Hiệu ứng hạt vô hướng trong mô hình randall sundrum

BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM HÀ NỘI BÙI THỊ HÀ GIANG HIỆU ỨNG HẠT VƠ HƯỚNG TRONG MƠ HÌNH RANDALL-SUNDRUM LUẬN ÁN TIẾN SĨ VẬT LÍ Hà Nội – Năm 2020 BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM HÀ NỘI BÙI THỊ HÀ GIANG HIỆU ỨNG HẠT VÔ HƯỚNG TRONG MƠ HÌNH RANDALL-SUNDRUM Chun ngành: Vật lí lí thuyết vật lí tốn Mã số: 9440103 LUẬN ÁN TIẾN SĨ VẬT LÍ NGƯỜI HƯỚNG DẪN KHOA HỌC: GS TS Đặng Văn Soa PGS TS Đào Thị Lệ Thủy Hà Nội – Năm 2020 i L i cam oan T i xin cam oan: Lu n n "Hi u ng h t v h ng m h nh Randall-Sundrum" l c ng tr nh nghi n c u ri ng c a t i C c s li u tr nh b y lu n n l trung th c, c ng t c gi cho ph p v ch a t ng c c ng b b t c c ng tr nh n o kh c H N i, ng y 30 th ng 12 n m 2019 ii MCLC L i cam oan i Mclc ii Danh m c c c t vi t t t v Danh m c c c k hi u c b n vi Danh m c c c b ng vii Danh m c c c h nh v , M U th ix Ch ng 1- T NG QUAN V M H NH RANDALL SUNDRUM V V T L U-H T 1.1 M h nh Randall-Sundrum 1.1.1 T c d ng c a m h nh 1.1.2 Kh i l ng v t l c a tr ng Higgs 1.1.3 C ch Goldberger Wise 1.1.4 Kh i l ng c a tr ng chu n photon, W, Z 12 1.1.5 S tr n Higgs-radion 17 1.1.6 T ng t c c a Higgs, radion v i tr ng chu n 19 1.1.7 M t s nghi n c u g n y 21 iii 1.2 V t l U-h t 25 1.2.1 Gi i thi u v U-h t 25 1.2.2 H m truy n v t ng t c hi u d ng c a U-h t v h ng 26 1.2.3 M t s nghi n c u g n y 29 K t lu n ch ng 32 Ch ng 2- M T S QU TR NH SINH V R H T V H NG 33 2.1 Qu tr nh t n x e+e− → hZ 33 2.1.1 Tr ng h p ch m e−, e+ kh ng ph n c c 34 2.1.2 Tr ng h p ch m e−, e+ c ng ph n c c tr i ho c c ng ph n c c ph i 39 2.1.3 Tr ng h p ch m e− ph n c c tr i, ch m e+ ph n c c ph i v ng c l i 45 2.2 Qu tr nh t n x γe− → he− 50 2.2.1 Tr ng h p ch m e− kh ng ph n c c 50 2.2.2 Tr ng h p ch m e− ban u, ch m e− t o th nh c ng ph n c c tr i ho c c ng ph n c c ph i 51 2.2.3 Tr ng h p ch m e− ban u ph n c c tr i, ch m e− t o th nh ph n c c ph i v ng c l i 52 2.3 Qu tr nh t n x e+e− → φφ/φh/hh 57 2.3.1 Tr ng h p ch m e−, e+ kh ng ph n c c 58 2.3.2 Tr ng h p ch m e−, e+ c ng ph n c c tr i ho c c ng ph n c c ph i 60 2.3.3 Tr ng h p ch m e− ph n c c tr i, ch m e+ ph n c c ph i v ng c l i 62 2.4 Qu tr nh t n x γγ → φφ/φh/hh 65 2.5 Qu tr nh r h t v h ng 70 iv 2.5.1 B r ng ph n r c a m t s qu tr nh r h t v h ng 70 2.5.2 K t qu t nh v th o lu n 74 K t lu n ch ng 82 Ch ng 3- NG G P C A U-H T V H NG TRONG M T S QU TR NH T N X 84 3.1 Qu tr nh t n x e+e− → hh/φφ 84 3.2 Qu tr nh t n x γγ → hh/φφ 88 3.3 Qu tr nh t n x gg → hh/φφ 94 3.4 Qu tr nh t n x e+e− → Uh/Uφ 98 3.5 Qu tr nh t n x γγ → Uh/Uφ 101 3.6 Qu tr nh t n x gg → Uh/Uφ 104 K t lu n ch ng 108 K T LU N 110 DANH M C C C C NG TR NH C NG B LI N QUAN N T I LU N N 113 T I LI U THAM KH O 114 PH L C A 125 PH L C B 127 PH L C C 130 v Danh m c c c t vi t t t Vi t t t T vi t t t SM Standard model KK Kaluza-Klein RS Randall-Sundrum IR Infrared UV Ultraviolet ADD Arkani Hamed, Dimopoulos, Dvali GW Goldberger-Wise BZ Banks-Zaks LEP Large Electron Positron Collider LHC Large Hadron Collider ILC International Linear Collider LSP Lightest Supersymmetric Particle CLIC Compact Linear Collider MSSM Minimal Supersymmetric Standard Model vi Danh m c c c k hi u c b n K hi u T n g i √ s N ng l ng t n x mh Kh i l ng c a Higgs mφ Kh i l ng c a radion pi Xung l ng c a c c h t tr ng th i u ki Xung l ng c a c c h t t o th nh Λφ Gi tr trung b nh ch n kh ng c a radion ψ − G c t n x h p b i (→ p 1, k ) ξ Th ng s tr n σ Ti t di n t n x to n ph n Γ B r ng ph n r dU Th nguy n t l c a to n t U-h t ΛU Thang n ng l ng L Pi − → tr ng c a m y gia t c H s ph n c c vii Danh m c c c b ng √ 2.1 Ti t di n t n x ng v i m t s gi tr c a s v Λφ tr ng h p P1 = P2 = m y gia t c ILC 56 2.2 B r ng ph n r c a c c k nh r Higgs kh i l ng 125 GeV γγ, gg ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 74 2.3 B r ng ph n r c a c c k nh r Higgs kh i l ng 125 GeV e−e+, µ−µ+, τ −τ + ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 75 2.4 B r ng ph n r c a c c k nh r Higgs kh i l ng 125 GeV uu, dd, cc, bb, ss ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 76 2.5 B r ng ph n r c a k nh r Higgs kh i l ng 125 GeV φφ ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ = 1/6 76 2.6 B r ng ph n r c a c c k nh r radion γγ, gg ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 78 2.7 B r ng ph n r c a c c k nh r radion e−e+, µ−µ+, τ −τ + ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 79 viii 2.8 B r ng ph n r c a c c k nh r radion uu, dd, cc, bb, ss ng v i m t s gi tr c a kh i l ng radion mφ v th ng s tr n ξ 80 3.1 B ng gi tr ti t di n t n x to n ph n c ng g p c aUh t v h ng qu tr nh t n x e+e− → hh/φφ tr n m y gia t c ILC 87 3.2 B ng gi tr ti t di n t n x to n ph n c ng g p c aUh t v h ng qu tr nh t n x γγ → hh/φφ tr n m y gia t c CLIC 94 3.3 B ng gi tr ti t di n t n x to n ph n c ng g p c aUh t v h ng qu tr nh t n x gg → hh/φφ tr n m y gia t c CLIC 97 3.4 B ng gi tr ti t di n t n x to n ph n c a qu tr nh t n x e+e− → Uh/Uφ tr n m y gia t c ILC 101 3.5 B ng gi tr ti t di n t n x to n ph n c a qu tr nh t n x γγ → Uh/Uφ tr n m y gia t c CLIC 104 3.6 B ng gi tr ti t di n t n x to n ph n c a qu tr nh t n x gg → Uh/Uφ tr n m y gia t c CLIC 107 116 20 D V Soa, Takeo Inami and H N Long (2004), "Bilepton production in e−γ collisions", Eur Phys J C 34, 285 21 D W Jung, P Ko (2014), "Higgs-dilaton(radion) system confronting the LHC Higgs data", Phys Lett B 732, 364 22 E Boos, S Keizerov, E Rakhmetov, K Svirina (2014), "Higgs bosonradion similarity in production processes involving off-shell fermions", Phys Rev D 90, 095026 23 E Boos, S Keizerov, E Rakhmetov, K Svirina (2016), "Comparison of associated Higgs boson-radion and Higgs boson pair production processes", Phys Rev D 94, 024047 24 E E Boos, V E Bunichev, M A Perfilov, M N Smolyakov, I P Volobuev (2015), "Higgs-radion mixing in stabilized brane world models", Phys Rev D 92, 095010 25 E O Iltan (2008), "Unparticle physics and lepton flavor violating radion decays in the Randall-Sundrum scenario", Eur.Phys.J.C 56, 105 26 F Abu-Ajamieh (2018), "The Radion as a Dark Matter Candidate", Int J Mod Phys A 33, No.24, 1850144 27 G Aad et al (2014), "Search for Scalar Diphoton Resonances in the Mass Range 65 600 GeV with the ATLAS Detector in pp Collision √ Data at s = TeV", ATLAS Collaboration, Phys Rev Lett 113, No 17, 171801 28 G Aad et al (2012), "Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC", ATLAS Collaboration, Phys