SGC - 48
208X Y Z Z 2006 1930 β Z 2006! 1 2 3
Z 1930 SGC -12, 2001 5 6 http://www.saiensu.co.jp/support.htm http://www.shinshu-u.ac.jp/ haru/ xy.z :-P 3 4 2006 3 ii
1 1 1.1... 1 1.2 1930... 1 1.3 1930... 4 2 9 2.1... 9 2.2... 12 2.3... 14 2.4... 16 2.5... 19 3 β 21 3.1... 21 3.2... 22 3.3... 23 3.4... 26 3.5... 27 4 29 4.1... 29 4.2... 30 4.3 π... 34 4.4... 36 5 37 5.1... 37 5.2... 38 5.3 e + e + μ + μ +... 40 5.4... 42 5.5... 43 5.6... 44 5.7... 47
6 48 6.1... 48 6.2... 51 6.3... 54 6.4... 56 7 58 7.1... 58 7.2... 59 7.3 ρ... 61 7.4... 62 7.5... 65 8 66 8.1... 66 8.2... 69 8.3... 70 8.4... 72 9 74 9.1... 74 9.2 θ τ... 77 9.3... 80 9.4 CPT... 81 9.5... 82 10 84 10.1... 84 10.2... 85 10.3... 87 10.4... 89 10.5... 92 11 93 11.1... 93 11.2... 94 11.3... 96 11.4... 98 11.5... 99 11.6...100 iv
12 101 12.1...101 12.2...101 12.3...106 12.4...108 12.5...109 13 111 13.1...111 13.2 σ...113 13.3...116 13.4...117 13.5...120 14 CP 121 14.1 K...121 14.2...122 14.3 K 0 K 0 CP...124 14.4 CP...127 14.5...129 14.6...130 15 131 15.1...131 15.2...133 15.3...139 16 141 16.1 π 0 2γ...141 16.2...144 16.3...148 17 149 17.1...149 17.2...152 17.3...157 18 159 18.1...159 18.2...163 18.3...168 v
19 169 19.1...169 19.2...171 19.3...174 19.4...176 19.5...178 20 179 20.1...179 20.2...180 20.3...183 20.4...185 20.5...187 21 189 21.1...189 21.2 K 0 K 0 CP...192 21.3...193 21.4...196 22 197 22.1...197 22.2...199 22.3...203 22.4...204 23 207 23.1...207 23.2...210 23.2.1...210 23.2.2...212 23.2.3...215 23.3...217 219 vi
1 2 1930 1.1 1. 2. 3. 1.2 1930 1930 β 1 Lorentz 2 3 gauge
2 1 4 2.1 4 x μ =(ct, x, y, z) =(ct, x) μ =0, 1, 2, 3 x μ x μ x μ + dx μ 2 ds 2 3 ds 2 c 2 dt 2 dx 2 dy 2 dz 2 = η μν dx μ dx ν = η μν dx μ dx ν, (2.1) μ,ν=0 1 0 0 0 η μν 0 1 0 0 0 0 1 0. (2.2) 0 0 0 1 c η μν metric (2.1) 2.1 3 Lorentz boost (x x) (t t) {x μ } {x μ } 1 x μ x μ = L μ ν x ν, x μ x μ = L μ ν x ν, (2.3) η αβ L α μl β ν = η μν. (2.4) 1 3
3 β β β 3.1 (U) (Th) (Ra) (Po) 3 α β γ α β γ α β γ ( 4 He) (e ) (γ) α γ β β 3.1 α γ (A) 60 1 A 4 He 4 He α (Z) 2 A 4 Z A α :(Z, A) (Z 2,A 4) + 4 He. (3.1) γ (γ) Z A γ :(Z, A) (Z, A)+γ. (3.2)
4 4.1 1932 (A) ( A/2) H + 2 1/2 2 2 ( ) p(x) N(x) =. (4.1) n(x) N(x) SU(2) ( ) 3 N(x) N (x) = exp i θ a τ a N(x). (4.2) 2 a=1 θ a τ a
