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MINISTRY OF EDUCATION AND TRAINING HANOI NATIONAL UNIVERSITY OF EDUCATION BUI THI HA GIANG PHENOMENOLOGY OF SCALAR PARTICLE IN THE RANDALL–SUNDRUM MODEL Speciality: Theoretical and mathematical physics Classification: 9440103 SUMMARY OF PhD DISSERTATION HA NOI – 2020 The work was completed at Hanoi National University of Education Science supervisor: Prof Dr Dang Van Soa Assoc Prof Dr Dao Thi Le Thuy The first reviewer: Prof Dr Ha Huy Bang VNU University of Science The second reviewer: Assoc Prof Dr Phung Van Dong Phenikaa University The third reviewer: Assoc Prof Dr Luu Thi Kim Thanh Hanoi Pedagogical University The dissertation will be defended at Hanoi National University of Education at… o’clock …, day… moth… 2020 The dissertation is available at: - The Library of HNUE - The National Library of Vietnam INTRODUCTION Rationale The Standard model (SM) is the successful model in describing the elementary particle physics, some SM results have been fitted in the experiment Although the SM has been considered to be successful model, the SM suffers from many theoretical drawbacks Therefore, the requirement of the extended Standard model has been natural There are many attempts to extend the SM based on gauge groups in solving drawbacks However, the hierarchy problem is one of the theoretical faults which has not been resolved yet In 1999, Lisa Randall and Raman Sundrum suggested the Randall–Sundrum model (RS) which has been unified interactions and solved the hierarchy problem simply, naturally [Phys Rev Lett 83, 3370] In addition, the RS model has presented the attractive phenomenology, including Dark Matter candidates [Int J Mod Phys A 33, No.24, 1850144; JHEP 10, 094] In this dissertation, our research has based on the RS model In 2012, the 125 GeV Higgs boson was discovered by LHC (Large Hadron Collider) However, the observed boson at 125 GeV may not be the SM Higgs, it can be a dilaton/radion [Phys Lett B 712, 70; Phys Rev D 85, 095020; Phys Rev D 86, 115004; JHEP 1304, 015] The scalar state in the RS model discovered at 125 GeV is a Higgsdominated state Therefore, in this work, 125 GeV Higgs is concerned in Beside researching on radion (the new particle in the RS model) and Higgs, the influence of scalar unparticle on the production of particles at the high energy colliders in the RS model has been studied For those reasons mentioned above, I chose the topic: “Phenomenology of scalar particle in the Randall–Sundrum model” Objectives The main objectives of dissertation are to: - Evaluate the available parameters to take the signal of Higgs and radion in the collisions and decay processes in the future ILC (International Linear Collider) and CLIC (Compact Linear Collider) accelerators; - Show the contribution of the scalar unparticle in some colliders in the high energy Methodology In the dissertation, we have used the quantum field method such as Feynman diagram method to calculate the analytic formulas of scattering processes We also have used the Mathematica software to plot graphs of the cross–sections, the numerical decay rate of Higgs and radion which depend on some parameters of the RS model New contributions of the thesis Using the Feynman diagram method, we construct the analytic formulas of square scattering amplitude in the e+ e− ,  e− ,  collisions without the contribution of the scalar unparticle and in the e+ e− ,  , gg collisions with the contribution of the scalar unparticle; the formulas of decay rate of 125 GeV Higgs and the light radion in the RS model Using the analytic formuals, we plot the graphs of the dependence of the differential cross-section on scattering angle, the total cross-section on some parameters such as the polarized coefficients of electron and s , the radion mass m , the vacuum expectation value of radion   , the energy scale U and the scaling dimension dU Some results are predictive, oriented for experiment positron beams, the collision energy Dissertation outline In addition to the introduction, the conclusions, the appendix and the references, the dissertation is divided into chapters Contents of the dissertation are presented in 124 pages with 14 tables, 