Lett B 716, 117 29 G C Cho, D Nomura, Y Ohno (2013), "Constraints on radion in a warped extra dimension model from Higgs boson searches at the LHC", Mod Phys Lett A 28, 1350148 30 G C Cho and Y Ohno (2014), "Production and decay of radion in Randall-Sundrum model at a photon collider", Mod Phys Lett A 29, No.27, 1450136 31 G F Giudice, R Rattazzi and J D Wells (2001), "Graviscalars from higher-dimensional metrics and curvature-Higgs mixing", Nucl Phys B 595, 250 32 H Abramowicz et.al (2017), "Higgs Physics at the CLIC ElectronPositron Linear Collider", Eur Phys J C 77, 475 33 H Davoudiasl, J L Hewett and T G Rizzo (2000), "Phenomenology of the Randall-Sundrum Gauge Hierarchy Model", Phys Rev Lett 84, 2080 34 H Davoudiasl, J L Hewett and T G Rizzo (2001), "Experimental probes of localized gravity: On and off the wall", Phys Rev D 63, 075004 35 H Davoudiasl, J L Hewett and T G Rizzo (2000), "Bulk Gauge Fields in the Randall-Sundrum Model", Phys Lett B 473, 43 36 H Georgi (2007), "Unparticle Physcis", Phys Rev Lett 98, 221601 37 H Georgi (2007), "Another Odd Thing About Unparticle Physics", Phys Lett B 650, 275 38 H Kubota, M Nojiri (2014), "Prospect for Study of Randall-Sundrum model from Higgs decay at future colliders", Phys Rev D 90, 035006 118 39 H Nakada, S V Ketov (2016), "Randall-Sundrum brane-world in modified gravity", Phys Rev D 94, 103503 40 H Zhang, C S Li and Z Li (2007), "Unparticle physics and supersymmetry phenomenology", Phys Rev D 76, 116003 41 I F Ginzburg, G L Kotkin, S L Panfil, V G Serbo and V I Telnov (1984), "Colliding γe and γγ beams based on single-pass e+e− accelerators II Polarization effects, monochromatization improvement" Nucl Instr and Meth 219, 5; V I Telnov (2000), "Status of gamma-gamma, gamma-electron colliders", Nucl Phys Proc Suppl 82, 359 42 J F Gunion, M Toharia and J D Wells (2004), "Precision electroweak data and the mixed Radion-Higgs sector of warped extra dimensions", Phys Lett B 585, 295 43 J M Maldacena (1998), "The Large N Limit of Superconformal Field Theories and Supergravity", Adv Theor Math Phys.2, 231 44 I Sahin and B Sahin (2008), "Unparticle Physics in the Moller Scattering", Eur Phys J C 55, 325 45 K Agashe, A Delgado, M.J May and R Sundrum (2003), RS1, custodial isospin and precision tests , JHEP 0308, 050 46 K Agashe, R Contino and A Pomarol (2005), The minimal composite Higgs model , Nucl Phys B 719, 165 47 K Agashe and R Contino (2006), The minimal composite Higgs model and electroweak precision tests , Nucl Phys B 742, 59 48 K Cheung (2001), "Phenomenology of Radion in Randall-Sundrum Scenario", Phys.Rev D 63, 056007 119 49 K Cheung and T-C Yuan (2012), "Could the excess seen at 124-126 GeV be due to the Randall-Sundrum Radion?", Phys.Rev.Lett 108, 141602 50 K Cheung, W-Y Keung and T-C Yuan (2007), "Collider Signals of Unparticle Physics", Phys Lett 99, 051803 51 K Cheung, W-Y Keung and T-C Yuan (2007), "Collider phenomenology of unparticle physics", Phys Rev D 76, 055003 52 K Oda and A Weiler (2005), Wilson Lines in Warped Space: Dynamical Symmetry Breaking and Restoration , Phys Lett B 606, 408 53 L Randall and R.Sundrum (1999), "A Large Hierachy from a Small Extra Dimension", Phys Rev Lett 83, 3370 