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1 Physics Workshop 2017
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4 Contents CP
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6 1932
7 10 4 p + p! p + p + p + p P. Blasi,
8 d d. 10 Gpc 10 0 Cohen, De Rujula, Glashow (1997) d B<0 B>0 Flux [photons cm -2 s -1 MeV -1 sr -1 ] COMPTEL Schönfelder et al. (1980) Trombka et al. (1977) White et al. (1977) d=20mpc d=1000mpc Photon Energy [MeV]
9 n B n
10 T (, )= X`,m a`m Y`m (, ) D` = 1 2` +1 `X m= ` a`m D TT [µk 2 ] D TT Planck 2015
11 TT+lowP TT+lowP+lensing TT+lowP+lensing+ext TT,TE,EE+lowP TT,TE,E Parameter 68 % limits 68 % limits 68 % limits 68 % limits 68 b h ± ± ± ± c h ± ± ± ± MC ± ± ± ± ± ± ± ± ln(10 10 A s ) ± ± ± ± n s ± ± ± ± H ± ± ± ± ± ± ± ± m ± ± ± ± m h ± ± ± ± m h ± ± ± ± ± ± ± ± ± ± ± ± Planck 2015
12 n B n PDG review
13 (e 60 ) GeV 1MeV 1eV 10 4 ev Baryogenesis T
14 (Non) thermal Leptogenesis Affleck-Dine baryogengesis Spontaneous baryogengesis Electroweak baryogengesis and many others New Physics
15 Sakharov (1967) C, CP X! Y C,CP = (X! Y ) (X C! Y C ) (X! Y ) = (Y! X) (X C! Y C ) = (Y C! X C ) hbi =0
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17 U(1) U(1) B i! e iq i i q i = 1 3 for quarks q i = 0 for others U(1) B µ J µ B =0 J µ B = X i q i i µ i
18 L = iq i µ D µ Q i + iu i µ D µ u i + id i µ D µ d i +il i µ D µ L i + ie i µ D µ e i D µ H F µ F µ 1 4 W µ W a µ a 1 4 Ga µ G µ a V (H) +L yukawa L yukawa = y u ijq i H d j + y d ijq i e Huj + yìj L i Hl j +h.c. SU(3)xSU(2)xU(1) Q i! e i Q i, u i! e i u i, d i! e i d i L i! e i L i, e i! e i e i
19 B, L L QQQL M 2, uude M 2, QQue M 2, QLud (LH) 2 M 2, M
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26 = ~x ~x
27 hf ii = Z f i [D ]exp(is[ ]) S[ ]= Z d 4 xl( ) V ( ) 0 (~x) (a) ~x (b) (a) (b)
28 SU(2) L = 1 4 F a µ F µ a A a µ =0 A µ = i g U@ µu 1 A U =exp(i a T a µ A a µt a ) U(t, ~x) =U(~x) lim ~x!1 U(~x) =1 U(~x) S 3 SU(2) 3 (SU(2)) = Z N =0 N =1 A µ (~x) N
29 r!1 U(x) = x 4 + i ~ T ~x r S = Z d 4 x 1 4 F µ F a µ a = 8 2 g 2 N = g Z N =0 N =1 d 4 xf a µ e F µ a = N + N A µ (~x)
30 µ J µ µ J µ = g F µ a F eµ a
31 J µ B = J µ B(L) + J µ B(R) = 1 3 J µ L = J µ L(L) + J µ L(R) = X i X (q µ Li q Li + q µ Ri q Ri ) i (l Li µ l Li + l Ri µ l Ri µ J µ B µj µ L = N g 32 2 g 2 W a µ f W µ a + g 02 B µ e B µ N g =3 n n B = n L = N g g Z d 4 xw a µ f W µ a = N g n
