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

The urgency of the thesis The standard model SM of particle physics is based on two principal ories including electroweak theory with the SU 2L× U 1Y gauge symmetryand QCD theory with SU

MINISTRY OF EDUCATION VIETNAM ACADEMY

GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY

***

-NGUYEN THI NHUAN

SOME NEW PHYSICAL EFFECTS

IN THE 3 − 2 − 3 − 1 AND 3 − 3 − 3 − 1 MODELS

Major: Theoretical and Mathematical PhysicsCode: 9 44 01 03

SUMMARY OF PHYSICS DOCTORAL THESIS

Hanoi - 2019

1 The urgency of the thesis

The standard model (SM )of particle physics is based on two principal ories including electroweak theory with the SU (2)L× U (1)Y gauge symmetryand QCD theory with SU (3)c gauge symmetry The SM describes elementaryparticles which create matter and their interactions which make the entireuniverse In the SM, three interactions of particles are described successfully:strong interactions, electromagnetic interactions and weak interactions Manypredictions of the SM such as: the existence ofW±, Z boson, quark c, t, neutralcurrents have been verified with high fidelity by experiments W, Z found

the-in 1981 with the masses measured as the model proposed There are manyways to expand SM such as introducing the spectral particles, extend gaugegroup,etc Therefore, we would suggest two expansion models: the 3 − 2 − 3 − 1and 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 3 − 2 − 3 − 1 model solves the trino masses problem, provides naturally candidate for dark matter, indicatesthe existence of FCNC at the approximate tree caused by the gauge bosonsand Higgs, explains why are there three fermion generations The 3 − 3 − 3 − 1model is based on the gauge group SU (3)C ⊗ SU (3)L ⊗ SU (3)R ⊗ U (1)X Itunifies both the left-right and 3-3-1 symmetries, so it inherits all the good fea-tures of the two models Therefore, the 3 − 3 − 3 − 1 model solves problems offermion generation numbers, neutrino masses problems, dark matter problems,parity symmetry in electroweak theory In particular, the model predicts lep-ton flavor violation of the charged lepton Especially, on 4/7/2012, a particelwas discovered at the Large Hadron Collider (LHC) located at the EuropeanNuclear Research Center using two independent detectors, A Toroidal LHCApparatuS (ATLAS) and Compact Muon Solenoid (CMS), with a mass mea-sured about 125 − 126 GeV This particel has characteristics identical to the

neu-1

boson Higgs predicted by SM that has not been found previously It was thelast piece for the picture called "Standard Model" to be completed It can bestated 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 do nos have mass? SM does not identify the candidates for dark matter particles

neutri-SM does not explain some abnormal decay channels of mesons, higgs neutri-SMalso does not answer the questions: Why are there three fermion generations?Why is asymmetrical between matter and antimatter? Why is mass graded inthe fermion spectrum? So, an expansion is necessary

For the mentioned reasons, we choose the subject "Some new physics effects

in the 3 − 2 − 3 − 1 and 3 − 4 − 1 models"

2 The objectives of the thesis

• Resolve the neutrino mass problem Parameterize the parameters in themodel 3 − 2 − 3 − 1 to seek for dark matter for each version of the modelwith q = 0 and q = −1 Research for Z1 and Z10 at LEPII and LHC

• Survey in detail the mass of gauge bosons, Higgs bosons, flavor-changingneutral current in the model 3 − 3 − 3 − 1 and calculate the branch ratio

of the decay process mu → eγ, µ → 3e in the model

3 The main contents of the thesis

• Overview of SM, flavor-changing neutral current, neutrino masses anddark matter problems in SM

• Investigate the 3 − 2 − 3 − 1 model with any charge of new leptons,neutrino masses, and identify dark matter candidates in the model andsearch for dark matter by the method direct search

• Investigate the model 3 − 3 − 3 − 1 with any charge of new leptons, gaugeboson masses, Higgs mass, FCNCs, cLFV in decay process µ → eγ,

µ → 3e

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CHAPTER 1 OVERVIEW

1.1 The Standard Model

SM describes strong, electromagnetic and weak interactions based on thegauge symmetry group SU (3)C⊗SU (2)L⊗U (1)Y (3−2−1) In particular, thegauge groupSU (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:

,

uaR ∼



3, 1, 43

, daR ∼

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,

The Yukawa interaction:

− LY = heijψ¯Li φejR +hdijQ¯iLφdjR +huijQ¯iL(iσ2φ∗)ujR +H.c., (1.5)for fermion mass matrices: Meij = he

ij v

√

2, Md

ij = hd

ij v

√

2, và Muij = hu

ij v

√

2.Diagonalization of these mass matrices will determine the physical fermionstates and their masses

1.2 GIM mechanism and CKM matrix

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 flavorchanging 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 thefour quark, which is now called the charm quark c,

uR, cR, dθcR, sθcR (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 CPviolation To solve the CP symmetry violating problem, scientists supposedthe existence of the third quark generation The expansion of the model tothree generations schemd, in order to accommodate the observed violation in

