m 4000 5000 Hình 2.1: The cross-section σ(pp → Z1 → l¯l) [pb] as a function of mZ1 [GeV], where the points are the observed limits according to the different widths extracted at the resonance mass in the dilepton final state using 36.1 fb−1 of √ proton-proton collision data at s = 13 TeV with ATLAS detector The star √ and plus lines are the theoretical predictions for β = ±1/ 3, respectively Experimental results show that a negative signal for new high-mass phenomena in the dilepton final state It is converted into the lower limit on the √ Z1 mass, mZ1 > TeV, for models with β = ±1/ 2.3.3 Dark matter phenomenology A dark matter particle must satisfy the following conditions: Electrically neutral, colorless, the lightest mass of parity odd particles and the dark matter 0.1pb relic density agreement with the experiment Ωh2 0.11 In this model, the dark matter candidates are: • q =0: E1 , H6 , H7 , XR • q = -1: H8 , YR E1 Fermion dark matter Dominated annihilator channels of E1 : − + E1 E1c → νν c , l− l+ , να ναc , lα lα , qq c , ZH1 (2.18) where the first two productions have both t-channel by respective XR , YR and s-channel by Z1 , Z1 , while the remainders have only the s-channel There may exist some contributions from the new scalar portals, but they are small and neglected There is no standard model Higgs or Z portal In Fig 2.2 we display the dark matter relic density as a function of its mass It is clear that the relic density is almost unchanged when mZ1 changes he stabilization of dark matter yields only a Z1 resonance regime For instance, 11 w = TeV, the dark matter mass region is 1.85 < mE1 < 2.15 TeV, given that it provides the correct abundance 10 mZ1 = 4.13 TeV mZ2 = 81 TeV Z1 Resonance h2 0.1 0.01 500 w = TeV = 100 TeV 1000 1500 2000 mE1 GeV 2500 3000 Hình 2.2: The relic density of the fermion candidate as a function of its mass, mE , in the limit Λ w, Z1 ≡ Z1 Z2 ≡ Z1 10 44 10 45 10 46 10 47 10 48 500 Events day kg Σ E1 Xe cm2 Currently, there are three ways to search for dark matter: search at the LHC, direct search and indirect search The three methods have their own strengths Using Micromegas software, we drawn a graph for the direct search process The direct detection experiments measure the recoil energy deposited 1000 1500 2000 mE1 GeV 2500 0.001 10 10 10 3000 500 1000 1500 2000 mE1 GeV 2500 3000 Hình 2.3: The scattering cross-section (left-panel) and the total number of events/day/kg (right-panel) as functions of fermion dark matter mass by the scattering of dark matter with the nuclei This scattering is due to the interactions of dark matter with quarks confined in nucleons Fig 2.3 shows that the predicted results are consistent with the XENON1T experiment since the dark matter mass is in the TeV scale H6 scalar dark matter The scalar H6 transforms as a SU (2)L doublet The field H6 can annihilate into W + W − , ZZ, H1 H1 and f¯f since its mass is beyond the weak scale The 12 annihilation cross-section is given by: α 150 GeV σv 2 600 GeV mH6 x × 1.354 TeV mH6 + , (2.19) where x ∼ λSM 0.127 In order for H6’s density to reach the thermal abundance density or below the thermal abundance density, its mass must meet mH6 < 600 GeV.However, when mH6 > 600 GeV is large, the scalar dark matter can (co)annihilate into the new normal particles of the 3-2-3-1 model via the new gauge and Higgs portals similarly