38 figures and graphs and 100 references CHAPTER I A REVIEW OF RANDALL–SUNDRUM MODEL AND UNPARTICLE PHYSICS A review of Randall–Sundrum model In 1999, Lisa Randall and Raman Sundrum extended the 4D Minkowski space to the 5D space The fifth dimension is compacted in the circle S The RS setup involves two 3-branes bounding a slice of 5D compact anti-de Sitter space Gravity is localized at the ultraviolet 3brane, while the strong, weak, electromagnetic interactions are supposed to be localized at the infrared 3-brane The separation between the two 3branes leads directly to the existence of an additional scalar called the radion ( ) corresponding to the quantum fluctuations of the distance between the two 3-branes The mixing between radion and Higgs boson follows from principle of general covariance The Higgs-radion mixed system is described by four independent parameters such as the physical masses of the two mixed scalars mh and m , the vacuum expectation value of radion (VEV)   , the mixing parameter ξ The physical phenomena which have been based on the experiment results at the LEP (Large Electron–Positron Collider), LHC and given forecast at the ILC accelerator have been concerned and studied A radion with mass below 100 GeV has been ruled out by any experiments [Mod Phys Lett A 28, 1350148] The results of production and decay of radion in the RS model in photon–photon subprocess at the ILC accelerator were obtained as follows:  → gg was shown to be the dominant mode for the light radion with mass below 150 GeV and   < TeV [Mod Phys Lett A 29, No.27, 1450136] Moreover, authors in [Phys Rev D 91, 016008] showed that: The cross-section for the light radion with mass below 125 GeV was studied in the allowed parameter space of VEV (2 TeV <   < TeV) through gluon fusion; The dominant modes were gluon–gluon and bb in the region of the radion mass which was about 100 GeV or downward However, because a peak in the diphoton invariant mass was a spectacular signal of new physics, the techniques to isolate two photons could be useful Therefore,  →  channel was shown to be the best mode for observing the light radion at the LHC Besides, many authors have concerned in physical signals in RS model with four allowed parameters: The physical masses of mixed scalar particles m , mh , the radion VEV   ,the mixing parameter ξ Initially, the results of evaluating the radion mass m have been given as follows: In the region of the radion mass 40 – 60 GeV and mh = 120 GeV, h →  channel was unique allowed mode with   [Nucl.Phys B 671, 243] The region 80 GeV < m < 350 GeV is the region in which radion was coupled maximally to the massless gauge bosons The region of parameter space was studied at the 13 and 14 TeV LHC through  final state  decay channel was the mode to observe −1 directly at the 14 TeV LHC with the luminosity 1000 fb [Phys.Rev D 94, 055016] When   = 10 TeV,  → bb channel for m < 135 GeV,  → W + W − mode for m > 135 GeV ,  → ZZ mode for m > 200 GeV were the dominant mode [Phys Rev D 90, 035006] The radion which was associated with the massive gauge boson and quark b was studied at the LHC and ILC [Phys.Rev D 94, 055016] Although the final states were hadron, the heavy radion was discovered by the lepton decay channels of the gauge bosons at the accelerator with high luminosity Therefore, authors studied of the ZZ decay mode of the radion when the radion mass could be upward 450 GeV at the 14 TeV LHC In this region, the prominent decay channels of radion were b quark when m < 160 GeV, WW/ZZ when m > 160 GeV The Z and WW final states could be found at the ILC Although the radion mass in the region m > 250 GeV could not be probed by the LHC through the diphoton final state, it could be probed through the ZZ final state, with the Z decaying to lepton Secondly, the results of evaluating the Higgs mass mh have been given as follows: When mh ranged (130 – 180) GeV, the W+ W− final state was the dominant decay mode of Higgs boson The bb channel was the prominent mode of Higgs boson when mh < 135 GeV [Phys Rev D 90, 035006] Based on the vacuum expectation value of the radion   , authors showed that the light radion signal in the range 50 GeV – 100 GeV could be