( ) 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 ( - ) L L d u + e + ν e 1 1 0 0 0 0 1 1 µ e + ν e + ν µ 1 1 1 1 µ 1 0 0 1 e 0 1 1 0 * 1) * 2) * 3) SU(3) 1
(A,Z) (A,Z 1) + e + + ν e (A,Z) (A,Z + 1) + e + ν e (2a) (2b) µ e + ν e + ν µ (3) 1 µ eγ µ e + γ < 1.2 10 11 (4) 2 π π 1: µ eγ π + µ + + ν µ ( 2(b)) ν µ (ν e ) ( 2(a) ) ( 2(c)(d)) 1962 2: (a) d (b) π + u d W + µ + ν µ (c)(d)(e) ν e, ν µ, ν τ ( ) e + e + τ + τ + (5a) e + ν e + ν τ τ (5b) µ + ν µ + ν τ 2
ν τ ν τ ν e (ν µ ) τ e(µ) + γ ν e (ν µ ) µ eγ, τ µγ e +X µ +Y ( ) Z e + e + Z (q i + q i ) or (l i + l + i ) or (ν i + ν i ) (6) i 3 m Z /2 * 4) ( BR = Γ(Z ) Γ(Z all) e e + E(e e + ) s = mz σ(e e + hadrons) = σ(e e + Z)BR(Z hadrons) (8) ( 3) (7) N ν = 2.994 ± 0.012 (9) 3: e + e + Z N ν =3,4,5 m z /2 8.2 (1930) 30 (1956) ν e + p e + + n e + + e n +Cd γ + γ Cd Cd + (3 4) γ s (10a) (10b) * 4) m Z = 91GeV, m top = 185GeV m u 3MeV, m s 6MeV, m s 120MeV, m c 1.3GeV, m b 4.2GeV m e 0.51MeV, m µ = 105.7MeV, m τ 1777MeV, m νi = 0 3
Cd Cd W e + W p( u ) (d ) 2m e 3-4 10 4 1m ( ) ( ) 4 4: Reines-Cowan(1954) γ (Cd) 1kW 2 10 14 10 13 /sec/cm 2 100 ( ) 20 8.3 8.3.1 d u + e + ν e (11) W f i = 2π H i f 2 ρ, ρ = (12) H f i 2 4
Γ ρ = δ(e 0 E e E ν ) d3 p e (2π) 3 d 3 p ν (2π) 3 (13a) dγ = G2 β 2π M 3 2 F(Z,E)p e E e p ν E ν de e (13b) p ν E ν = (E 0 E e ) (E 0 E e ) 2 m 2 ν, E 0 = M(Z,A) M(Z + 1,A) m ν = E e,max (13c) M 2 = < 1 > 2 + C GT 2 < σ > 2 (13d) F(Z,E) [ ] dγ 1/2 de K(E) = e (14) F(Z,E)p e E e m ν = 0 K(E) E 0 E e ( 5) m ν 0 5: ( ) m ν 0 m ν ( ) (1) E 0 m ν E 0 ( 3 H, E 0 = 18KeV ) E e = E 0 E 0 E e > E 0 ε = R E0 E 0 E2 (E 0 E) 2 ( ) de 3 R E0 0 E 2 (E 0 E) 2 de = 10 (15) E 0 = 1eV ε 2 10 13 m ν 5
(2) E E 6 R OP (E) E EL(E) BS(E) N(E ) Z N(E) obs = N(E )R(E,E )de (16) 6: ( 5 ) (3) V p ν E ν = P i (E 0 V i E e ) i (E 0 V i E e ) 2 m 2 ν ) (17) P i i * 5) 7 3 H p/p = 0.02%( E = 8eV ) E 0 1600eV m ν = 0 m ν < 13eV m νe < 2eV 8.3.2 π + (p) µ + (q) + ν µ (k) (18) π m π = q 2 + m 2 µ + k 2 + m 2 ν, k = k = q = q (19a) q m π = 139.56995 ± 0.00035MeV m µ = 105.658389 ± 0.000034MeV q = 29.79200 ± 0.00011MeV m 2 ν = 0.016 ± 0.023 (20a) m ν µ < 0.17MeV (90%CL) (20b) * 6) * 5) Phys. Lett. B187(1987)198-204 * 6) K.AssamaganPhys. Rev. D53(1996) 6065 6
7: m ν = 0 m ν < 13eV e e + π + e + e + τ + τ m 2 ν = E(ν) 2 p(ν) 2 = (m τ i τ ± π ± + π + + π + ν τ E(π i )) 2 ( p(π i )) 2, E(π i ) = i p(π i ) 2 + m 2 π (21a) (21b) (21c) m τ = 1777 +0.30 0.27 MeV m ν τ < 18.2MeV (95%CL) (22) (1998) ( 8) 8: m j = m i j m top 175GeV,m b 4.3GeV,m c 1.25GeV,m s 105MeV,m d 6MeV,m u 3MeV,m τ = 1777MeV,m µ = 105.7MeV,m e = 0.511MeV m top 175GeV m ν m top < 10 13 (23) 7