5 QED QED 1 5.1 (M) (L) (T ) 3 (kg) (m) (s) MKS SI MKS (kg) (m) (s) (A) (K) (cd) (mol) SI 3 [E] =ML 2 T 2, [S] =ML 2 T 1, [v] =LT 1. (5.1) (ev) 10 3 1keV =10 3 ev 1MeV = 10 6 ev 1GeV = 10 9 ev 1TeV = 10 12 ev ~ (= 6.58211915 10 22 MeV s) c (= 2.99792458 10 8 m/s) MKS 3 1kg = 5.61 10 29 MeV/c 2, 1m = 5.07 10 12 ~c/mev, 1s = 1.52 10 21 ~/MeV (5.2) ~c = 197 10 15 MeV m ( ) ~ MeV Mc = Mc 2 197 10 15 m. (5.3) ~ = c =1 1 7
6 QED 1 2 3 4 e 6.1 1 = + =. (6.1) QED (a) (b) (c) 1 6.1(a) (b) (c) (a) (b) (c) 6.1 1 1
7 QED QED QED 7.1 QED (L QED ) L QED = ψ(x)(iγ μ ( μ + ieqa μ (x)) m) ψ(x) 1 4 ( μa ν (x) ν A μ (x))( μ A ν (x) ν A μ (x)). (7.1) 7.1 L QED U(1) ψ(x) ψ (x) =e iqθ(x) ψ(x), A μ (x) A μ(x) =A μ 1 e μθ(x). (7.2) θ(x) U(1) ψ(x) (=ψ (x)γ 0 ) D μ ψ(x) ( μ + ieqa μ (x))ψ(x) U(1) ψ(x) ψ (x) = ψ(x)e iqθ(x), D μ ψ(x) D μψ (x) =( μ + ieqa μ(x))ψ (x) =e iqθ(x) D μ ψ(x). (7.3) L QED 1 U(1) L QED 2 F μν (x) μ A ν (x) ν A μ (x) QED U(1) H. Weyl QED L D = ψ (iγ μ μ m) ψ L QED 7.2 QED
8 3 β 8.1 0 0 H β = G β ( p(x)γ μ n(x) ē(x)γ μ ν e (x) + h.c. + ). (8.1) C V =1 ( ν e ) β ν e (8.1) ν e + p n + e +. (8.2) 8.1 (8.2) (σ W ) G β /(~c) 3 =1.2 10 5 GeV 2 σ W [σ W ]=L 2 σ W G β 2 σ W = G2 β E2 c 4 ~ 4 =0.56 10 37 (E/GeV) 2 cm 2 =0.056 (E/GeV) 2 pb. (8.3) E ν e 8.2 ν e e + e + μ + μ + σ W (σ S ) π π (m π ) ( ) 2 ~ σ S = 10 26 cm 2. (8.4) m π c e + e + μ + μ + (σ EM ) s =2E
9 9.1 t t = t, x =(x, y, z) x = x =( x, y, z). (9.1) (r, θ, φ) (r, π θ, φ + π) θ φ (9.1) p L p p = p, L x p L = x p = L. (9.2) yz (x, y, z) ( x, y, z) x 180 3 9.1 m d2 x = F (x) (9.3) dt2 F (x) = F ( x) = F (x ) {x } V (x) V (x) =V ( x) i~ ( ) t ψ(x,t)= ~2 2m 2 + V (x) ψ(x,t) (9.4) V (x) =V ( x) {x } ψ (x,t )=e iθ P ψ(x,t) θ P (P ) ψ(x,t) O Pψ(x,t)=ψ( x,t), POP 1 = O. (9.5)
10 π 200 10.1 1 π 2 2 3 10 23 s 4 10 10 s 1 meson baryon hadron 2 2 10.2 3 4 V V V π + p K 0 +Λ 0, K 0 π + + π, Λ 0 p + π. (10.1) K 0 Λ 0 V 10.1 (E) ψ(t) exp( iet/~) N(t) ψ(t) 2 (τ) (exp( t/τ)) (τ) E = E 0 i Γ 2, τ = ~ Γ. (10.2) t <0 ψ(t) =0 ψ(t) φ(e) = 1 2π ψ(t)e i ~ Et dt = ψ(0) 2π i~ E E 0 + i Γ 2. (10.3)
11 0 11.1 100 10 18 m 15 15 11.1 F. W. London H. London 1935 j = 1 μ 0 λ 2 A. (11.1) λ j = 1 (A + θ). (11.2) μ 0 λ2 B = μ 0 j B = A 2 B = 1 λ 2 B (11.3) (11.3) q (= eq)