54 M A Stephanov (2007), "Deconstruction of unparticles", D 76, 035008 Phys Rev 55 M Battaglia, S De Curtis, A De Roeck, D Dominici and J F Gunion (2003), "On the Complementarity of Higgs and Radion Searches at LHC", Phys.Lett B 568, 92 56 M.C Kumar, P Mathews, V.Ravindran and A.Tripathi (2008), "Unparticle physics in diphoton production at the CERN LHC", Phys Rev D 77, 055013 57 M Carena, E Ponton, J Santiago and C.E.M Wagner (2007), Electroweak constrains on warped models with custodial symmetry , Phys Rev D 76, 035006 58 M Chaichian, A Datta, K Huitu and Z h Yu (2002), "Radion and Higgs mixing at the LHC", Phys Lett B 524, 161 120 59 M Frank, K Huitu, U Maitra, M Patra (2016), "Probing Higgsradion mixing in warped models through complementary searches at the LHC and the ILC", Phys.Rev D 94, 055016 60 M Geller, S Bar-Shalom, A Soni (2014), "Higgs-radion unification: Radius stabilization by an SU(2) bulk doublet and the 126 GeV scalar", Phys Rev D, 89, 095015 61 M Quiros (2015), "Higgs bosons in extra dimensions", Mod A 30(15), 1540012 Phys Lett 62 M Toharia (2009), "Higgs-Radion Mixing with Enhanced Di-Photon Signal", Phys Rev D 79, 015009 63 N Arkani-Hamed, S Dimopoulos and G R Dvali (1998), "The Hierarchy Problem and New Dimensions at a Millimeter", Phys Lett B 429, 263 64 N Arkani-Hamed, S Dimopoulos and G R Dvali (1999), "Phenomenology, astrophysics and cosmology of theories with subMillimeter dimensions and TeV scale quantum gravity", Phys Rev D 59, 086004 65 N Desai, U Maitra, B Mukhopadhyaya (2013), "An updated analysis of radion - Higgs mixing in the light of LHC data", JHEP 2013, 093 66 N Greiner (2007), "Constraints On Unparticle Physics In Electroweak Gauge Boson Scattering", Phys Lett B 653, 75 67 P Mathews and V Ravindran (2007), "Unparticle physics at hadron collider via dilepton production", Phys Lett B 657, 198 121 68 R Barate et al (2003), "LEP working group for Higgs boson searches and ALEPH and DELPHI and L3 and OPAL Collaborations", Phys Lett B 565, 61 69 R Contino, Y Nomura and A Pomarol (2003), Higgs as a holographic pseudo-Goldstone boson , Nucl Phys B 671, 148 70 S Bae, P Ko, H S Lee and J Lee (2000), "Phenomenology of the radion in the Randall-Sundrum scenario at colliders", Phys Lett B 487, 299 71 S Bhattacharya, M Frank, K Huitu, U Maitra, B Mukhopadhyaya, S K Rai (2015), "Probing the light radion through diphotons at the Large Hadron Collider", Phys Rev D 91, 016008 72 S Casagrande, F Goertz, U Haisch, M Neubert, T Pfoh (2008), "Flavor Physics in the Randall-Sundrum Model: I Theoretical Setup and Electroweak Precision Tests", JHEP 0810, 094 73 S Chatrchyan et al (2012), "Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC", CMS Collaboration, Phys Lett B 716, 30 74 S Khatibi, M M Najafabadi (2013), "Top quark asymmetries and unparticle physics at the Tevatron and LHC", Phys Rev D 87, 037701 75 S Majhi (2008), "W-pair production in Unparticle Physics", Lett B 665, 44 Phys 76 S Matsuzaki and K Yamawaki (2012), "Techni-dilaton at 125 GeV", Phys Rev D 85, 095020 77 S Matsuzaki and K Yamawaki (2012), "Discovering 125 GeV technidilaton at LHC", Phys Rev D 86, 035025 122 78 S Matsuzaki and K Yamawaki (2012), "Holographic techni-dilaton at 125 