produced by the e + e − → Z collision at the LEP when   > 1.0 TeV, at the LHC when  − TeV [Phys Rev Lett 113, No 17, 171801; Phys Lett B 565, 61; Phys Lett B 483, 196] When   > 10 TeV, the contribution of loop and Higgs – radion mixing to the couplings became very small and the mixing parameter was nearly zero When   > 15 TeV, any signals of the model could not be found However, there were model points accessible at the future ILC even if   = 50 TeV Finally, based on the mixing parameter ξ: The experimental data showed that the allowed range of ξ for m = 140 GeV was from 0.04 to 0.13 through the diphoton decay channel of radion [Phys Rev D 94, 055016] At the 500 – 1000 GeV ILC with luminosity of 500 – 1000 fb −1 , the allowed range of ξ was 0.11 - 0.13 In case of   = TeV, the experimentally allowed range of ξ for m = 140 GeV was 0.01 – 0.28 at −1 the 14 TeV LHC with 3000 fb through the diphoton channel of −1 radion, and at the TeV ILC with 1000 fb The available parameter space for the m < 400 GeV consisted of two regions, one near ξ = and another for ξ > 0.5 The region near ξ = was fully explored at the LHC through the diphoton mode Another region ξ > 0.5 could be explored through ZZ mode but not fully at the LHC However, at the 1000 GeV ILC, the radion signal could be fully found through WW production mode in the region ξ > 0.5 Besides the Higgs, radion decay modes, the production of the associated Higgs–radion, the couple of Higgs are researched through the f f , gg collisions However, the authors have calculated the analytic formulas In conclusion, most of authors studing the theorical signals of the RS model have concerned in the Higgs and radion decay channels to evaluate the suitable parameter space, the observability of Higgs and radion Unparticle physics The experimenters measured the cross-section of processes in the laboratory, however there were differences between theory and experiment The theoretical cross-section which has been obtained is smaller than the experimental data Therefore, there may be any additional process In 2007, Howard Georgi proposed an interesting idea about unparticle which has been similar to particles but is not a particle [Phys Rev Lett 98, 221601] Unparticle has not be massive and scale invariant theory Georgi also assumed that unparticle theory has been which the very high theory contains the SM fields and the Banks-Zaks (BZ) fields Following Georgi, many groups have studied the phenomena of scalar, vector and tensor unparticle in the SM The contribution of vector unparticle in propagator with different values has been concerned The + − + − total cross-section in the e e →   collision was illustrated the dependence on s with the  , Z and vector unparticle propagators Authors forcused the effect for dU = 3/2 in the region s < 200GeV [Phys Lett B 650, 275] Moreover, unparticle physics has been studied in couplings in the SM extension to hope to illustrate the experimental data Unparticle physics was considered in the Supersymmetry Standard Model [Phys Rev D 76, 116003] Because the unparticle operator coupled to the supercurrent of Minimal Supersymmetric Standard Model, the couplings broke supersymmetry clearly Since the unparticle appeared at TeV scale where supersymmetry was broken, unparticle was not the reason for supersymmetry breaking However, the method of unparticle which affected the supersymmetry breaking space was explained Some authors studied unparticle physics in the RS model However, authors considered the theoretically simple calculation for unparticle couplings to particles in the branes, evaluated lepton flavor violating radion decays [Phys Lett B 678, 149; Eur Phys J C 56, 105] Scalar unparticle signal was concerned at the LHC [Phys Rev D 93, 052011, Phys Rev D 95, 095005] Authors not only evaluated the selfinteractions of unparticles but also considered the possible interaction of scalar unparticle in the processes at the 14 TeV LHC The cross-section was studied in the ( U , dU ) plane U was chosen as TeV and TeV dU was chosen as 1.1, 1.5, 1.9 Authors analysed the signals which were obtained as a base of the SM theory In the pp → 2 collision at TeV, unparticle physics was expected to be seen