(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 0 0 1 1 L L µ e + ν e + ν µ 1 1 1 1 µ 1 0 0 1 e 0 1 1 0 * 1) * 2) SU(3) µ e + ν e + ν µ (2.2)

2 2 2.1 µ eγ µ e + γ < 1.2 10 11 (2.3) ν e ν µ π π π + µ + + ν µ 2.1: µ eγ ( 2.2(b)) ν µ (ν e )( 2.2(a) ) ( 2.2(c)(d)) 1962 2.2: (a) d (b) π + u d W + µ + ν µ (c)(d)(e) ν e,ν µ,ν τ ( ) e + e + τ + τ + (2.4a) e + ν e + ν τ τ (2.4b) µ+ ν µ + ν τ ν τ ν τ ν e (ν µ ) τ e(µ) + γ ν e (ν µ ) µ eγ, τ µγ e + X µ+y ( )

2 3 Z e + e + Z {(q i + q i ) + (l i + l + i ) + (ν i + ν i )} (2.5) i Z 2m i m Z * 3) BR = Γ(Z ) Γ(Z all) (2.6) e e + E(e e + ) = m z σ(e e + hadrons) = σ(e e + Z)BR(Z hadrons) (2.7) ( 2.3) N ν = 2.994 ± 0.012 (2.8) 2.3: e + e + Z N ν =3,4,5 m z /2 ( ) T D ( ) Ω B (= ρ B /ρ c, ρ c = 3H0 2 /8πG) D/H Ω B 2.4 D/H WMAP Ω B N ν WMAP ( 2.4 ) D/H = 2.6 ± 0.4, Y = 0.238 ± 0.005 N ν = 1.7 3.0 (2σ ) * 4) * 3) 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 * 4) V.Barger et al., Phys. Lett. B566 (2003) 8-18 hep-ph/0305075

2 4 2.4: (G.Steigman; Neutrino06) D/H Y(He) 2σ WMAP N ν N ν = 2.75 2.2 (1930) 30 (1956) ν e + p (e + +W ) + p e + + n (2.9a) e + + e γ + γ (2.9b) n +Cd Cd Cd + (3 4) γ s W e + W p( u ) (d ) 2m e 3-4 10 4 1m ( ) ( ) 2.5 1kW 2 10 14 10 13 /sec/cm 2 100 ( ) 20

2 5 2.5: Reines-Cowan(1954) γ (Cd) 2.3 2.3.1 d(p d ) u(p u ) + e (p e ) + ν e (p ν ) (2.10) ( ) Z H f i =< f H (x)d 4 x i > = G Z β 2 G β = G F cosθ C d 4 xe i(p e+p ν )x < f u(x)γ µ (1 γ 5 )d(x) i > [u(p e )γ µ (1 γ 5 )v(p ν )] (2.11a) (2.11b) d u < u j µ (x) d > u(p u )γ µ (1 γ 5 )d(p d )e i(p d p u )x (2.12) (= E) u(p u )γ µ u(p d ) δ µ0, u(p u )γ µ γ 5 u(p d ) (0,σ) (2.13a) MeV/c 1/p 100 10 13 m 10 14 m (p e + p ν )x 1 e i(p e+p ν )x 1 Z Z < 1τ + >= d 3 xφ f (x)1τ + Φ i (x), < στ + >= d 3 xφ f (x)στ + Φ i (x), (2.14) τ ± n p eν 1 J = 0, J = 0,±1

2 6 H f i H fi 2 (2.14) dγ = G2 β 2π M 3 2 F(Z,E)p e E e p ν E ν de e (2.15a) 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 (2.15b) M 2 = < 1 > 2 + C GT 2 < σ > 2 (2.15c) F(Z,E) [ ] dγ/de 1/2 e K(E) = (2.16) F(Z,E)p e E e m ν = 0 K(E) E 0 E e ( 2.6) m ν 0 2.6: ( ) m ν 0 ( ) (σ) (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 (2.17) E 0

2 7 = 1eV ε 2 10 13 m ν 2.7: ) (2) E E 2.7 R OP (E) E EL(E) BS(E) N(E ) Z N(E) obs = N(E )R(E,E )de (2.18) ( 2.6 (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) (2.19) P i i * 5) 2.8 p/p = 0.02%( E = 8eV ) E 0 1600eV m ν = 0 m ν < 13eV KATRIN KATRIN 2.9 * 6) * 7) * 8) 10 m ν < 0.23eV (MAC-EF=Magnetic Adiabatic Collimator with Electrostatic Field) 2.10 B s B D B min ( ) ( 2π) E T = µ B, µ = E T B = (2.20) * 5) Phys. Lett. B187(1987)198-204 * 6) http://www-ik.fzk.de/ katrin/index.html * 7) Phys. Lett. B460 (1999) 219 * 8) Phys. Lett. B460 (1999)227-235