GeV", Phys Rev D 86, 115004 79 S Matsuzaki and K Yamawaki (2013), "Is 125 GeV techni-dilaton found at LHC?", Phys Lett B 719, 378 80 T Banks and A Zaks (1982), "On the phase structure of vector-like gauge theories with massless fermions", Nucl Phys B 196, 189 81 T D Rueter, T G Rizzo and J L Hewett (2017), "Gravity-Mediated Dark Matter Annihilation in the Randall-Sundrum Model", JHEP 10, 094 82 T Kikuchi, N Okada and M Takeuchi (2008), "Unparticle physics at the photon collider", Phys Rev D 77, 094012 83 T M Aliev, S Bilmis, M Solmaz and I Turan (2017), "Scalar unparticle signals at the LHC", Phys Rev D 95, 095005 84 U Mahanta and A Datta (2000), "Search prospects of light stabilized radions at Tevatron and LHC", Phys Lett B 483, 196 85 V Barger, M Ishida and W -Y Keung (2012), "Differentiating the Higgs boson from the Dilaton and Radion at Hadron Colliders", Phys Rev Lett 108, 101802 86 V P Goncalves and W K Sauter (2010), "Radion production in exclusive processes at CERN LHC", Phys Rev D 82, 056009 87 W D Goldberge and I Z Rothstein (2003), "Systematics of coupling flows in AdS backgrounds", Phys Rev D 68, 125012 88 W D Goldberge and I Z Rothstein (2000), "Quantum stabilization of compactified AdS5", Phys Lett B 491, 339 123 89 W D Goldberge and I Z Rothstein (2002), "High Energy Field Theory in Truncated AdS Backgrounds", Phys Rev Lett 89, 131601 90 W D Goldberge and I Z Rothstein (2003), "Effective field theory and unification in AdS backgrounds", Phys Rev D 68, 125011 91 W D Goldberger and M B Wise (1999), "Modulus Stabilization with Bulk Fields", Phys Rev Lett., 83, 4922 92 W D Goldberge and M B Wise (2000), "Phenomenology of a Stabilized Modulus", Phys Lett B 475, 275 93 Y Hosotani and M Mabe (2005), Higgs boson mass and electroweak gravity hierarchy from dynamical gauge-Higgs unification in the warped space-time , Phys Lett B 615, 257 94 Y Hosotani, S Noda, Y Sakamura and S Shimasaki (2006), GaugeHiggs Unification and Quark-Lepton Phenomenology in the Warped Spacetime , Phys Rev D 73, 096006 95 Y Hosotani and Y Sakamura (2007), Anomalous Higgs couplings in the SO(5) × U (1) gauge-Higgs unification in warped spacetime , Prog Theor Phys 118, 935 96 Y Sakamura and Y Hosotani (2007) , WWZ, WWH and ZZH couplings in the dynamical gauge-Higgs unification in the warped spacetime , Phys Lett B 645, 442 97 Y Sakamura (2007), Effective theories of gauge-Higgs unification models in warped spacetime , Phys Rev D 76, 065002 98 Z Chacko, R Franceschini, and R K Mishra (2013), "Resonance at 125 GeV: Higgs or Dilaton/Radion?", JHEP 1304, 015 124 99 Z Chacko and R K Mishra (2013), "Effective Theory of a Light Dilaton", Phys Rev D 87, 115006 100 Z Chacko, R K Mishra and D Stolarski (2013), "Dynamics of a stabilized radion and duality", JHEP 1309, 121 125 PH L C A Khi t nh ti t di n t n x kh ng quan t m n ph n c c, ta l y t ng Σ −p , s)u(→ −p , s)β = (p + m)β , uα (→ / α (3.70a) −p , s)υ(→ −p , s)β = (p − m)β α υα (→ / (3.70b) s Σ s Khi t nh ti t di n t n x c quan t m n ph n c c, c ng th c (3.70) c d ng Σ s Σ s −p , s)β = uα( −→ p , s)u( → (p/ + m) (1 ± γ ) β , (3.71a) β − → − → υα( p , s)υ( p , s)β = (p/ − m) (1 ∓ γ5) α (3.71b) α C ng th c l y t ng c a c c vect ph n c c i v i