m ν m e < 10 7 (24) v= 250GeV m gv (25) ( ) MeV ( ) 3-4 Z N ν L ν L N = 3 2 ( ) ν L ν R m R * 7) ν L, ν R M [ ] [ ] m L 0 m L m D M = 0 m R m D m R (26) (26) ν,n m ν,m N L R ν R m L = 0 m D m R m D m d /m R ν > ν L > m D m R ν R >, N > ν R > + m D m R ν L > (27a) m ν m2 D m R, m N m R (27b) ν >= γ 5 ν > m ν m R = m 2 D (28) m R m ν m D m W, m R 10 16 GeV m ν 10 3 ev * 7) (ν L ) c ν R 4 {ν L, (ν L ) c = (ν c ) R }, {ν R, (ν R ) c = (ν c ) L } 8
10 16 GeV 8.4 π π + µ + + ν µ, π + e + + ν e (29) π π µ + (e + ) π π µ + (e + ) ( 9 µ + (e + ) 1 v (1/2)(m 2 /p 2 ) π µ 9: π ( ) µ + Γ(π µ + ν) m 2 (m 2 π m 2 µ) 2 µ m 5 π (30) Γ(π e + ν) Γ(π µ + ν) = m2 e(m 2 π m 2 e) 2 m 2 µ(m 2 π m 2 µ) 2 = 1.284 10 4 (31) 1.233 10 4 1.218 ± 0.014 10 4 µ eν * 8) ν e ν µ π ( ) ( ) * 8) 9
( µ = (e/2m µ ) s ) ( 10 ) 10: π (H = µ B) ( ( 10 ) 11 11: #1, #2 #3( ) #4 #4 #3 #4 (Phys.Rev.Lett.7(1961)23) 43MeV 10 ( ) 4 3 10 P y A = L R L + R = ±0.09, f or P y = 1 (32) A = 0.09 ± 0.031 P y = 0.9 µ 100% 10
8.5 2ν 0ν ( 12(a),(b)) 2ν : (Z) (Z + 2) + 2e + 2 ν e (33a) 0ν : (Z) (Z + 2) + 2e (33b) 2ν 12: 2 (a) 2ν (b) 0ν (3) 0ν 12(b) (1) ν L (2) 2 (m ν /m e 2 ) 13: (a) 2ν (b) 0ν (c) 1.29kg y ( ) 90%CL 11
0ν 2ν ( 13 ) 10 18 10 24 ( ) 2 100% 13( ) 2ν * 9) 100 Mo 100 Ru + 2e + 2 ν e τ 1/2 = 7.1 ± 0.4 10 18 (34a) 76 Ge 76 Se + 2e + 2 ν e τ 1/2 = 1.5 ± 0.1 10 21 (34b) 0ν 0ν 180 ( ) (Ge) τ 0ν > 1.9 10 25 (35) m ν < 1eV (36) * 9) A.S.Barabash Neutrino2006, SantaFe 12
A A.1 E i, p i (37) t ( 1 ) ψ E = p 2 /2m +V i [ ] t ψ = Hψ = 2 2m +V ψ (38) E 2 = p 2 + m 2 (39) (KG) [ ] 2 t 2 2 + m 2 φ = 0 (40) ( 2 ) - (39) 2 ψ {ψ = (ψ 1,ψ 2, ) T ; T } * 10) i [ t ψ = Hψ = α ] i + βm ψ Eψ = [α p + βm]ψ (42) {α = (α i,i = 1 3),β} (39) E 2 = (α p + βm)(α p + βm) (43) (39) E 2 = p 2 + m 2 = i, j (α i α j + α j α i )p i p j + i (βα i + α i β)p i m + β 2 m 2 (44) α 2 i = β 2 = 1, α i α j + α j α i = 0 (i j), βα i + α i β = 0 (45) * 10) q = ω 2 q p q ṗ = ω 2 q ψ = (q, p) T i dψ dt = Sψ, S = 13 [ ] 0, 1 ω 2 0 (41)
4 2 2 3 m = 0 β α i = ±σ i [ ] [ ] 0 1 0 i σ 1 =, σ 2 =, σ 3 = 1 0 i 0 [ 1 0 0 1 ± φ R,L ], (46) Eφ L = σ pφ L, Eφ R = +σ pφ R (47) (E,p) φ(t,x) = φ(e,p)e ip x iet * 11) φ R = p σ p E p φ R, h = σ p p φ L = p σ p E p φ L (48) (49) A.1. p (θ,φ) [ ] σ p cosθ sinθe iφ = p sinθe iφ cosθ (50) [ χ + = cos θ 2 e iφ/2 sin θ 2 eiφ/2 ] [, χ = sin θ 2 eiφ/2 cos θ 2 e iφ/2 ] (51) m = 0 p /E = ±1 χ ± φ L,R φ R E 0 φ R = χ + E > 0, φ R = χ E < 0 (52) m = 0 φ R φ L ( ) φ R φ L (47) x x, p p φ R φ L * 12) φ R φ L 4 [ ] [ ] [ ] φ L σ 0 0 1 ψ =, α, β 0 σ 1 0 * 11) ψ(t,x) = 1 (2π) 3 φ(e,p)e ip x iet d 3 p * 12) m(ν) 0 φ R 14 (53)