12 SU(3) 12.1 1 (B) 2 B =0 B ( =1 2 Q = I 3 + B + S ) 2 3 SU(3) 1 8 10 10 4 M = a + by + c [I(I +1) 14 ] Y 2. 12.1 1 4 3 SU(3) 3 1 2 4 (Y ) Y 12.2 1964 G. Zweig 1/2 SU(3) 3 quark
13 12 π 13.1 13.1 3 q f =(u, d, s) q f =(u, d, s) 1/2 m f =(m u,m d,m s ) L q = f q f (x)(iγ μ μ m f )q f (x). (13.1) L q (1) SU(3) V U(1) V m u = m d = m s L q ( ) 8 SU(3) V : q(x) q (x) = exp i θ α λα q(x), 2 α=1 (13.2) U(1) V : q(x) q (x) =e iθ q(x). (13.3) θ α (α =1,, 8) θ λ α SU(3) V : Fμ α λ α (x) = q(x)γ μ 2 q(x), Qα F0 α (x)d 3 x, (13.4) U(1) V : J μ (x) = q(x)γ μ q(x), Q V J 0 (x)d 3 x. (13.5) (2) SU(3) A U(1) A m u = m d = m s =0 L q ( ) 8 SU(3) A : q(x) q (x) = exp i ζ α λα 2 γ 5 q(x), (13.6) α=1 U(1) A : q(x) q (x) =e iζγ 5 q(x). (13.7)
14 CP K (K 0, K0 ) K 0, K0 CP K 0, K0 14.1 K K 0, K 0 S = +1, 1 K 0 d s, K 0 s d (d d, s s) K 0 K 0 CPT K 0 K 0 14.1 K 0, K0 K 0, K0 1 π + p K 0 +Λ 0, 14.1(a) 2 K + p K 0 + n, 14.1(b) 14.1 K S K 0, K0 K 0 K 0 (leptonic decay) 3 K 0 π + e + + ν e, 14.2(a) 4 K 0 π + + e + ν e, 14.2(b) non-leptonic decay 5 K 0 π + π +, K 0 π 0 + π 0, 14.3(a) (b) 6 K 0 π + π +, K0 π 0 + π 0, 14.3(a) (b)
15 15.1 β n p + e + ν e μ μ ν μ + e + ν e L β = G F 2 a p(x)γ μ (1 g A γ 5 )n(x) ē(x)γ μ (1 γ 5 )ν e (x) + h.c., (15.1) L μ = G F 2 ν μ (x)γ μ (1 γ 5 )μ(x) ē(x)γ μ (1 γ 5 )ν e (x) + h.c.. (15.2) a 0.975, g A 1.26 G F μ τ(μ ν μ + e + ν e )= 192π3 G 2 (1 + f(m e,m μ, )), τ μ F m5 exp =2.19703 10 6 s μ (15.3) G F =1.16637 10 5 /GeV 2 f(m e,m μ, ) G F Λ 0 p + π, (15.4) π + μ + + ν μ, π μ + ν μ, (15.5) K + π + + π 0, π + + π + + π, K 0 π + + π 0. (15.6) 1/4 15.1 V A β μ Λ V A
16 π (π 0 ) π 0 16.1 π 0 2γ π 0 π 0 1 m π 0 = (134.9766 ± 0.0006)MeV/c 2. 2 (B) 0 (Q) 0 3 SU(2) 3 3 I G =1. 4 J PC =0 +. 5 2 98.798 6 τ π 0 =(8.4 ± 0.6) 10 17 s 16.1 π 0 π 0 2γ π 0 π ~/(m π c) 10 15 m 2 2 π 0 (τ EM ) ( ) 2 4π~c ~ τ EM e 2 m π c 2 10 19 s. (16.1) 16.2 π 0 2γ π 0 2γ (M ) 16.1(a) (b) M = ε μ (k 1 )ε ν (k 2 )Λ μν (k 1,k 2,q)=iε μ (k 1 )ε ν (k 2 )ε μναβ k1 α k β 2 Λ(q2 ). (16.2) M Λ μν (k 1,k 2,q) (j μ ) Λ μν (k 1,k 2,q)=e 2 d 4 ye ik2y 0 T (j μ (0)j ν (y)) π 0,q
17 10 12 17.1 1 2 1 1. Regge trajectories (J) 2 (m 2 ) 17.1 J = α m 2 + α(0). α α 1(GeV) 2 α(0) ρ(m)dm = Am B e β0m dm. (17.1) ρ(m) m m + dm A, B T 0 1/β 0 160MeV Hagedron tempareture 17.1 ρ