c c tr ng chu n giao ho n nh photon Σ λ=1,2 (3.72) ε∗µ (k, λ)εν (k, λ) = −ηµν C ng th c l y t ng c a c c vect ph n c c i v i c c tr ng chu n (v kh ng chu n) c kh i l ng nh W ±, Z, Σ3 ε∗ (k, λ)εν(k, λ) = µ λ=1 −ηµν + kµkν m2 (3.73) −p = −→ −p , −p = → X t qu tr nh t n x h kh i t m, ta c → − → − → − → → − −p k = k = −k , g c t n x ψ = (→ , k ), s = (p1 + p2 )2 C c bi n s ng l c h kh i t m −p ), p = (E , −→ − p1µ = (E1 , → 2µ p ), − → − → k1µ = (E3 , k ), k2µ = (E4 , −k ) S d ng c c c ng th c sau s = (E1+E2)2 = (E3+E4)2, (3.74) 126 −p |2, m21 = E 12 − |→ (3.75) −p |2, m22 = E 22 − |→ − → m23 = E 32 − |k |2, − → m24 = E 42 − |k |2, (3.76) (3.77) (3.78) √ y Ei, mi l n l t l n ng l ng v kh i l ng c a c c h t, s g i l n ng l ng c a ch m h t t i, ta thu c bi u th c c a c c t ch v h ng √ (p1p2, p1k1, k1k2, ) ph thu c v o n ng l ng s, g c t n x ψ, Ti t di n t n x vi ph n h kh i t m c a qu tr nh p1 + p2 → k1 + k2 c d ng − → dσ k = |Mf i | , − → dcosψ 32πs |p | (3.79) |Mfi|2 ta l y t ng theo c c tr ng th i spin c a c c h t tr ng th i cu i v trung b nh c ng theo tr ng th i spin c a c c h t tr ng th i u 127 PH L C B Gi n Feynman m t c c qu tr nh t n x lu n n H nh 3.19: Gi n Feynman m t qu tr nh t n x e+e− → hZ H nh (a), (b), (c) l n l t ng v i c c k nh s, u, t H nh 3.20: Gi n Feynman m t qu tr nh t n x γe− → he− H nh (a), (b), (c) l n l t ng v i c c k nh s, u, t H nh 3.21: Gi n Feynman m t qu tr nh t n x e+e− → hh/φφ v i h m truy n φ, h, U H nh (a), (b), (c) l n l t theo c c k nh t n x s, u, t 128 H nh 3.22: Gi n Feynman m t qu tr nh t n x γγ → hh/φφ v i h m truy n φ, h, U H nh (a), (b), (c) l n l t l c c k nh t n x s, u, t H nh 3.23: Gi n Feynman m t qu tr nh t n x gg → hh/φφ v i h m truy n φ, h, U H nh (a), (b), (c) l n l t m t c c k nh t n x s, u, t H nh 3.24: Gi n Feynman m t qu tr nh t n x e+e− → Uh/Uφ H nh (a), (b), (c) l n l t m t k nh t n x s, u, t 129 H nh 3.25: Gi n Feynman m t qu tr nh t n x γγ → Uh/Uφ H nh (a), (b), (c) l n l t m t k nh t n x s, u, t H nh 3.26: Gi n Feynman m t qu tr nh t n x gg → Uh/Uφ H nh (a), (b), (c) l n l t m t k nh t n x s, u, t 130 PH L C C i n t ch v kh i l ng c a m t s h t c b n m h nh chu n Htc bn K hi u i n t ch Kh i l ng electron e− -1 0.511 (MeV/c2) neutrino electron νe < 1.0 (eV/c2) muon µ− -1 105.66 (MeV/c2) neutrino muon νµ < 0.17 (MeV/c2) tau τ− -1 1.77 (GeV/c2) neutrino tau ντ < 18.2 (MeV/c2) quark up u 2/3 2.2 (MeV/c2) quark down d -1/3 4.7 (MeV/c2) quark charm c 2/3 1.28 (GeV/c2) quark strange s -1/3 96 (MeV/c2) quark top t 2/3 173.1 (GeV/c2) quark bottom b -1/3 4.18 (GeV/c2) photon γ 0 gluon g 0 boson Z Z 91.19 (GeV/c2) boson W ± W± ±1 80.39 (GeV/c2) ... PHẠM HÀ NỘI BÙI THỊ HÀ GIANG HIỆU ỨNG HẠT VƠ HƯỚNG TRONG MƠ HÌNH RANDALL- SUNDRUM Chun ngành: Vật lí lí thuyết vật lí tốn Mã số: 9440103 LUẬN ÁN TIẾN SĨ VẬT LÍ NGƯỜI HƯỚNG DẪN KHOA HỌC: GS TS Đặng... ng l ng s 6 CH NG T NG QUAN V M H NH RANDALL SUNDRUM V V T L U-H T 1.1 M h nh Randall- Sundrum 1.1.1 T c d ng c a m h nh N m 1999, Lisa Randall v Raman Sundrum m r ng kh ng th i gian b n chi... a chi u th m v o R '' 1mm v i gi tr th c c a n l R '' 10−33cm N m 1999, Lisa Randall v Raman Sundrum a m h nh Randall- Sundrum (RS) M h nh RS th ng nh t c c c t ng t c: h p d n, m nh, y u v i n