β φ L φ R α, β (45) Eψ = [α p + βm]ψ (α, β 4 4 ) (54) 4 Eφ L = σ pφ L + mφ R (55a) Eφ R = σ pφ R + mφ L (55b) * 13) (47) φ L,R p >> m A.2. φ L,R = aχ + + bχ (56) (55) a,b φ L,R ( v, v= p /E ± E + p E p 1 ± v 1 v φ L = 2E χ + 2E χ + = 2 χ + 2 χ + (57) E + p E p 1 ± v 1 v φ R = 2E χ + + 2E χ = 2 χ + + 2 χ (58) E m = 0 E = p (48) h < h >= < φ L,R h φ L,R > < φ L,R φ L,R > = a 2 b 2 a 2 + b 2 = p = v (59) E m 0 E = p 2 + m 2 p + m 2 /2p, m << p φ L χ + 2p m φ L χ +, E > 0 (60) χ + + 2p m χ, E < 0 ( ) m/p * 13) m/p m = 0 15
A.2 β γ 0 = β, γ i = βα i, (61) [Eγ 0 p γ m]ψ = [iγ 0 0 + iγ i i m]ψ = [iγ µ µ m]ψ = 0 * 14) (62) γ µ γ µ γ ν + γ ν γ µ = 2g µ ν, g 00 = g 11 = g 22 = g 33 = 1, g µ ν = 0 (µ ν) (63a) γ 0 = γ 0, γ i = γ i, γ 0 γ i γ 0 = γ i (63b) ψ ψ γ 0 (64) ψ (adjoint) (63) ψ i µ ψγ µ + mψ ψ(iγ µ µ +m) = 0 (65) (62) ψ (65) ψ µ (ψγ µ ψ) = 0 (66) ψγ µ ψ ψγ µ ψ ( ) Γ 2 ψγψ ψ [ ] γ 5 iγ 0 γ 1 γ 2 γ 3 1 0 = iα 1 α 2 α 3 = (67a) 0 1 A.3. (γ 5 ) 2 = 1, γ 5 γ µ + γ µ γ 5 = 0 (68a) [ ] [ ] ψ L = 1 γ 5 φ L ψ =, ψ R = 1 + γ 5 0 ψ = 2 0 2 φ R (69) γ 5 ψ L = ψ L, γ 5 ψ R = ψ R (70) ψ L,R ψψ, ψγ 5 ψ * 15) ( ) * 14) A µ = (A 0 ;A) A µ = (A 0 ; A) A B = A 0 B 0 A B = A µ B µ ( ) * 15) ψ ψ = ψγ 0 ψ 16
A.3 (63) γ SγS 1 (63) E, p >> m (p << m, E m + p 2 /2m) β β D,W [ ] ψ D = Sψ W, S = 1 1 1, γ µ D 2 1 1 = Sγ µ W S 1 (71a) [ ] [ ] [ ] 0 σ 1 0 α D =, β D =, γ 5 0 1 D = (71b) σ 0 0 1 1 0 i ψ t [ = α i + βm α ] ψ (72) r A.4. (54) x x, p p, ψ βψ ψ βψ m 0 0 0 H = mβ = 0 m 0 0 0 0 m 0 (73) 0 0 0 m H m=0 (47) (47) iσ iσ 2 σ i = iσ i σ 2 E( iσ 2 φ L ) = σ ( iσ 2 φ L ) (74) 17
( iσ 2 φ L ) φ R +iσ 2 φ R φ L φ L (φ L ) c = φ c R iσ 2φ L, φ R (φ R ) c = φ c L iσ 2φ R (75) [ ] 4 ψ ψ c 0 iσ 2 ψ = iβα 2 ψ = iγ 2 ψ = iγ 2 γ 0 ψ T Cψ T (76) iσ 2 0 (C =charge conjugation ) * 16) z (1,0) T,(0,1) T [ ] [ ] 1 φ L (t) = a e i( E )t 0 + b e iet (77) 0 1 L R C p p ea, E E + eφ µ µ + iea µ A µ = (A 0, A) (78) (47) ( ) (i t eφ)φ L,R = σ i ea φ L,R (79) [φ L,R ] c φ L,R ( ) (i t + eφ)[φ L,R ] c = σ i + ea [φ L,R ] c (80) (79) iσ 2 (80) φ L e [φ L ] c = φ c R = iσ 2φ L -e L R φ R = iσ 2 φ L, φ L = iσ 2 φ R (81) (55) (E + σ p)φ L = im L σ 2 φ L (82a) (E σ p)φ R = im R σ 2 φ R (82b) 4 (55) 2 φ L φ R m L m R (82a) ( ) (82b) ( ) L R LR * 16) L R (75) 2 φ L φ R 2 18
m L m R LR (82) (47) 1/2 L R 4 (= ) 2 2 (φ 1, φ 2 ) (ψ, ψ ) = {φ 1 + iφ 2 )/ 2, (φ 1 iφ 2 )/ 2} 4 19