at the LHC when U was around TeV and dU was about 1.1 The unparticle contribution to the Casimir effect was shown that dU was about [Phys Lett B 772, 675] In summary, although the contribution of unparticle in the high energy processes has been discussed by several authors, the vector and tensor unparticles have been focused [Phys Lett B 678, 149; EPL, Vol.84, No.1, 11001; Phys Lett B 694, 393; Eur Phys J C 55, 325] Moreover, influence of scalar unparticle on the production at the high energy collisions in the RS model has not concerned yet CHAPTER THE PRODUCTION AND DECAY SCALAR PARTICLES In this chapter, we have studied the production of Higgs and radion on the e+ e− ,  e− ,  collisions with the polarization of the electron and positron in high energy Besides, the decay rate of 125 GeV Higgs and radion are evaluated the ability of observed 125 GeV Higgs, radion through the decay channels These results in this chapter were made public through articles at Adv Stud.Theor Phys, Vol 11, No, 12, 629; Comm Phys, Vol 26, No 1, 19; Vol 27, No 1, 83; Journal of science of Hnue: Math and Phys, Vol 62, Is 8, 89 2.1 The e + e − → hZ collision In this section, the total cross-section in e+ e− → hZ collision is evaluated with P1 , P2 which are the polarization coefficients of e + and e − beams, respectively  is the angle between the e − and Higgs directions We choose mh = 125 GeV (CMS),  = 1/ [Nucl Phys B 595, 250],  = TeV [Nucl Phys B 671, 243] Fig 2.1 The total cross-section of + − Fig 2.2 The differential cross-section e e → hZ collision as a function of e+ e− → hZ collision as a function of P1 , P2 when s = TeV of cos when s = TeV 11 The total cross-section has a maximum value at m = 110 GeV, the cross-section is given by  4.62 pb The result could be compared to the signals of Higgs including to the lepton flavor violation at ILC [J Phys G 42, 075003] 2.3 The e + e − →  /  h / hh collisions In this section, the dependence of total cross-sections on the collision s in e+ e− →  /  h / hh collision are plotted with m = 10 GeV,  = 1/ [Nucl Phys B 595, 250],  = TeV [Nucl Phys B 671, 243] energy + − + − Fig 2.9 The total cross-sections of (a) e e → hh, (b) e e →  , (c) e+ e− →  h collisions as the function of P1 , P2 when s = 500 GeV + − Fig 2.10 The total cross-sections of (a) e+ e− → hh , (b) e e →  , (c) e+ e− →  h collisions as the function of s in case of unpolarized e+ , e− beams Fig 2.9 – 2.10 show that the total cross-section reachs the maximum value when P1 =1, P2 = −1 or P1 = − 1, P2 = and receives the minimum value when P1 = P2 = 1 The cross-sections for pair production of Higgs or radion decrease rapidly when the collision energy s increases In 12 the production of associated Higgs–radion, the cross-section increases when the collision energy increases 2.4 The  →  /  h / hh collisions Fig 2.11 The total cross-section of (a)  → hh , (b)  →  , (c)  →  h collisions as a function of s at the ILC accelerator Fig 2.12 The total cross-section of (a)  → hh , (b)  →  , (c)  →  h collisions as a function of s at the CLIC accelerator The Fig 2.11 – 2.12 show that in ILC accelerator, the cross-section for pair production of Higgs is the largest and the cross-section for pair production of radion is the smallest in the pair production of scalar particles However, in CLIC accelerator, the associated production crosssection of Higgs–radion is the largest, the pair production cross-section of radion is the smallest 2.5 The decay of scalar particles 13 We calculated the decay rate of the 125-GeV Higgs and radion which were dependent on the radion mass with   = 5000 GeV However, in this dissertation, figures with the mixing parameter  in which the decay rate reachs maximum value are indicated In this summary, we only present the results of some typical decay processes 2.5.1 The decay processes of Higgs boson Table 2.2 The decay rate of the 125-GeV Higgs in  , gg , e − e + channels in cases of m and  (h →  ) (1019 s −1 ) (h → gg ) (1021 s −1 ) ( h → e − e + )  = −0.119  = 0.04  = 0.069 10 2.8574 5.0932 3.2337 20 2.8577 5.0918 3.2336 30 2.8592 5.0893 3.2333 40 2.8590 5.0856 3.2329 50 2.8601 5.0802 3.2324 60 2.8616 5.0726 3.2317 70 2.8636 5.0614 3.2305 80 2.8663 5.0447 