to the 3-3-1 model, and this can reduce the abundance of dark matter to the observed value, so H6 is not a good candidate for dark matter H7 scalar dark matter Since H7 is a singlet of the SU (2)L group, it has only the Higgs (H1,2,3,4,6,7 ), new gauge, and new fermion portals The annihilation products can be the standard model Higgs, W, Z, top quark, and new particles we chose the the parameter space to the primary annihilation channels is Higgs in SM through the new Higgs ports H7 h H7 H6 H7 h H7 h H7 h H7 h H7 H7 H3 H7 h H7 h H7 H4 h H7 h H7 h H7 h h H7 h H2 h h Hình 2.4: Diagrams that describe the annihilation H7∗ H7 → H1 H1 via the Higgs portals, where and in the text we sometimes denote h ≡ H1 for brevity We calculate the total amplitude of diagrams Feymman and build the expression of the dark matter relic density as: Ωh2 mH7 0.1 1.354 TeV • mH7 m2H3 λ5 λ6 ¯ λ− +λ 2(λ1Ξ + λ2Ξ ) 4m2H7 − m2H3 −2 (2.20) mH3 mật độ tàn dư: Ωh 0.1 λeff 13 mH7 × 1.354 TeV (2.21) Để Ωh2 graph: 0.11 thì: mH7 ≤ |λeff | × 1.354TeV ∼ 1.354 TeV, We draw the BLE 0.20 h2 P-UN STA 0.15 WIM 0.10 0.05 0.00 0.5 1.0 1.5 2.0 mH 2.5 3.0 3.5 TeV Hình 2.5: The relic density depicted as a function of the scalar H7 mass In figure 2.5: The straight line is experimental line correspond to Ωh2 0.11, the resonance width mH7 ∼ 2.6 = mH3 /2, Unstable bound is blocked by YR mass XR gauge boson dark matter , YR : The mass of XR m2XR 2 gR gR 2 2 u + ω + Λ , mYR = v2 + ω2 = 4 (2.22) In (2.22) show that the mass of the vector gauge boson XR is radically larger ± than that of the vector gauge boson YR So, the vector gauge boson X cannot be a dark matter candidate since it is unstable, entirely decaying into the YR± and standard model gauge bosons (W ∓ ) H8 scalar dark matter The scalar field, H80 , is considered as a LWP Because it transforms as the doublet of SU (2)L group, it directly couples to the standard model gauge boson and behaves like the H60 scalar field So, H8 is not a good candidate for dark matter YR gauge boson dark matter YR directly couples to the W ± , Z gauge bosons, and the dominated annihilation channels are YR0 YR0∗ → W + W − , ZZ The dark matter thermal relic 14 abundance is approximated as Ω YR h Because the fraction m2W m2Y −3 10 m2W m2YR is very small, their relic abundance is ΩYR h2 (2.23) 10−3 , R much lower than that measured by WMAP/PLANCK 2.4 Conclusions The neutrino masses are naturally induced by a seesaw mechanism and the seesaw scale ranges from 104 GeV or 1016 GeV depending on the weak scale ratio u/v At the low seesaw scale, the lepton flavor violation decays µ → 3e and µ → eγ are dominantly induced by a doubly-charged Higgs exchange The decay rates are consistent with the experimental bounds if the doubly-charged Higgs mass varies from few TeVs to hundred TeVs The LEPII constrains the Z1 mass at O(1) TeV, while the LHC searches √ show that the Z1 mass is larger than TeV for s = 13 TeV The model q = contains two types of dark matter, fermion and scalar fields The model q = −1 there is no candidate for dark matter 15 CHAPTER PHENOMENOLOGY OF THE MINIMAL − − − MODEL 3.1 The − − model 3.1.1 Anomaly cancellation and fermion content The − − − model, a framework for unifying the 3-3-1 and left-right symmetries is based on: SU (3)C ⊗ SU (3)L ⊗ SU (3)R ⊗ U (1)X , (3.1) gauge group Fermion content: Các hạt xếp sau:  ψaL  νaL   =  eaL  ∼ q NaL  1, 3, 1, q−1 , ψaR  νaR   =  eaR  ∼ q NaR 1, 1, 3, q−1 , (3.2)   QαL  dαR q  −u  ∗ QαR =  , αR  ∼ 3, 1, , − −q− JαR (3.3)   u3R q+1  d  Q3R =  3R  ∼ 3, 1, 3, , q+ J3R (3.4) dαL q  −u  ∗ , = αL  ∼ 3, , 1, − −q− JαL  Q3L  u3L   =  d3L  ∼ q+ J3L 3, 3, 1, q+1  , 3.2 Research results of phenomenology of the − − − model 3.2.1 FCNCs As mentioned, the tree-level FCNCs arise due to the discrimination of quark generations, i.e the third generations of left- and right-handed quarks Q3L,R 16 transform differently from the first two QαL,R under SU (3)L,R ⊗ U (1)X gauge symmetry, respectively Hence, the neutral currents will change ordinary quark flavors that nonuniversally couple to T8L,R The effective Lagrangian that these terms contribute to the meson mass mixing parameter as follows: f Lef F CN C ¯ = −Υij L q iL γµ qjL ¯ − Υij R q iR γµ qjR , (3.5) where: ij ΥL ij ΥR = = ∗ VqL ∗ VqR 3i 3i 3j (VqL ) (VqR ) 3j  g2 cξ3 − g3 sξ3 g2  + mZ m2Z R L   g c2 g s2  ξ3 + ξ3  m2Z m2Z R + g2 sξ3 + g3 cξ3 m2Z   , (3.6) R (3.7) R Mass diference:: ∆mK ∆mBd ∆mBs = = = ΥL12 + ΥR12 mK fK , (3.8) ΥL13 + ΥR13 mBd fB2 d , (3.9) ΥL23 + ΥR23 mBs fB2 s (3.10) The total mass differences can be decomposed as: (∆mM )tot = (∆mM )SM + ∆mM , (3.11) In the moedel: 0.37044 × 10−2 /ps < (∆mK )tot < 0.68796 × 10−2 /ps, (3.12) 0.480225/ps < (∆mBd )tot < 0.530775/ps, (3.13) 16.8692/ps < (∆mBs )tot < 18.6449/ps (3.14) We make contours of the mass differences, ∆mK and ∆mBd,s in w-ΛR plane as Fig 3.1 The viable regime (gray) for the kaon mass difference is almost entirely the frame The red and olive regimes are viable for the mass differences ∆mBs and ∆mBd , respectively Combined all the bounds, we obtain w > 85 TeV and ΛR > 54 TeV for the model with β = − √13 , whereas w > 99 TeV, ΛR > 66 TeV for the model with β = √13 17 Hình 3.1: Contours of ∆mK , ∆mBs , and ∆mBd as a function of (w, ΛR ) according to β = − √13 (left panel) and β = √13 (right panel) 3.2.2 Charged LFV µ → eγ process We are going to derive an expression for the branching decay ratio of µ → eγ in the model − − − Similarly to the standard model, the decay µ → eγ in the present model cannot occur at tree-level, but prevails happening through one-loop diagrams, which are contributed by new Higgs scalars, new gauge bosons, and new leptons The branch ratio of the process µ → e + γ: Br(µ → e + γ) = 384π (4παem ) |AR |2 + |AL |2 , (3.15) where, αem = 1/128 and Form factors: AR = AL =  mk L L ∗ R L ∗   Y Y × F (Q) + Y Y × × F (r, s , Q) √ k H µk H ek H µk H ek 192 2π GF M mµ H H Q ,k   ∗ ∗ mk Q Mw L Q R L  UL  , (3.16) U G (λ ) − U U R (λ ) + k k Aµ Aµ γ Aµ Aµ γ 32π M µk ek µk ek mµ Q A µ Aµ ,k −    YR − √ H µk 192 2π GF M Q H H ,k  g2 Mw R  UR + Aµ 32π M g2 µk Q A L µ Aµ ,k mk R ∗ YH ì F (Q) + ek mà R UA ∗ ek Q Gγ (x) − L YH µk L UA àk R YH ì ì F (r, sk , Q) ek R UA µ ∗ mk ek mµ  Q Rγ (λk ) (,3.17) A The µ → eγ process when there is left-right asymmetry When there is left-right asymmetry, this mean wL = 0, at one-loop approx± imations, the diagrams with Wiµ , Hi± , Hi±± contribute mainly We draw the graphs of the branch ratio: 18 ± Hình 3.2: The branching ratio Br(µ → eγ) governed by intermediate W1,2 ± ±± gauge bosons (left panel) and Higgs bosons H1,2 and H1,2 (right panel), which is given as a function of ΛR for the selected values of their mixing angle ξw The upper and lower blue lines