2 8 2.8: m ν = 0 m ν < 13eV 2.9: ATRIN: m ν < 0.2eV

2 9 2.10: KATRIN ( µ ) (E T ) min = µb min (2.21) E 0 > E e > E 0 (E T ) min E (E T ) min = E e B min 18KeV 3 10 4 T B max 6T m ν < 0.23eV 1eV (2.22) 2.10 (2006) m ν < 2.3eV 2.3.2 π + (p) µ + (q) + ν µ (k) (2.23) π m π = q 2 + m 2 µ + k 2 + m 2 ν, k = k = q = q (2.24a)

2 10 2.11: m ν < 2.3eV 90%CL q m π = 139.56995 ± 0.00035MeV m µ = 105.658389 ± 0.000034MeV m 2 ν = 0.016 ± 0.023 (2.25a) q = 29.79200 ± 0.00011MeV m νµ < 0.17MeV (90%CL) (2.25b) * 9) 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 (2.26a) (2.26b) (2.26c) m τ = 1777 +0.30 0.27 MeV m ν τ < 18.2MeV (95%CL) (2.27) m νi 0.3 1eV (2.28) i * 9) K.AssamaganPhys. Rev. D53(1996) 6065

2 11 Ω ν < 0.015 (95%CL) Ω ν 2.12: ( ) ( ) (m) m m 2 23 = m 2 3 m 2 2 2.6 10 3 (2.29a) m 2 12 = m 2 2 m 2 1 8 10 5 (2.29b) m 2 23 m 1 < m 2 < m 3 (normal hierarchy) m 3 < m 1 < m 2 (Inverted hierarchy) m ( ) m 2 i j Max{m i 2,m 2 j } m ev 1eV m 1 << m 2 << m 3 m ν3 0.05eV, m ν2 0.01eV (2.30)

2 12 2.4 π π + µ + + ν µ, π + e + + ν e (2.31) π π π π µ + (e + ) ( 2.13 µ + (e + ) 1 v m 2 /p 2 π 2.13: π µ + µ Γ(π µ + ν) m 2 (m 2 π m 2 µ) 2 µ m 5 π (2.32) 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 (2.33) 1.233 10 4 1.218 ± 0.014 10 4 µ eν * 10) ν e ν µ 2.14: π π ( ) * 10)

2 13 ( ) ( 2.14 ) (H = µ H) ( ( 2.14 ) 2.15 43MeV 2.15: #1, #2 #3( ) #4 #4 #3 #4 (Phys.Rev.Lett.7(1961)23) 10 ( ) (4) 3 10 P y A = L R L + R = ±0.09, f or P y = 1 (2.34) A = 0.09 ± 0.031 P y = 0.9 µ 100% 2.5 * 11) 2ν 0ν ( 2.16(a),(b)) * 11)

2 14 2ν : (Z) (Z + 2) + 2e + 2 ν e (2.35a) 0ν : (Z) (Z + 2) + 2e (2.35b) 2ν 2.16: 2 (a)2ν (b)0ν (3) 0ν 2.16(b) (1) ν L (ν c ) R (2) (m ν /m e ) 2 ) 2.17: (a)2ν (b)0ν (c) 1.29kg y. 90%CL 0ν 2ν ( 2.17 ) 10 18 10 24 ( ) 100%

2 15 2.17( ) 0ν 180 NEMO3 * 12) 2.18 2.19 2.18: NEMO3 : ββ 10kg 20m 2 (40 60)mg/cm 2 10 (6180) σ i = 0.5mm, σ z = 1cm, 1940 PM.,FWHM(1MeV ) 11 14.5% (30G) (20cm)+ (30cm H 2 O) / τ 10 24 y/m ν 0.1eV 2ν * 13) 100 Mo 100 Ru + 2e + 2 ν e τ 1/2 = 7.1 ± 0.4 10 18 (2.36a) 76 Ge 76 Se + 2e + 2 ν e τ 1/2 = 1.5 ± 0.1 10 21 (2.36b) 0ν (Ge) τ 0ν > 1.9 10 25 (2.37) m ν < 1eV (2.38) * 12) http://nemo.in2p3.fr/ * 13) A.S.Barabash Neutrino2006, SantaFe

2 16 2.19: NEMO3 2ν 2ν 0ν 180 m j < m ν >= j Ue 2 jm j = η j U e j 2 m j (2.39) j η j CP < m ν >