KL decay, was first proposed by Kobayashi and Maskawa in 1973 The CP

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violation via a phase in quark mixing matrix The quark mixing matrix hasthree angles and one phase and is generalized from the Cabibbo mixing matrixinto six quarks with three quark generations represented through the 3 × 3matrix called the Cabibobo-Kobayashi-Maskawa matrix (CKM ) In 1977, thequark b was officially discovered, confirming the hypothesis of scientists hasaccurated It also mark proposal of Kobayashi-Maskawa that is success beforfinding 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 Kobayashiand 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 parameterizationwhich is is characterized in terms of three angles θ12, θ23, θ13 and a phase

antin-|4S| = 2, while charge do not

Their mass diference:

∆mK ≡ mKL − mKS w 2M12, (1.10)According to Feynman rule, effective Lagrangian:

L|∆S|=2ef f = αGF

4 √ 2πsin 2 θ W

X

i,j=c,t

(Vis∗V id )(Vjs∗V jd )E(x i , y j )(¯ sγ µ P L d)(¯ sγµP L d, (1.11)

5

xi − 1 −

32

1(xi − 1)2].(1.12)

To get M12, we need to evaluate the matrix element of respect to kaons states:

hK0|(¯sγµLd)| ¯K0i = 2

3fK2m2KB, (1.13)where, fk = 160 MeV is decay constant, mK is the mass of K-meson (mK w

M ) and B is the "bag-parameter", which parameterizes the ambiguity due

to the non-perturbative QCD effects to form the bound states K0 and ¯K0 Hamiltonian is the mass-squared matrix reads as:

2 δm22M

δm22M M2

The contribution of SM to K-meson mass different: bea

∆mK = 0.467.10−2/ps (1.16)According to recent calculations, B = 0.72 ± 0.04, K-meson mass different: bea

∆mK = (3.483 ± 0.006)µeV = (5.292 ± 0.009).10−3/ps (1.17)

Thus, there is a difference in K-meson mass between SM theory andexperiment

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CHAPTER 2 PHENOMENOLOGY OF THE 3 − 2 − 3 − 1

MODEL

2.1 The anomaly cancellation and fermion content

The electric charge operator: Q = T3L+T3R+βT8R+X The right-handedfermions are arranged as:

2.2 Symmetry breaking schemes

To break the gauge symmetry and generate the particle masses ately, the scalar content is introduced as

√

2 Ξ−−22 Ξ

q−1 23

√ 2

Ξq13

√ 2

The spontaneous symmetry breaking is implemented through three possibleways

The first way assumes w  Λ  u, v, and the gauge symmetry is brokenas:

SU (3) C ⊗ SU (2) L ⊗ SU (3) R ⊗ U (1) X

w

−→ SU (3) C ⊗ SU (2) L ⊗ SU (2) R ⊗ U (1) B−L Λ

−→ SU (3) C ⊗ U (1) Q ⊗ W P

Conclusion: every symmetry breaking scheme leads to the matter parity WP as

a residual gauge symmetry, which is not commuted with the beginning gaugesymmetry The normal particles have WP = 1 They are particles in SM Thewrong particles have WP = P+ or P− They could be dark matter particles.2.3 Research results of phenomenology of the 3 − 2 − 3 − 1 model

2.3.1 Neutrino mass and lepton flavor violation

Neutrino mass

The Yukawa interaction:

L ⊃ hlabΨ¯aLSΨbR +hEabE¯aLφ†ΨbR +hRabΨ¯caRΞ†ΨbR+H.c (2.9)

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The neutral leptons get Dirac masses via u and right-handed Majorana massesvia Λ, given in the basis (νL, νc

R) as follows

Mν = −√1

2

0 hlu(hl)Tu 2hRΛ

2ml/v and mν ∼ 0.1 eV, we evaluate

hR ∼ √1

2

uv

Lepton flavor violation

The processes like µ → 3e happen at the tree level by the exchange ofdoubly-charged scalar (Ξ±±22 ) Branch ratio of the process µ → 3e:

Br(µ → eγ) ' α

48π

2516

|(hR†hR)12|2

MΞ422G2F , (2.14)where, α = 1/128 Taking the experimental bound Br(µ → eγ) < 4.2 × 10−13leads to mΞ 22 = 1–100 TeV for |(hR†hR)12| = 10−3–10, respectively Compar-ing to the previous bound, this case translates to hR

eτ,µτ ' 0.03–3.16

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2.3.2 Search for Z1 and Z10 at colliders

LEPII

The LEPII at CERN searched for new neutral gauge boson signals thatmediate the processes such as e+e− → (Z1, Z10) → f ¯f , where f is ordinaryfermion in the final state From the neutral currents, we obtain effective inter-actions describing the processes,

!(¯eγµPLe)( ¯f γµPLf )

we get: mZ1 > O(1) TeV

LHC

The LEPII at CERN searched for new neutral gauge boson signals thatmediate the processes such as pp → Z1 → f ¯f , where f is ordinary fermion inthe final state The cross-section for dilepton final states f ¯f :

σ(pp → Z1 → f ¯f ) =





13X

q =u,d

 dLq q ¯

dm2Z1

ˆσ(q ¯q → Z1)



× Br(Z1 → f ¯f ) (2.17)

10

+ + + + + + + + + + + + + + + + + ++ ++ + + + +

* Model : Β = 1 ‘ 3

10 -5

10 -4 0.001 0.01 0.1 1

s = 13 TeV with ATLAS detector The starand plus lines are the theoretical predictions for β = ±1/√3, respectively.Experimental results show that a negative signal for new high-mass phe-nomena in the dilepton final state It is converted into the lower limit on the

Z1 mass, mZ1 > 4 TeV, for models with β = ±1/√3

2.3.3 Dark matter phenomenology

A dark matter particle must satisfy the following conditions: Electricallyneutral, colorless, the lightest mass of parity odd particles and the dark matterrelic density agreement with the experiment Ωh2 ' <σv0.1pb

rel > ' 0.11 In thismodel, the dark matter candidates are:

• q =0: E1, H6, H7, XR

• q = -1: H8, YR

E1 Fermion dark matter

Dominated annihilator channels of E1:

E1E1c → ννc, l−l+, ναναc, lα−l+α, qqc, ZH1 (2.18)where the first two productions have both t-channel by respective XR, YR ands-channel by Z1, Z10, while the remainders have only the s-channel There mayexist some contributions from the new scalar portals, but they are small andneglected 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 mZ 0

1 changes hestabilization of dark matter yields only a Z1 resonance regime For instance,

11

w = 9 TeV, the dark matter mass region is 1.85 < mE1 < 2.15 TeV, given that

it provides the correct abundance

0.01 0.1 1 10

m E1 HGeVL

Hình 2.2: The relic density of the fermion candidate as a function of its mass,

mE 0, in the limit Λ  w, ở đây Z1 ≡ Z1 và Z2 ≡ Z10

Currently, there are three ways to search for dark matter: search at theLHC, direct search and indirect search The three methods have their ownstrengths Using Micromegas software, we drawn a graph for the direct searchprocess The direct detection experiments measure the recoil energy deposited

H6 scalar dark matter

The scalar H6 transforms as a SU (2)L doublet The field H6 can annihilateinto W+W−, ZZ, H1H1 and ¯f f since its mass is beyond the weak scale The

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annihilation cross-section is given by:

where x ∼ λSM ' 0.127 In order for H6’s density to reach the thermal dance density or below the thermal abundance density, its mass must meet

abun-mH6 < 600 GeV.However, when mH6 > 600 GeV is large, the scalar dark ter can (co)annihilate into the new normal particles of the 3-2-3-1 model viathe new gauge and Higgs portals similarly to the 3-3-1 model, and this canreduce the abundance of dark matter to the observed value, so H6 is not agood candidate for dark matter

mat-H7 scalar dark matter

SinceH7 is a singlet of theSU (2)Lgroup, it has only the Higgs (H1,2,3,4,6,7),new gauge, and new fermion portals The annihilation products can be thestandard model Higgs, W, Z, top quark, and new particles we chose the theparameter space to the primary annihilation channels is Higgs in SM throughthe new Higgs ports

Hình 2.4: Diagrams that describe the annihilation H7∗H7 → H1H1 via theHiggs portals, where and in the text we sometimes denote h ≡ H1 for brevity

We calculate the total amplitude of diagrams Feymman and build the pression of the dark matter relic density as:

Để Ωh2 ' 0.11 thì: mH7 ≤ |λeff| × 1.354TeV ∼ 1.354 TeV, We draw thegraph:

WIMP-UNSTABLE

0.00 0.05 0.10 0.15 0.20

m H7HTeVL

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 isblocked by YR mass

XR gauge boson dark matter

H8 scalar dark matter

The scalar field, H80, is considered as a LWP Because it transforms asthe doublet of SU (2)L group, it directly couples to the standard model gaugeboson and behaves like the H60 scalar field So, H8 is not a good candidate fordark matter

YR gauge boson dark matter

YR directly couples to the W±, Z gauge bosons, and the dominated hilation channels are YR0YR0∗ → W+W−, ZZ The dark matter thermal relic

anni-14

is very small, their relic abundance is ΩYRh2  10−3,much lower than that measured by WMAP/PLANCK.

2.4 Conclusions

The neutrino masses are naturally induced by a seesaw mechanism and theseesaw scale ranges from 104 GeV or 1016 GeV depending on the weak scaleratio u/v At the low seesaw scale, the lepton flavor violation decays µ → 3eand µ → eγ are dominantly induced by a doubly-charged Higgs exchange Thedecay rates are consistent with the experimental bounds if the doubly-chargedHiggs mass varies from few TeVs to hundred TeVs

The LEPII constrains the Z1 mass at O(1) TeV, while the LHC searchesshow that the Z1 mass is larger than 4 TeV for √

s = 13 TeV

The model q = 0 contains two types of dark matter, fermion and scalarfields The model q = −1 there is no candidate for dark matter

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