3.2286 90 2.8697 5.0174 3.2251 100 2.8734 4.9671 3.2179 110 2.8681 4.8464 3.1953 120 2.4064 4.1939 2.9518 m (GeV ) (1013 s −1 ) The Table 2.2 shows the results of the 125-GeV Higgs decay as follows: In the Higgs decay processes into  , gg e− e+ ( f f ), the decay rate decrease gradually in the region 10 GeV  m  110 GeV and decreases fast in the region 110 GeV  m  120 GeV The gg mode is the dominated channel 14 2.5.2 The decay processes of radion Table 2.6 The decay rate of radion in  , gg , e − e + channels in cases of m and  ( →  ) (1016 s −1 ) ( → gg ) (1020 s −1 ) ( → e− e+ ) (1011 s −1 )  = 0.153  = 0.137  = 0.157 10 0.0059 0.0118 0.0636 20 0.0567 0.0757 0.1320 30 0.2005 0.2418 0.2109 40 0.5017 0.5703 0.3085 50 1.0617 1.1236 0.4376 60 2.0565 1.9725 0.6208 70 3.8282 3.2039 0.9024 80 7.1336 4.9415 1.3804 90 13.9615 7.3991 2.3110 100 31.1023 11.0745 4.5623 110 96.1291 17.7951 12.9120 120 1162.5200 52.8022 163.7360 m (GeV ) The results of the radion decay are shown as follows: In the decay processes into diphoton, e− e+ ( f f ), the decay rate nearly unchange in the region 10 GeV  m  110 GeV and increase fast in the region 110 GeV  m  120 GeV In the decay process into the pair of gluon, the decay rate increases gradually in the region 10 GeV  m  80 GeV and increase fast in the region 80 GeV  m  120 GeV The gg channel is the most dominated channel in the radion decay channels In conclusion, in Higgs and radion decay channels, the dominant decay mode is the pair of gluon channel The observable ability of Higgs and radion base on most of the signal of e− e+ final The range of ξ 15 (−1/ 6, 1/ 6) is the region in which the Higgs, radion signals are the best observability CHAPTER THE CONTRIBUTION OF SCALAR UNPARTICLE IN SOME COLLISION PROCESSES At the high energy region (above TeV), the contribution of scalar unparticle in the collsion processes is significant In this chapter, we evaluate the contribution of scalar unparticle in the high energy e− e+ ,  and gg collisions We compare the results in case of the scalar unparticle contribution with the results without the scalar unparticle contribution These results in this chapter were made public through the article at Nuclear Physics B 936, 3.1 The e + e − → hh /  collisions Fig 3.1 The cross-section as a function of dU in a) e+ e− → hh , + − (b) e e →  collisions when s = 500 GeV, U = 1000 GeV Fig 3.2 The total cross-section as a function of s in (a) e+ e− → hh , (b) e + e − →  collisions when U = 1000 GeV 16 Fig 3.3 The total cross-section as a function of U in (a) e+ e− → hh , (b) e + e − →  collisions when s = 500 GeV, dU = 1.1 Some estimates for the cross-sections are given as follows: In case of additional scalar unparticle propagator, when s = 500 GeV, the crosssections decrease rapidly in the region 1.1  dU  1.6 and they flat when dU  1.6 The total cross-sections decrease when the collision energy s increases The total increases rapidly in the region of 2TeV  U  5TeV The above figures show that the cross-section in case of the scalar unparticle, radion and Higgs propagators, the crosssection is much larger than that in case of radion, Higgs propagators The cross-section in e − e + →  collision is larger than that in e− e+ → hh collision under the same conditions 3.2 The  → hh /  collisions Fig 3.4 The total cross-section as a function of dU in (a)  → hh , (b)  →  collisions when s = 3000 GeV , U = 1000 GeV 17 Fig 3.5 The total cross-section as a function of s in (a)  → hh , (b)  →  collisions when U = 1000 GeV Fig 3.6 The total cross-section as a function of U in (a)  → hh , (b)  →  collisions when s = 3000 GeV, dU = 1.1 In this section, the results are given as follows: When the collision energy s is chosen as 3000 GeV, the total cross-section decreases and achieves the minimum value as dU = 1.65, then increases as dU > 1.65 The total cross-section decreases gradually when the collision energy increases In the region of 1000 GeV  U  5000 GeV , the total crosssection decreases gradually The total cross-section in the radion pair production is larger unsignificantly than that in the Higgs pair production under same conditions 3.3 The gg → hh /  collisions 18 Fig 3.7 The total cross-section as a function of dU in (a) gg → hh , (b) gg →  collisions when s = 3000 GeV, U = 1000 GeV Fig 3.8 The total cross-section as a function of s in (a) gg → hh , (b) gg →  collisions when U = 1000 GeV Fig 3.9 The total cross-section as a function of U in (a) gg → hh , (b) gg →  collisions when s = 3000 GeV , dU = 1.1 From Fig 3.7 – 3.9, some estimates are given as follows: When the s is chosen as 3000 GeV, the curve of cross-section goes the minimum value as dU = 1.45 then increases as dU > 1.45 The collision energy total cross-section decreases gradually when the collision energy 19 increases In the region 1000 GeV  U  5000 GeV , the cross-section decreases The total cross-section in the radion pair production is larger unsignificantly than that in the Higgs pair production under same conditions 3.4 The e + e − → Uh / U collisions + − Fig 3.10 The total cross-section as a function of dU in (a) e e → Uh , (b) e+ e− → U  collisions when s = 500 GeV, U = 1000 GeV Fig 3.11 The total cross-section as a function of the collision energy + − s + − in (a) e e → Uh , (b) e e → U  collisions when U = 1000 GeV + − Fig 3.12 The total cross-section as a function of U in (a) e e → Uh , + − (b) e e → U  collisions when s = 500 GeV, dU = 1.1 20 From Fig 3.10 – 3.12, the results are shown as follows: The crosssection declines rapidly in the region 1.1  dU  1.4 and decreases gradually in the region 1.4  dU  1.9 The total cross-sections decrease when the collision energy s increases In the region 1000 GeV  U  5000 GeV , the cross-section increases The total cross-section in the associated production Uh is about 103 times larger than that in the associated production U under same conditions 3.5 The  → Uh / U collisions Fig 3.13 The total cross-section as a function of dU in (a)  → Uh , (b)  → U collisions when s = 3000 GeV, U = 1000 GeV Fig 3.14 The total cross-section as a function of (b)  → U s in (a)  → Uh , collisions when U = 1000 GeV 21 Fig 3.15 Total cross-section as a function of U in (a) (b)  → U collisions when  → Uh , s = 3000 GeV From Fig 3.13 – 3.15, we show the results as follows: The crosssections decrease rapidly when dU increases from 1.1 to 1.6 and it is flat with dU > 1.6 When the collision energy s increases then the total cross-sections increase gradually The cross-sections decrease gradually as U increases in the region 1000 GeV  U  5000 GeV The total cross-section in  → Uh collision is larger than that in  → U collision under the same conditions 3.6 The gg → Uh / U collisions Fig 3.16 The total cross-section as a function of dU in (a) gg → Uh , (b) gg → U collisions when s = 3000 GeV, U = 1000 GeV 22 Fig 3.17 The total cross-section as a fuction of s in (a) gg → Uh , (b) gg → U collisions when U = 1000 GeV Fig 3.18 The total cross-section as a function of U in (a) gg → Uh , (b) gg → U collisions when s = 3000 GeV From Fig 3.16 – 3.18, the results for associated production are given as follows: The cross-section decreases rapidly as dU increases and it is flat when dU > 1.45 The total cross-sections increase gradually when the collision energy s increases The cross-sections decrease as U increases from 1000 GeV to 5000 GeV The thesis shows that the total cross-section in gg → Uh collision is larger than that in gg → U collision under the same conditions 23 CONCLUSION The production and decay processes of Higgs boson and radion in the RS are studied in the dissertation The contribution of the scalar unparticle in the high energy collisions are also studied The following results have been obtained in the dissertation as follows: We have calculated the analytic formulas and plotted the crosssection of e+ e− ,  e− ,  collisions which produce Higgs boson, the pair of scalar particles such as radion–radion, Higgs–Higgs, the associated pair Higgs–radion The results have been shown that the observable Higgs signal from the e+ e− → hZ process reachs the maximum value in e+ e− collisions in the dissertation because the hZZ coupling is larger than the other couplings In  e− collision, the cross-sections are enhanced at the fixed radion mass m given by  max 110 GeV The cross-section is 4.62 pb The result could be compared to the signals of Higgs including to the lepton