18 18.1 (e ) (ν e ) (N) e e + N e + N e 18.1 e + N e + X X 18.1 18.1 e + N e + X N Q 2 q μ q μ, ν P μ q μ M, W 2 (P + q) 2 q μ, P μ (γ ) N 4 M N 4 p μ, p μ E, E e (mc 2 ) e e z θ x 4 P μ =(M,0, 0, 0), p μ =(E,0, 0,E), p μ =(E,E sin θ, 0,E cos θ), q μ = p μ p μ =(E E, E sin θ, 0,E E cos θ). (18.1)
19 19.1 1 (Q) (S) (B) CP 2 3 3 1 π 0 2γ, R SU(2) L U(1) Y 4 m π m N. 5 6 5 8 1 2 2 (H + ) 2 Q, S, B, CP 3 4
20 QCD QCD 20.1 4 φ(x) ( φ f,t f φ i,t i ) n (G (n) (x 1,,x n )) φ f,t f φ i,t i = N Dφe is, tf [ ] (20.1) 1 S = dt d 3 x t i 2 ( μφ μ φ m 2 φ 2 )+L int, DφΨ f[φ(t f )]Ψ i [φ(t i )]φ(x 1 ) φ(x n )e is G (n) (x 1,,x n )=. (20.2) DφΨ f[φ(t f )]Ψ i [φ(t i )]e is N L int Ψ i [φ(t i )] (Ψ f [φ(t f )]) e is e is 20.1 t τ = it 4 φ(x) n φ f,t f φ i,t i =N Dφe S E, τf [ ( S E = dτ d 3 1 x ( τ φ) 2 + ) ] (20.3) ( i φ) 2 + m 2 φ 2 L int, τ i 2 i DφΨ f[φ(t f )]Ψ i [φ(t i )]φ(x 1 ) φ(x n )e S E G (n) (x 1,,x n )=. (20.4) DφΨ f[φ(t f )]Ψ i [φ(t i )]e S E
21 CP 21.1 n g ( ) u LA q LA =, u RA, d RA (A =1, 2,,n g ) (21.1) d LA L (q) Y = A,B ( f (d) AB q LAΦd RB + f (u) AB q Φu ) LA RB + h.c.. (21.2) L (q) Y L (q) Y A,B ( 1 2 f (d) AB v d LA d RB + 1 ) f (u) AB vū LAu RB + h.c.. (21.3) 2 2 (S X,T X )(X = d, u) (m (X) A ) ( ) (S 1 X ) AC 2 f (X) CD v (T X ) DB = m (X) A δ AB. (21.4) C,D ψ (W ) I d (W ) LA d (W ) RA = B = B ψ (M) I S X, T X (S d ) AB d (M) LB, u(w ) LA = (S u ) AB u (M) LB, B (T d ) AB d (M) RB, u(w ) RA = (T u ) AB u (M) RB. (21.5) B j +μ (q) = A q (W ) LA γμ τ + q (W ) LA = A ū (W ) LA γμ d (W ) LA = q (M) LA γμ (S us d ) AB d (M) LB. (21.6) A,B V KM S us d Kobayashi Maskawa n g =2 21.1 n g CP
22 22.1 J. N. Bahcall pp (ν e ) ν e ν e 1968 ν e + 37 17Cl 37 18Ar + e ( 37 18Ar) ν e 0.81MeV pp 8 B 7 Be ν e 3 1 ν e 22.1 ν e pp 4p 4 He+2e + +2ν e +26.7MeV 26.7MeV γ 26.7MeV 2 ν e (I ) I =0.86 10 12 MeV/cm 2 s ν e N νe =2I /26.7 =6.4 10 10 /cm 2 s N νe 8 B 7 Be 22.2 ν e 1 2 8 B ν e (T C ) 18
23 23.1 1.1 1 2 3 1/2 23.1 (ν er ) 2 3 23.2 0 +1 1 1 23.3 W μ ± (Wμ 1 iwμ)/ 2 2 Wμ 0 Wμ 3 23.1 1 SU(3) C SU(2) L TL 3 Y Q ψ! ul q L = 3 2 d L 0 @ 1 2 1 2 u R 3 1 0 1 0 A 1 @ 2 3 6 1 3 2 3 2 3 1 A d R 3 1 0 1 3 ψ! νel l L = 1 2 e L 0 @ 1 2 1 2 1 3 1 A 1 2 ψ 0 1 e R 1 1 0 1 1 ν er 1 1 0 0 0!
