ヒッグスの発見 ２０１２年ヒッグス粒子 だと思われる 新粒子が LHC 実験によって 発見されました LHC 加速器の周の長さ 27km! 山手線は 35km 陽子と陽子を反対方向に加速してぶつけて新粒子を探す 陽子 陽子 衝突際のエネルギーはそれぞれの陽子を 1.5V の乾電池を約 2,500,0
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2 ヒッグスの発見 ２０１２年ヒッグス粒子 だと思われる 新粒子が LHC 実験によって 発見されました LHC 加速器の周の長さ 27km! 山手線は 35km 陽子と陽子を反対方向に加速してぶつけて新粒子を探す 陽子 陽子 衝突際のエネルギーはそれぞれの陽子を 1.5V の乾電池を約 2,500,000,000,000 個直列に繋いだ時の電位差による加速で得られるエネルギーに相当 ( 8TeV)!
3 ヒッグスの発見 ２０１２年ヒッグス粒子 だと思われる 新粒子が LHC 実験によって 発見されました ATLAS 検出器 CMS 検出器 衝突によって飛び出して来た粒子の崩壊を見る ことでどんな粒子が生成されたのかを調べる 陽子 陽子 ヒッグス粒子の寿命は 秒
4 ヒッグスの発見 アトラス検出器で捉えられたヒッグス粒子事象 ヒッグス粒子が生成され直後に２つのウィークゲージ粒子に崩壊 それらがそれぞれ２つのミュー中間子に崩壊 (赤い４本の線が４本のミュー中間子の軌跡)
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10 photon in 1923 Compton Scattering PETRA in 1979 Z,W bosons (~90 x proton SPS in 1983
11 photon in 1923 Compton Scattering PETRA in 1979 Z,W bosons (~90 x proton SPS in 1983
12 ~1.67x10-27 kg ~ 0.938GeV (natural unit) cf. Natural Unit : h 197MeV fm = 1, c 3.0x10 10 cm/s = 1
13 i t Ψ(t, x 1,, x N )=H N Ψ(t, x 1,, x N ) H N = N H 1 = i=1 N i=1 H 1 φ n (x) =ε n φ n (x) { 1 } 2m 2 V (x i ) Ψ(t, x 1,, x N )= 1 N! E = i permutation ε li φ l1 (x 1 ) φ l1 (x 1 )e it i ε l i l i l n l
14 H N n 1,n 2, = n i ε n 1,n 2, N = i i=1 n i [a i,a j ]=δ ij a i 0 =0 n 1,n 2, =Π i 1 ni! (a i )n i 0 H = i ε i a i a i
15 ˆϕ(x) = i a i φ i (x) [ˆϕ(x), ˆϕ (x )] = δ 3 (x x ) [ˆϕ(x), ˆϕ(x )] = 0 x 1,, x N = 1 N! ˆϕ (x 1 ) ˆϕ (x 1 ) 0 x 1,, x N t; n 1,n 2, = Ψ(t, x 1,, x N )
16 a i φ i (x)e iε it H = ε i a i a i = i ˆϕ(t, x) = i d 3 x ˆϕ (t, x) ( ) 1 2m 2 V (x) ˆϕ(t, x) [ˆϕ(t, x),iˆϕ (t, x )] = iδ 3 (x x ) ϕ(t, x)
17 x i (i =1 N) ˆϕ(t, x) L = N i ( m 2 x 2 i V (x i ) L =ˆϕ (t, x) i t 1 ) 2m 2 V (x) ˆϕ(t, x) p i = mx i [x i,p j ]=iδ ij ˆπ(x) =i ˆϕ(x) [ˆϕ(t, x),iˆϕ (t, x )] = iδ 3 (x x )
18 L =ˆϕ (t, x) ( i t 1 ) 2m 2 V (x) ˆϕ(t, x) L = µ φ (x) µ φ(x) m 2 φ (x)φ(x) φ 1 2m e imt ˆϕ E = p 0 = ±(m 2 p 2 ) 1/2 φ = d 3 p (2π) 3/2 2p 0 (ae ipx b e ipx )
19 L int = φ 1 φ 2 φ 3 L int = φ 1 φ 2 φ 3 φ 4 igqa µ ψγ µ ψ
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25 素粒子の分類 レプトンの実験事実 cu t cu $ t c $ t $ レプトンの相互作用は(質量の違いを除き)３世代平等 (Lepton universality) d s d b s dｇb s ｇb ｇ e! e "!e Z "! Z " Z Q=1 Q=0 u #e #!#e #"#!#ew#"#! H H W#" W H ex) W, Z ボゾンの崩壊分岐比 Br(W eνe)= Br(W μνμ)= Br(W τντ)=11% Br(Z ee-)= Br(Z μμ-)= Br(Z ττ-)=3.4% Lepton universality は W Zボゾンとレプトンの３点相互作用の 結合定数が共通であることを示している [さらには quark が感じる弱い相互作用と lepton が感じる弱い相互作用の強さも同じ]
26 156 素粒子の分類 CHAPTER 8. CHAPTER 8. QCD IN E E ANNIHILATIONS 8.1. THE BASICQCD PROCESS: QQ INEEE E ANNIHILATIONS basic process: e e q q of the quarks and the fact that the ncesクォークカラー自由度 are the fractional electric charges 157 The only di erences are the fractional electric charges of the quarks and the fact that the n Nc = 3 di erent colors which cannot be IN distinguished by measurement. CHAPTER 8. QCD E E ANNIHILATIONS quarks appear in N = 3 di erent colors which cannot be distinguished by measurement. c ee μμ 反応断面積 alculated theiscross sectionby for efactor e Nµc. µ ross section increased Forand the found quark-antiquark Therefore, the crossa section is increased by a factor Nc. Forcase the one quark-antiquark case one 2 2 m q = 0)are thus nbgev finds (for m = 0) erences the fractional electric charges of the quarks and the fact that the q em e e µ µ = = (8.1) 2 3s 2 r in Nc = 3 di erent 4 colors which cannot be distinguished by measurement. snbgev e e q q nbgev em CHAPTER 8. QCD IN E E ANNIHILATIONS e e q q em 2 = e N = e N. (8.2) c c e cross section is increased by a factor N. For the quark-antiquark case one = e N = e N. (8.2) 0 q q c 0 q c we consider the q c electron and muon masses neglected. Here, 3s have been s ee qq 反応断面積 3s s rm = 0) q