32 / exp 8 2 g Z 1 g 2 d 4 xf 2 g 2 R 4 F 2 F (gr 2 ) 1 E R 3 F 2 (g 2 R) 1 E. T! R & (g 2 T ) 1 Kuzmin, Rubakov, Shaposhnikov (1985) R 4 2T 4 5 2T 4 Arnold,Son,Yaffe (1996)
33 H T 2 M P 4 2T T GeV T 100 GeV t 100 GeV. T GeV
34 (T >>100GeV)
35
36 Dirac L = [i µ (@ µ iga µ ) m] 1 4 F µ F µ U(1) (C) µ! C µ C = µ C = C T = i 2 A µ! A µ! C
![L = [i µ (@ µ iga µ ) m] 1 4 F µ F µ (P) (t, ~x)! (t, ~x) @ µ! @ µ A µ! A µ µ!](/docs-images/104/164531269/images/37-0.jpg "µ! 0 L $ R (T) (t, ~x)! ( t, ~x) @ µ! @ µ A µ! A µ µ! µ! i 1 3 (i! i,! ) C,P,T")
37 L = [i µ (@ µ iga µ ) m] 1 4 F µ F µ (P) (t, ~x)! (t, µ A µ! A µ µ! µ! 0 L $ R (T) (t, ~x)! ( t, µ A µ! A µ µ! µ! i 1 3 (i! i,! ) C,P,T
38 ~ C = C = i 2 = C,P ~
39 L = i µ 1 L (@ µ iga µ ) L 4 F µ F µ C, P CP (t, ~x)! (t, µ = 0 A µ! A µ CP = 0 L µ L! L µ L! CP = i 0 2
40 CP CP L m m 2 1 L CP m m 1 2 CP 1 2! 2 1 m CP m
41 CP:! L µ 2 V ( ) V ( )=m 2 2 +(µ 2 2 +c.c.) µ 2 µ2 = µ 2 e i 0 e i /2
42 CP:! L µ 2 V ( ) V ( )=m 2 2 +(µ 2 2 +c.c.) +(M 3 +c.c.) µ 2 µ2 = µ 2 e i 0 e i /2
43 CP:! L µ 2 V ( ) V ( )=m 2 2 +(µ 2 2 +c.c.) +(M 3 +c.c.) µ 2 µ2 = µ 2 e i 0 e i /2 M
44 CP:! L µ 2 V ( ) V ( )=m 2 2 +(µ 2 2 +c.c.) +(M 3 +c.c.) µ 2 µ2 = µ 2 e i 0 e i /2 M
45 L yukawa = y u ijq i H d j + y d ijq i e Huj + yìj L i Hl j +h.c. y ij (i, j =1, 2, 3) L mass = m d ijd Li d Rj + m u iju Li u Rj +h.c. m ij (i, j =1, 2, 3)
46 V ij : u 0 Li V (u L) u ij Lj u 0 Ri V (u R) ij d 0 Li V (d L) d ij Lj d 0 Ri V (d R) ij u Rj d Rj V ij bi-unitary M! V MU = diagm 0 L mass = m d i d 0 Li d0 Ri + m u i u 0 Li u0 Ri +h.c. u_l d_l
47 L gauge = iq Li µ (@ µ igt a W a µ )Q Li g p 2 u Li µ W + µ d Li + d Li µ W µ u Li = g p 2 u 0 Li µ W µ + Vij CKM d 0 Lj + d 0 Li µ W µ V CKM ij u 0 Li V CKM V (u L) V (d L) CP L CP gauge = g p 2 d 0 Li µ W µ Vij CKM u 0 Lj + u 0 Li µ W µ + Vij CKM d 0 Lj V CKM ij = V CKM ij CP
48 CKM nxn n^2 (n=3 n ) u Li,d Li 2n u Ri,d Ri u Li,d Li V CKM u Li,d Li nc 2 = n 2 (2n 1) n(n 1) 2 = (n 1)(n 2) 2 n(n 1) 2 CP
49 L mass = m d i d 0 Li d0 Ri + m u i u 0 Li u0 Ri +h.c. L = g2 s 32 2 Ga µ e G µ a = 0 + arg Det[m u m d ] CP CP CKM +Strong CP
50 SU(2)L theta angle g 2 L = W µ a W fµ a CKM u Li! e i u Li u Ri! e i u Ri d Li! e i d Li d Ri! e i d Ri U(1)Y theta angle g 02 L = Y 32 2 F e µ F µ a Witten
51 X(B = 0), Y(B = +1) B =0 X! Y CP = (X! Y ) (X C! Y C ) (X! Y ) = (Y! X) (X C! Y C ) = (Y C! X C ) hbi =0
52 N I GUT B-L I =1, 2, 3 singlet L = 1 2 M IJN c I N J + y l ijl i He j + y N ijl i e HNJ +h.c. CP