correspond to the MEG current bound and near-future sensitivity limit In figure 3.2 , the branch ratio depends strongly on the mixing angle and ΛR When the mixing angle increases, the branch ratio increases and vice ± versa The left panel shows that, with W1,2 gauge bosons contribute mainly, ΛR increases to a certain value, the branch ratio is almost unchanged But ± ±± the right panel, with Higgs bosons H1,2 and H1,2 , the branch ratio decreases monotonically by ΛR Comparing both graphs in the figure 3.2 shows, the contribution of the ± ± ±± gauge gauge W1,2 and the Higgs boson H1,2 and H1,2 is equivalent B The µ → eγ process when there is left-right symmetry When there is left-right symmetry, this mean wL = 0, at one-loop ap±(q+1) ±(q+1) ± proximations, the diagrams with Wiµ , Yiµ , Hi± , Hi±± , Hi contribute mainly We draw the graphs of the branch ratio: If one uses the same values of the model’s parameters involved in the process, the contributions to the de±(q+1) cay µ → eγ by virtual charged Higgs H1,2 exchanges are extremely small ±(q+1) comparing to those by Y1,2 gauge bosons 19 Hình 3.3: Dependence of the branching ratio Br(µ → eγ), governed by the ±(q+1) virtual Y1,2 gauge boson exchanges (lef panel), and the virtual charged ±(q+1) Higgs H1,2 exchanges (right panel) on wL for different values of the mixing angle ξY The upper and lower lines correspond to the MEG current bound and the near future sensitivity limit 3.2.3 µ → 3e processes The effective Lagrangian as: RR ¯c LL ¯c (eR µR ) (e¯cR eR ) = gLS (eL µL ) (e¯cL eL ) + gRS Lef f (µ → 3e) LR ¯c RL ¯c (eL µL ) (e¯cR eR ) + gRS (eR µR ) (e¯cL eL ) + gLS (3.18) Here, we denote MHi (i = 1, 2) to be the masses of doubly charged Higgs bosons and LL gLS = − i=1 LR gLS = − i=1 2 MHi L yH i ee , RR gRS =− i=1 MHi L yH i eµ L yH i eµ R yH i ee , RL gRS =− i=1 MHi R yH i eµ R yH (3.19) , i ee R yH i eµ L yH (3.20) i ee MHi The branching ratio: Br(µ → 3e) = LL RR LR RL |gLS | + |gRS | + |gLS | + |gRS | , 32GF where GF = 1.166 × 10−5 GeV2 is the Fermi coupling constant We draw graph of the branching ratio: 20 (3.21) Hình 3.4: Branching ratio Br(µ → 3e) as a function of doubly charged Higgs masses The three blue lines, Br(µ → 3e) = 10−12 ; 10−15 ; 10−16 , correspond to the current experimental upper bound, the sensitivities of PSI and PSI upgraded experiments, respectively The figure reveals a line of monotonically decreasing function as increasing of MH , which is consistent to the fact that the branching ratio is inversely Thus we apparently conclude that the future PSI experproportional to MH iment is more sensitive to the new physics of the considering model than the Mu to E Gamma experiment (MEG), which gives a lower bound MH = 53 TeV for the case ξH = 0.1 3.2.4 Conclusion The 3−3−3−1 model resolves the generation number and the weak parity violation Additionally, it generates neutrino masses and dark matter naturally via the gauge symmetry We have demonstrated that FCNC makes a new contribution to the mass ¯ Combining the predictions of the mixing parameters of mesons Bd,s −B d,s model and the experimental limits, we forecast model new physical scale T eV or several tens of T eV All the results indicate that the − − − model is possibly flipped at tens of TeV Additionally, the contributions of the new particles other than the left-right symmetric model are important