7, 29 6 166 117 176 90 18 8 95 181 Wilson loop 183 50 50 62 34 sea quark 165 104 chirality 77 112 112 valence quark 165 2, 29 6 29 62 173 33 136 19, 87 7, 30 132 133 25 color 107 164 119 current algebra 112 strangeness 85 84 63 18, 74 6 12 quark 101 178 168, 176, 183 101 177 157 31 43 173 renormalization 45, 48 51, 57 52 52, 185 49 51 gluon 170 166 9 path integral 56 146 214 7, 58 12 18 12 58 91 89 string theory 152 lattice gauge theory 180 119
4 95 96 117 166 189 191 intrinsic parity 75 42 MSSM 210 regeneration 123 88 142 3 129 143 38 201 18, 80 g 46 7 46, 106 U(1) 19, 99 112 dimensional transmutation 185 naturalness 187 186, 210 38 95 215 weak isospin 134 weak hypercharge 134 6, 55 81 14, 95 45 deep inelastic scattering 160 210 19 2 20 regularization 45 cut-off parameter 45 186 54 26 168, 174 σ 114 counter term 52 151, 156 16 203 3 212 197 109 7 charm 108 c 108 30 118 136 K 121 216 supernova 204 supersymmetry 210 55 33 116 6, 11 11 210 16 17 14 12 209 electroweak theory 136 70 propagator 39 8 106 4, 10 t 190 55 167 87 220
99 95 95 153 187 23 22 71, 198 19 94 parton 163 parton model 163 6 hypercharge 86 26 2, 16 149, 155 running coupling constant 54 eightfold way 90 4 8 hadron 84 baryon 84, 102 74 79 18 144 59 63 24 σ 115 98, 135 135 38 standard model 209 17 38 172 26 131 25 27 88 2 181 23 4, 32 129 39 universality 25, 131, 186 161 174 85 plaquette 182 flavor 102 205 Proca field 94 103 26 145 111 151, 156 helicity 77 12 178 10 85 2 75 b 190 153 10 8, 93 200 11 69 41, 150 71 215 9 meson 84, 102 area law 184 44 195 59 63 221
179 effective coupling constant 53 effective action 52, 145 113 31 33 30 194 Unitarity 133 215 8, 215 24 vier Bein 64 43 44 Lamb shift 46 QCD 171 QED 17, 37 anomaly 143 link 182 Regge trajectories 149, 152 lepton 71 200 12 9 9 93 6 77 77 136 136 2 β double beta decay 202 3 2 215 α 21 BRS 172 B 195 CPT 81 CP 127 CP 126, 192 CP 123 γ 21 GIM 139 G 87 K 0 K 0 124, 192 Λ Λ 0 88 LSP 211 MSW 199 μ 24, 35 PCAC 115 π 0 2γ 141 π 31 π 115 QCD 174 ρ 136 R 211 R 107 SU(6) 105 S 26, 55 τ 109 θ τ 78 θ 170 V A 80 V 84 X, Y 212 β 22 222
1985 3 1987 3 1990 3 1990 4 1999 4 2006 4 2012 SGC -48 2016 3 10 ISBN 978 4 7819 9903 6 2006 6 25 TEL.(03)5474 8816 FAX.(03)5474 8817 http://www.saiensu.co.jp sk@saiensu.co.jp C TEL.(03)5474 8500 ( ) 151 0051 1 3 25
1 A U(1) (η η ) U(1) η η A.1 U(1) 13 S U(3) L S U(3) R U(1) V U(1) A S U(3) 8 1 NG η η A.1 η η S U(3) 8 8 η 8 A.1: 0 (MeV/c 2 ) (s) π + 139.57018 π + µ + + ν µ 2.6033 10 8 π 0 134.9766 π 0 2γ 8.4 10 17 π 139.57018 π µ + ν µ 2.6033 10 8 K + 493.677 K + µ + + ν µ, π + + π 0 1.2384 10 8 K 0 S 497.648 K 0 S π+ + π, 2π 0 0.8953 10 10 K 0 L 497.648 K 0 L π± + e + ν e, 3π 0, π + + π + π 0 5.18 10 8 K 493.677 K µ + ν µ, π + π 0 1.2384 10 8 η 547.74 η 2γ, 3π 0, π + + π + π 0 1.29keV η 975.78 η π + + π + η, ρ 0 + γ, 2π 0 + η 0.202MeV 1 η 0 13.9 0 8 NG 1 NG 1. m η 3m π 2. η Γ(η π + + π + π 0 ) 200eV U(1) 1974