53 U (N) IJ N I U T MU V (L) L ij i V (e) ij e i V MU L = 1 2 M IN c I N I + y l il i He i + y N ijl i e HNJ y N ij L N I =0 L = y l ijl i He j yn Iiy N Jj(M 1 ) IJ (L c i H)(L jh)
54 L = 1 2 m( ) ij c i j +h.c. m ( ) ij = v2 M I y N Iiy N Ij i! V ( ) ij j L gauge = il i µ (@ µ igt a W a )L i g p µ i W µ + Vij MNS e j + e µ i W µ V MNS j 2 ij V MNS ij = V ( ) ij
55 MNS 3x3 9 CKM i OK e Li n 2 n n(n 1) 2 = n(n 1) 2 =3 CP
56
57 m ( ) ij = v2 M I y N Iiy N Ij OK MNS CP y N ij CP CP
58 N 1 L L h L N 1 N 1 N 2,3 N 2,3 L h h L h h (N 1! L + H) (N 1! L + H) (N 1! L + H)+ (N 1! L + H) ' 1 1 X h i apple 8 (yy Im (yy 2 M 2 ) 1i f i V ) 11 M1 2 i=1,2 CP + f S M 2 i M 2 1
59
60 CP CKM
61 h =0 h 6= 0 B
62 broken phase symmetric phase h B =0 B 6= 0 x q L ql CP q qr CP R CP n(q L ) 6= n(q CP L ) q L q CP L
63 V = 1 2 m g V 1 2 (g2 T 2 m 2 ) 2 g 3 T m T m /g 2 T<T c T m /g g 2 A 2 /
![1-loop ( ) V B/F T ( )= T 4 2 2 J B/F m 2 T 2 J B [m 2 β 2 ]= 0 dx x 2 log [1 e x 2 +β 2 m 2](/docs-images/104/164531269/images/64-1.jpg "] 3 W g 2 T m W 1 g 2 T 2 h 2 W m W T 1 g 2 T m W g 2 T 2 h 2 h h h h Arnold, Espinosa")
64 1-loop ( ) V B/F T ( )= T J B/F m 2 T 2 J B [m 2 β 2 ]= 0 dx x 2 log [1 e x 2 +β 2 m 2 ] 3 W g 2 T m W 1 g 2 T 2 h 2 W m W T 1 g 2 T m W g 2 T 2 h 2 h h h h Arnold, Espinosa (1993)
65 h h g3 T g 4 g 2 m h & 80 GeV Kajantie, Laine, Rummukainen, Shaposhnikov (1996) LHC( LEP )
66 CP Gavela, Hernandez, Orloff, Pene (1993) CP Singlet extension 2 Higgs doublet model
67 2 Higgs doublet model V = µ 2 1 H 1 2 µ 2 2 H H H c H 1 2 H 2 2 +c 0 H 1 H µ 2 12H 1 H (H 1 H 2 ) 2 +h.c. µ CP FCNC (flavor-changing neutral current) Z 2 H1 up-type, H2 down-type µ 12 Z 2
68 CP CKM
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-Goldstone ( ) 様々な物理状態 自発的対称性の破れ 並進対称性 U(1)ゲージ対称性 並進対称性 CC by-sa Didier Descouens ガリレイ対称性 CC by-sa Mai-Linh Doan 並進対称性 スピン対称性 CC by-sa Roger McLassus カイラル対称性 CC by-sa Aney CC by-sa Elijah van der Giessen
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YITP50.dvi
1 70 80 90 50 2 3 3 84 first revolution 4 94 second revolution 5 6 2 1: 1 3 consistent 1-loop Feynman 1-loop Feynman loop loop loop Feynman 2 3 2: 1-loop Feynman loop 3 cycle 4 = 3: 4: 4 cycle loop Feynman
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")
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物性物理学I_2.pptx
phonon U r U = nαi U ( r nαi + u nαi ) = U ( r nαi ) + () nαi,β j := nαi β j U r nαi r β j > U r nαi r u nαiuβ j + β j β j u β j n α i () nαi,β juβj 調和振動子近似の復習 極 小 値近傍で Tylor展開すると U ( x) = U ( x ) + (