to set the charged LFV and quark FCNC 21 GENERAL CONCLUSION PHENOMENOLOGY OF TWO THE MODELs A The − − − model Research on dark matter with two versions q = and q = -1 • The model q = contains two types of dark matter, fermion and scalar fields • The model q = −1 don’t contain good dark matter candidate Search for Z1 and Z1 constrains the new physic scale for mZ1 TeV Studying the decay process that violates the lepton position contributed by the double-charged Higgs in the processes µ → 3e, µ → eγ Hence the new physical prediction for hR 0.03 ÷ 3.16 and the doubly-charged eτ,µτ Higgs mass varies from few TeVs to hundred TeVs B − − − model: The contribution of new physics to meson mixing parameters gives a new physical scale • w > 85 TeV, ΛR > 54 TeV with β = − √13 , • w > 99 TeV, ΛR > 66 TeV with β = √1 ±(q+1) ± µ → eγ comes from contributions from all fields Wiµ , Yiµ , ±(q+1) Hi± , Hi±± , Hi • wL = - when there is left-right asymmetry, the contribution of fileds Wià , Hi , Hi is equivalent ã wL = - when there is left-right symmetry,the contribution of fileds ±(q+1) ±(q+1) ± Wiµ , Yiµ , Hi± , Hi±± , Hi The contributions to the decay ±(q+1) µ → eγ by virtual charged Higgs H1,2 small comparing to those by ±(q+1) Y1,2 exchanges are extremely gauge bosons µ → 3e specify a new physical scale với charged Higgs mass more than or equal to 53 TeV 22 NEW FINDINGS OF THE THESIS We show that the − − − model solves some problems beyond the standard model that that many scientists in the world are interested in such as the neutrino mass problem and the dark matter problem We suggest that neutrino masses and the candidates for dark matter are created naturally as a result of spontaneous symmetry breaking The term containing the neutrino mass is likewise the source of the lepton flavor violation We indicate that the − − − model arises naturally Flavor changing neutral current (FCNCs) at tree-level through Yukawa interaction The − − − model is also pregnant with candidates for dark matter like a consequence of the spontaneous symmetry breaking We identify a new physical scale in the model by investigating processes that are sources of the charged lepton flavor violation with the contribution of new Higgs and gauge bosons 23 LIST OF WORKS HAS BEEN PUBLISHED P V Dong and D T Huong, D V Loi, N T Nhuan, N T K Ngan, Phenomenology of the SU (3)C ⊗SU (2)L ⊗SU (3)R ⊗U (1)X gauge model, Phys Rev D 95, 075034, 2017 D.T.Huong, P.V.Dong, N.T.Duy, N.T.Nhuan, L.D Thien, Investigation of Dark Matter in the 3-2-3-1 Model, Phys Rev D 98, 055033, 2018 D N Dinh, D T Huong, N T Duy, N T Nhuan, L D Thien, and Phung Van Dong, Flavor changing in the flipped trinification, Phys Rev D 99, 055005, 2019 24 ... θ 12 , θ 23 , θ 13 and a phase δ 13 as:   −iδ 13 c 12 c 13 V =  −s 12 c 23 − c 12 s 23 s 13 eiδ 13 s 12 s 23 − c 12 c 23 s 13 eiδ 13 s 12 c 13 c 12 c 23 − s 12 s 23 s 13 eiδ 13 −c 12 s 23 − s 12 c 23 s 13 eiδ 13 s 13 e s 23 . .. S 12 S 13 −q? ?1 S 22 S 23  −q S 11 − S 21 ? ?1  −q? ?1   ? ?2 ∼ φ 03 ∼ 1, 1, 3, − 1, 2, 3? ?? , − 2q + , 2q + , (2. 5) (2. 6) Ξ  Ξ 011  =   Ξ− √ 12 Ξq 13 √ Ξ− √ 12 −− ? ?22 Ξq? ?1 23 √ Ξq 13 √ Ξq? ?1 23 √ 2q ? ?33 ... dark matter relic density as: Ωh2 mH7 0 .1 1 .35 4 TeV • mH7 m2H3 λ5 λ6 ¯ λ− +λ 2( ? ?1? ? + ? ?2? ? ) 4m2H7 − m2H3 ? ?2 (2. 20) mH3 mật độ tàn dư: Ωh 0 .1 λeff 13 mH7 × 1 .35 4 TeV (2. 21) Để Ωh2 graph: 0 .11 thì: