( ) 2007.5.14 1 3 1.1............................. 3 1.2 :........... 5 1.3........................ 7 1.4................. 8 2 11 2.1 (Technocolor)................ 11 2.2............................. 12 2.3 =............... 13 3 14
4 = 18 4.1..................... 18 4.2.......................... 22 4.3 BPS........................... 25 5 ( ) 26 6 U(N C ), N F 29 7 1/2 BPS 31 8 Conclusion 36 2
1 1.1 GeV SU(3) SU(2) U(1): W ±, Z 1. ( ) 2. W ±, Z 0 (1983), 3. 1. W, Z 1983 CERN 3
2. 1974 SLAC, BNL 3. 1977 SLAC 4. 1977 FNAL 5. 1995 FNAL 3 Z 3 CP B Cabibbo LHC 1. 4
2. ( ) 3. 4. 1.2 : 1. 2. ( ) ( ) 1. + + + + 5
2. + Kamiokande, SuperKamiokande, Kamland, 1. ( ) 2. 3. 1. ( + + ) ( ) ( ) ( ) 2. 6
( ) ( ) 3. ( ) 4. 1.3 LHC=Large Hadron Collider 2007 CERN 7TeV 7TeV ( 7 ) : Atlas, CMS, LHCb, Allice, 7
: : 1.4 1. ( ) M GUT c 2 10 15 10 16 GeV (1.1) 2. 8
( ) M W c 2 10 2 GeV (1.2) M GUT c 2 10 15 GeV M 2 W /M 2 GUT 10 26 1 (1.3) V (r) = G N m 1 m 2 r (1.4) G N M P c 2 c c 2 = 1.22 10 19 GeV (1.5) G N ( ) ( ) M 2 W /M 2 P 10 34 1 (1.6) 9
M W = 1. 1/2 2. ( ) (, ) 10
2 2.1 (Technocolor) TeV 11
L. Susskind,Phys. Rev.D20 (1979) 2619; S. Weinberg, Phys. Rev.D19 (1979) 1277; D13 (1976) 974; S. Dimopoulos, and L. Susskind,Nucl. Phys. B155 (1979) 237; 2.2 ( ) 0 : m B m B = m F 1 2 : m F m F = 0 S.Dimopoulos, H.Georgi, Nucl.Phys.B193 (1981) 150; N.Sakai, Z.f.Phys.C11 (1981) 153; E.Witten, Nucl.Phys.B188 (1981) 513; 0 12
( ) (MSSM) MSSM 2.3 = 4 (4 + n) ( ) n 2πR 1 M 1 M 2 V 4+n (r) = (M (4+n) ) 2+n r 1 M 1 M 2, for r R 1+n (M (4+n) ) 2+n R n r M 2 P = (M (n+4)) 2+n R 1 R n ( c ) n M (4+n) M P 10 19 GeV P.Horava and E.Witten, Nucl.Phys.B475, 94 (1996); N.Arkani-Hamed, SDimopoulos, G.Dvali, Phys.Lett.B429 (1998) 263 ; I.Antoniadis, N.Arkani-Hamed, S.Dimopoulos, G.Dvali, 13
3 Phys.Lett.B436 (1998) 257; Randall, Sundrum, Phys.Rev.Lett.83 (1999) 3370; 4690; 1. H 1, H 2 ( ) (a) 4 3 = 1 ( 2 H 3 W ±, Z ) h (b) 8 3 = 5 (H 1, H 2 3 W ±, Z ) (h, H, A) (H +, H ) 2. Lightest Supersymmetric Particle R R R 14
LSP 3. fine tuning (a) (b) 4. 15
1 U(1), SU(2), SU(3) α i = gi 2 /4π, (i = 1, 2, 3) 1: ( ) ( ) α i = gi 2 /4π, (i = 1, 2, 3) U(1), SU(2), SU(3) http://pdg.lbl.gov/2005/reviews/gutsrpp.pdf 16
5. 150GeV 4 m h m Z K. Inoue, A. Kakuto, H. Komatsu, and S. Takeshita, Prog. Theor. Phys. 67 (1982) 1889. 150GeV Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1; H. E. Haber and R. Hempfling, Phys. Rev. Lett. 66 (1991) 1815; J. R. Ellis, G. Ridolfi and F. Zwirner, Phys. 17 Lett. B257 (1991) 83.