flavor violation at ILC [J Phys G 42, 075003] The analytic formulas have been calculated and the numeral results of the decay rate of Higgs and radion in the RS model have been plotted We have evaluated the observable Higgs, radion signals which base on the decay channels In the decay processes of 125-GeV Higgs and radion which is below 120 GeV, the gluon channel is the main decay mode The decay rate in the e+ e− channel is minimum, so the time life of Higgs and radion in the e+ e− channel is maximum Therefore, the observable ability of Higgs and radion are based on most of the signal of e+ e− final mode The mixing parameter in the region (-1/6, 1/6) is shown to obtain the observable signals This result can be suitable to [Nucl Phys B 595, 250] Moreover, the 110 GeV radion signal is the concerned signal in the experiment 24 The signals of pair production of scalar particles with the contribution of scalar unparticle in the RS model have been evaluated in the e+ e− ,  and gg collisions The cross-sections in case of the contribution of scalar unparticle are much 106 − 1011 times than that without the contribution of scalar unparticle The cross–sections in the gg collision are larger than that in the  collision because the gluon couplings with scalar particles are larger than the photon couplings with scalar particles In conclusion, the results in the dissertation show the observable ability of Higgs and radion at the high energy colliders in the future ILC, CLIC accelerators and evaluate the contribution of the scalar unparticle on these collisions Specially, the existence of the unparticle could be discovered with the bounds on scale U are around few TeV and the low values of the scaling dimension ( dU is close to 1) This result can be suitable to the outcome of unparticle contribution to the Casimir effect [Phys Lett B 772, 675] Our results numerical calculations could be compared with other theoretical calculations as we know Our numerical calculations can be seen as the useful references for experiments in the future ILC, CLIC accelerators There are some physical processes which will be studied in the future, for instance,the lepton flavor violation, the CP violaion, the contribution of scalar unparticle to the dark matter Moreover, the collisions and the decay channels which include the contribution of unparticle in the extended Standard model will be studied LIST OF PUBLICATIONS INCLUDED AS PART OF THE DISSERTATION [1] D T L Thuy and B T H Giang (2015), “  e− → he− collision in Randall–Sundrum model”, Communication in Physics, Vol 25, No 3, pp 239 – 246 [2] Dao Thi Le Thuy and Bui Thi Ha Giang (2016), “ e− e+ → hZ collision in Randall–Sundrum model”, Communication in Physics, Vol 26, No 1, pp 19 – 24 [3] D V Soa, D T L Thuy, B T H Giang (2016), “Production and decay of radion and Higgs in e+ e− and  +  − colliders”, Journal of Physics: Conference Series, 726, 012027 [4] B T H Giang, D V Soa and D T L Thuy (2017), “Radion production in high energy photon collisions”, Communication in Physics, Vol 27, No 1, pp 83 – 89 [5] B T H Giang and D T L Thuy (2017), “Production of Higgs in two photon collision”, Journal of science of Hnue: Math and Phys, Vol 62, Iss 8, pp 89 – 95 [6] Dang Van Soa, Dao Thi Le Thuy, Bui Thi Ha Giang (2017), “The signal of Higgs from the dominated state – 125 GeV in Randall–Sundrum model via  e − colliders”, Advanced Studies in Theoretical Physics, Vol 11, No 12, pp 629 – 640 [7] Dang Van Soa, Bui Thi Ha Giang (2018), “The effect of the scalar unparticle on the production of Higgs–radion at high energy colliders”, Nuclear Physics B 936, pp – 18 ... and 100 references CHAPTER I A REVIEW OF RANDALL SUNDRUM MODEL AND UNPARTICLE PHYSICS A review of Randall Sundrum model In 1999, Lisa Randall and Raman Sundrum extended the 4D Minkowski space... Lisa Randall and Raman Sundrum suggested the Randall Sundrum model (RS) which has been unified interactions and solved the hierarchy problem simply, naturally [Phys Rev Lett 83, 3370] In addition,... he− collision in Randall Sundrum model”, Communication in Physics, Vol 25, No 3, pp 239 – 246 [2] Dao Thi Le Thuy and Bui Thi Ha Giang (2016), “ e− e+ → hZ collision in Randall Sundrum model”,