the same diagram contributes: e Feynman e hadrons e eq q. qin q principle, e e hadrons e q q e only We = assume 2are i. e.fractional the quark-antiquark pair will and the fact = produced, charges i. e. the produced quark-antiquark pair that will the 2electric q,the The di erences of the quarks nbgev e q q em 2 0ealways = eq Nc e= e2q Nc. (8.2) hadronize. ze. µ q quarks appear in N3s = 3 di erent colors which cannot be distinguished by measurement. s c Figure 8.3: Ratio R = e e hadrons / e e µ µ as a function of the center of mass With Eq. ande ects (8.2), neglecting mass e ects and gluon as well asroughly photon radiation, e q q e (8.1) and e(8.2), neglecting mass and gluon as well as photon radiation, ecross hadrons energy. As expected by Eq. (8.3), there is no energy dependence besides various Therefore, the section is increased by a factor N. For the quark-antiquark case one =, i. e. the produced quark-antiquark c pair will q q resonances. The data confirm that there are three quark colors. we find the following ratio: e 断面積の比 μ owing ratio: nize. finds (for mq = 0) thus e e hadrons variables We define the kinematic e mass e hadrons 2 2 ) and (8.2), neglecting e ects and gluon as well as photon radiation, 2 2 R = = N e. (8.3) pi Q Ei (8.3) c e µ µ 86.9 nbgev e q q 4 e R = = N e. e q c em 2xi = 2 2 = (8.4) q 2 ollowing ratio: µ µ Q E = e N = e N. (8.2) e e q beam c c 0 q - q - q q 3s s e μ 2 e e hadrons where Q = pe pe = p /Z and Q = s. Energy-momentum conservation ( i pi = Q) runs over all flavors 2 The R sum that can be produced atcase, the available energy. For ECM requires that, in this = = N e. (8.3) c over assume all flavors that be atq the available For Equark-antiquark e e e q q µ produced e e hadrons CM ecan µ q energy. 1 µ e We =, i. e. the produced pair will (8.5) below the Z peak and above the resonance (see Fig. 8.3), we expect q q 1 xq xq xg = 2 ak and above the resonance (see Fig. 8.3), we expect always hadronize. x (8.6) i 1. s over all flavors that can be produced at the available energy. For E CM One 2 the differential 2 cross section can calculate 2 as well1 as photon 11 radiation, peak and above the (see Fig. we expect 2andresonance 22 neglecting 228.3),mass and With Eq. (8.1) (8.2), gluon 2 1e ects R = N e = N = N. 2 xq xq c d c 1 c s q 2 = C (8.7) 0 3 F = Nthe = N. weeqfind ratio: dx dx 2 (1 x )(1 x ) c following c q q q q q c factor of the d where b fundamental representation. Note that this 1 1 u e2e hadrons 1 CF =s 4/3 11 is the color 2 e q = Nc u =is singular Nc.for expression s c d b = 3 3 = N 9 e2. R (8.3) q ce. g. q g, q in good agreement with ethe e data µ µ x 1, q This uis for N = 3 which confirms that there are three c Nc = 3 bで良く再現される c s d 実験結果は q x 1, e. g. q g, and Z peak one also has to include coupling to the Zforthree boson which can be created agreementcolors. with At thethe data for N = 3 which confirms that there are q c from the e e all pair instead of a photon. The visible in thefor plotecm small (xqthere, xq ) remaining can (1, 1), be e.the g. created xg di erence 0. peak one also has to include coupling to the Zbe boson which The sum runs over flavors can produced at available energy. od agreement with the data for Nc = 3that which confirms that are three March 6, 13ahas isalso because QCD corrections forzgluon radiation later). pair instead of photon. Thecoupling small remaining di erence visible inconstrains the plot ZWednesday, peak one toofinclude to the boson whichofcan be created Because the(see kinematic imposed by1energy-momentum conservation (Eq. (8.5)
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28 Φ = U Φ U = Exp[ iαt ] Φ = U(x) Φ Φ = U(x) Φ U(x) Φ L = Φ Φ...
29 Φ DΦ = ( - i g A )Φ L = DΦDΦ... Φ = U(x) Φ, DΦ = U(x) DΦ A = i/g U(x) U(x) U(x) A U(x) -1
30 SU(3)xSU(2)xU(1)! 1,2 q,3 L = u L # " U R 1,2,3 D R 1,2,3 1,2,3 d L 1,2,3! l L = L # " e L E R $ & % $ & % SU(3) SU(2) U(1) 3 2 1/6 3 * 3 * - - g Z,W, γ -2/3 1/3-2 -1/ Lorentz Lorentz
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32 L = - Fμν F μν / 4, ( Fμν = μ A ν - ν A μ ) μ ( μ A ν - ν A μ ) = 0, μ A μ = 0 A μ A μ = A μ μ λ
33 L = - Fμν F μν / 4 m 2 A μ Aμ /2, μ ( μ A ν - ν A μ ) = - m 2 A ν, μ A μ = 0 A μ A μ = A μ μ λ
34 V[Φ] cf. L = Φ Φ - V[Φ] Φ
35 V[Φ]= (Φ 2 - v 2 ) 2 V[Φ] V[Φ]= ( Φ 2 - v 2 ) 2 V[Φ] Φ Φ - Φ v complex Φ plane Φ = e iα Φ
36 V[Φ]= ( Φ 2 - v 2 ) 2 V[Φ] U(1) <Φ> = v L = DμΦ D μ Φ Φ Φ = e iα Φ L = g 2 v 2 A μ Aμ m = gv <Φ> <Φ> m 2 A μ A μ A μ A μ
![V[Φ]= λ( Φ 2 - v 2 ) 2 /4 V[Φ] Φ(x) = ( v h(x)/ 2](/docs-images/92/109118326/images/37-1.jpg ") e i θ(x) Φ h(x) θ(x) V[Φ] λ 2 v 2 h 2 SU(2) x")
37 V[Φ]= λ( Φ 2 - v 2 ) 2 /4 V[Φ] Φ(x) = ( v h(x)/ 2 ) e i θ(x) Φ h(x) θ(x) V[Φ] λ 2 v 2 h 2 SU(2) x U(1)
38 L Fermion = ψ iσ μ D μ ψ - y U HQ L U R - y D H Q L D R - y L H L L E R y U,D,E : 3x3! <H >= # 0$ " v% & m f = y f v
39 素粒子標準模型 強い相互作用の到達距離 標準模型の SU(3) ゲージ相互作用は距離が離れ るほど強くなって行く性質を持つ (漸近的自由性) カラー荷を持った粒子を ~fm 以上引き離せない Energy ~ GeV x ( L / fm ) カラーは閉じ込められ カラー中性な [ u u L >> fm に伸ばす u u u u u u 真空からクォーク対を取り出して二つのカラー 中性粒子に分かれた方がエネルギー的に得 束縛状態のみ粒子として取り出せる
40 Higgs = Strong CP phase [ ]
41 Higgs V[h]= λ( h 2 - v 2 ) 2 /4 h v (v = 174GeV) Higgs mh = λ v Higgs λ λ Higgs λ Higgs λ LHC 125GeV Higgs λ Higgs Higgs
42 M ~ E 2 /M PL 2 (M PL = (8πG N ) -1/2 2.1x10 18 GeV) E > M PL E > M PL
43 ! 1,2 q,3 L = u L # " U R 1,2,3 D R 1,2,3 1,2,3 d L 1,2,3! l L = L # " e L E R $ & % $ & % SU(3) SU(2) U(1) 3 2 1/6 3 * 3 * /3 1/3-2 -1/
44 SU(3) x SU(2) x U(1) SU(5)! # # # # # " 1 D R 2 D R 3 D R 1 L L 2 L L $ & & & & & % ψ(5 * ) = ψ(10) = " $ $ $ $ $ $ # 0 U R 3 3 U R 2 U R 1 U L 1 D L 0 U R 1 1 U R 2 U L 2 D L U R U L D L 0 U L 3 3 U L 3 D L 2 2 U L D L D L 3 0 E R E R 0 % ' ' ' ' ' ' &
45 GeV
46 L Fermion = - y L H L L E R! <H >= 0 " v # $ % & m l = y L v (l = e, μ, τ) m ν ~10 -(3-1) ev
47 L Fermion = - y L H L L E R - (H L L )(H L L ) / Λ! <H >= # 0$ " v% & m L = y L v (l = e, μ, τ) m ν = v 2 /Λ (l = ν e, ν μ, ν ν ) Λ~ GeV m ν ~10 -(3-1)
48 Energy of the Universe 73% Dark Energy 23% Dark Matter 4% Standard Model particles
49 Energy of the Universe 73% Dark Energy 23% Dark Matter 4% Standard Model particles
50 K -1/2 a H -1 a 3(1ω)/2 p=ωρ ω = 0, 1/3
51 K -1/2 a H -1 a 3(1ω)/2 p=ωρ ω = -1 ω = -1
52 H -1 a 3(1ω)/2 a ω = 0, 1/3
53 H -1 a 3(1ω)/2 a ω = 0, 1/3 ω = -1
54 (n B - n B ) / n γ ~ 10-9 n γ ~ n B (n B - n B ) / n B ~ 10-9
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56 Neutrino? 10 ~15 GeV Inflation? 10 ~16 GeV Grand Unification? GeV Quantum Gravity? GeV log E Standard Model ~10 2 GeV Dark Matter (WIMP)? GeV Dark Matter (axion)? GeV
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cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq
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素粒子物理学2 素粒子物理学序論B 2010年度講義第4回
素粒子物理学 素粒子物理学序論B 010年度講義第4回 レプトン数の保存 崩壊モード 寿命(sec) n e ν 890 崩壊比 100% Λ π.6 x 10-10 64% π + µ+ νµ.6 x 10-8 100% π + e+ νe 同上 1. x 10-4 Le +1 for νe, elμ +1 for νμ, μlτ +1 for ντ, τレプトン数はそれぞれの香りで独立に保存
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( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e
![( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e](/thumbs/98/136160482.jpg "( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e")
( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
余剰次元のモデルとLHC
余剰次元のモデルと LHC 松本重貴 ( 東北大学 ) 1.TeraScale の物理と余剰次元のモデル.LHC における ( 各 ) 余剰次元モデル の典型的なシグナルについて TeraScale の物理と余剰次元のモデル Standard Model ほとんどの実験結果を説明可能な模型 でも問題点もある ( Hierarchy problem, neutrino mass, CKM matrix,
7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
![7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±](/thumbs/91/106462075.jpg "7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±")
7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a
![(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a](/thumbs/100/144882653.jpg "(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a")
1 2 2.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a) L ( ) ) * 2) W Z 1/2 ( - ) d u + e + ν e 1 1 0 0
6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
![6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2](/thumbs/92/109118076.jpg "6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
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ATLAS実験におけるトップクォーク対系 質量を関数とした生成微分断面積の測定! 山田美帆 海野義信A 神前純一A! 総研大 KEKA! 2012年 9月12日! 日本物理学会 2012年秋季大会! 京都産業大学!
ATLAS実験におけるトップクォーク対系 質量を関数とした生成微分断面積の測定! 山田美帆 海野義信A 神前純一A! 総研大 KEKA! 212年 9月12日! 日本物理学会 212年秋季大会! 京都産業大学! Introduction! l トップクォーク対による標準理論の検証! 最も重い素粒子の生成断面積を高エネルギー 高ルミノシティーで精密測定する! è 標準理論を超える新しい物理の発見にも!
『共形場理論』
T (z) SL(2, C) T (z) SU(2) S 1 /Z 2 SU(2) (ŜU(2) k ŜU(2) 1)/ŜU(2) k+1 ŜU(2)/Û(1) G H N =1 N =1 N =1 N =1 N =2 N =2 N =2 N =2 ĉ>1 N =2 N =2 N =4 N =4 1 2 2 z=x 1 +ix 2 z f(z) f(z) 1 1 4 4 N =4 1 = = 1.3
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LHC の最新結果 Koji Nakamura (KEK) on behalf of ATLAS&CMS collaboration 26th March, 2016 Theory WS @ Matsue 1 Contents 13TeV で再開した今年度の状況 加速器の様子 LHC 13TeV での最新結果 Higgs 粒子の再探索 VVやγγに見つかった怪しい兆候 SUSY/Exotic の探索
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