: (sequestering) 4 = 4.1 N.Arkani-Hamed, SDimopoulos, G.Dvali, Phys.Lett.B429 (1998) 263 ; Kehagias,Sfetsos, Phys.Lett.B472 (2000) 39; 4 M c V (4) (r) G N M 1 (4.1) r c 1.61 c 10 33 cm, 1.22 10 19 GeV/c 2. (4.2) G N GN r 200µm (4.3) 18
4 V (4) (r) = G N M 1 r = M c 1 (M (4) ) 2 r. (4.4) 4 + n V (4+n) (r) = G 4+n M 1 (4.5) r n+1 4 + n n R V (4+n) (r) G 4+n M 1 m 1,,m n [r 2 + n i=1 (2πR (4.6) im i ) 2 ] 1+n 2 M (4+n) ( ) 1 n G n+4 = (M (4+n) ) 2+n c (4.7) c 4 + n ( ) V (4+n) 1 n (r) M (M (4+n) ) 2+n r 1+n c, r R i. (4.8) c 19
1 V (4+n) (r) M (M (4+n) ) 2+n = M 1 1 (M (4+n) ) 2+n R 1 R n r n vol(s n ) ( d n 1 m [r 2 + n i=1 (2πR c im i ) 2 ] 1+n 2 c vol(s n ( ) ) n c G N M 1 2 c r 1+n 2π 2 vol(s n ) = Γ( 1+n 2 ) (4.9) 4 G N = G 4+nvol(S n ) 2Π n i=1 (2πR i) G 4+n R 1 R n (4.10) M 2 P = (M (n+4)) 2+n R 1 R n ( c ) n (4.11) ) n 20
:, m e mr G 4+n M (4+n) TeV ( ) 2 (n 2) D = 6 TeV 21
4 TeV LHC 4.2 Randall, Sundrum, Phys.Rev.Lett.83 (1999) 3370; 4690; y 2πr c : y = y + 2πr c : y y ( ) y = πr c = ( ) (1 + d, d = 4) S = S bulk + S brane (4.12) S bulk = 1 d d+1 x G [ 12 ] κ R Λ (4.13) 2 d+1 22
S brane = 1 κ 2 d+1 d d+1 x G [ V 1 δ(y) V 2 δ(y πr c )] (4.14) R MN 1 2 G MNR = ΛG MN + g mn δ m M δn N [V 1δ(y) + V 2 δ(y πr c )] : (Warped metric) Randall-Sundrum ds 2 = e 2k y η µν dx µ dx ν + (dy) 2 (4.15) 2Λ 3Λ k = 6, V 1 = V 2 = (4.16) 2 5 4 ( ) Randall-Sundrum 1. y = 0 y = πr c 23
2. y = 0 3. y = 0 1/r 4. 5. Randall-Sundrum 1. 2. 3. ( ) 24
4.3 BPS = :,,... ( ) Landau-Ginzburg : U(1) φ L = 1 4e 2F µνf µν + D µ φ(d µ φ) λ ( φφ v 2) 2 (4.17) 4 : ( ) k = 1 d 2 x F 12 (4.18) 2π : = U(1) :, : λ < e 2 : (, ) 25
λ > e 2 : λ = e 2 : BPS BPS (SUSY) 5 ( ) ( ) : ( ) π 0 (M) 26
φ (λ > 0) L = µ φ µ φ λ(φ 2 v 2 ) 2 (5.1) : φ + v, φ v y = x 2 E = ( y φ) 2 + λ(φ 2 v 2 ) 2 = ( y φ + λ(φ 2 v 2 )) 2 + y [2 )] λ (v 2 φ φ3 3 [ dye 2 )] λ (v 2 φ φ3 3 Bogomol nyi-prasad-sommerfield (BPS) (5.2) Bogomol nyi, Sov.J.Nucl.Phys. 24 (1976) 449; Prasad and Sommerfield, Phys.Rev.Lett. 35 (1975) 760. BPS y φ + λ(φ 2 v 2 ) = 0 (5.3) 27
: φ = v tanh( λvy) (5.4) (a) BPS (b) dφ cl λv 2 dy = ( ) cosh 2 λvy References 28
y: 6 U(N C ), N F L = 1 2g 2Tr(F MN(W )F MN (W )) + 1 g 2Tr(DM ΣD M Σ) +Tr [ D M H(D M H) ] V (6.1) V = g2 [ (HH 4 Tr ) 2 ] c1 NC + Tr [ (ΣH HM)(ΣH HM) ] D M H i = ( M + iw M )H i, D M Σ = M Σ + i[w M, Σ] F MN (W ) = M W N N W M + i[w M, W N ] W M, Σ (N C N C ) U(N C ) g 29
: H ra H ra (N C N F matrix) (i = 1, 2 ; r = 1,, N C ; A = 1,, N F ), (M) A B m A δ A B : m A > m A+1 : U(1) N F 1 F : Σ 5 M, N, = 0, 1, 2, 3, 4 (8 SUSY) : A 1 A 2 A NC HH = c1 NC, ΣH HM = 0 (6.2) H ra = c δ A r A, Σ = diag(m A1,, m ANC ) (6.3) N : F! (N F N C )!N C! en F log(x x (1 x) (1 x)), x N C /N F : ( ),,, 30
2: A 1 A 2 A NC B 1 B 2 B NC. 7 1/2 BPS 1/2 BPS y x 4, 4 D W M y = 0 31
E [ E = Tr D y H ra 2] + Tr [ ΣH HM 2] + 1 ( g 2Tr (D y Σ) 2) + g2 [ (HH 4 Tr ) 2 ] c1 NC = Tr D y H + ΣH HM 2 + 1 ( g 2Tr D y Σ g2 ( c1nc HH )) 2 + c y TrΣ (7.1) 2 1/2 BPS : γ 4 ε i = i(σ 3 ) i jε j D y H = ΣH + HM, D y Σ = g 2 ( c1 NC HH ) /2 (7.2) labeled by A 1 A 2 A NC B 1 B 2 B NC BPS + [ ] + Edy c Tr(Σ) = c BPS N C m Ak k=1 N C k=1 m Bk (7.3) 32
Σ + iw y S 1 (y) y S(y) S(y) GL(N C, C) BPS : H(y) = S 1 (y)h 0 e My H 0 N C N F BPS : Ω SS ( y Ω 1 y Ω ) = g 2 c ( ) 1 C Ω 1 Ω 0, Ω0 c 1 H 0 e 2My H 0 H 0 Ω(y) S(y) Σ, W y, H 1 y = ±, U(1) H 0 V - : (S NC 2 ) (S, H 0 ) (S, H 0 ) H = S 1 H 0 e My (Σ, W y ) S S = V S, H 0 H 0 = V H 0, V GL(N C, C) 33
3: A B C ( ) A,B ( ) BPS : M = {H 0 H 0 V H 0, V GL(N C, C)} G NF,N C SU(N F ) SU(N C ) SU(N F N C ) U(1) ( ) N C Ñ C N C (N F N C ) : 1,, N C Ñ C + 1,, N F (7.4) dim R M 1,,N C Ñ C +1,,N F N F,N C = 2N wall = 2N C Ñ C (7.5) M = M 1/1 + M 1/2 = M 0 M 1 M N CÑC (7.6) 34
H 0 : 1 0.8 0.6 0.4 0.2-40 -20 20 40 y 4:. U(1) : H 0 = (e r 1, e r 2,, e r N F ), H = S 1 H 0 e My = S 1 (e r 1+m 1 y,, e r N F +m NF y ) (7.7) i i + 1 Rer i + m i y Rer i+1 + m i+1 y Im(r i r i+1 ) : U(N C ) : Ñ C N F N C BPS (T w : ) L = T w + d 4 θk(φ, φ ) + (7.8) 35
K(φ, φ ) = dy [ c log detω + ctr ( Ω 0 Ω 1) + 1 ( 2g 2Tr Ω 1 y Ω ) ] 2 K (g ) : g 2 c/ m 1: Ω = Ω 0 c 1 H 0 e 2My H 0 (7.9) g 2 : (NLSM) 8 Conclusion 1. 2. 3. 4. 5. Ω=Ω sol 36
6. 7. ( ) TeV 8. 9. ( )U(N C ) N F BPS 10. ( ) H 0 M NF,N C {H 0 H 0 V H 0, V GL(N C, C)} SU(N F ) G NF,N C SU(N C ) SU(Ñ C ) U(1) (8.1) 11. (g 2 ) ( ) 12. BPS 37
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