Baryogenesis Matter vs Anti-matter Earth, Solar system B made of - PowerPoint PPT Presentation

Baryogenesis

Matter vs Anti-matter Earth, Solar system B made of baryons Our Galaxy p Anti-matter in cosmic rays galaxy p/p ∼ O (10 − 4 ) ¯ secondary p + p → p + p + p + ¯ p γ Our Galaxy is made of baryons galaxy Cluster of Galaxies No strong rays are observed anti-galaxy γ Near clusters are made of baryons

BESS experiment BESS97

Asymmetry between matter and anti-matter How Large Asymmetry? Baryon density � b h 2 0.005 0.01 0.02 0.03 0.26 4 He 0.25 0.24 Y p Big Bang Nucleosynthesis 0.23 D ___ H 0.22 n B 10 � 3 = (6 − 8) × 10 − 11 3 He ___ CMB D/H p H s 10 � 4 s: entropy density 3 He/H p 10 � 5 10 � 9 Baryogenesis 5 7 Li/H p 2 before BBN after inflation 10 � 10 1 2 3 4 5 6 7 8 9 10 Baryon-to-photon ratio � 10

Baryogenesis Sakharov’ s Condition (1) B Violation (2) C, CP Violation (3)Out of Equilibrium

1. Necessary Obviously A c + B c → C c + D c 2. e.g. A + B → C + D C trans. Γ ( A c + B c → C c + D c ) = Γ ( A + B → C + D ) If C inv. B = 0 3. Thermal Equilibrium T invariance + CPT invariance CP invariance B = 0 Tr ( e − H/T B ) = Tr (( CPT )( CPT ) − 1 e − H/T B ) � B � = Tr (( CPT ) − 1 e − H/T B ( CPT ) = − Tr ( e − H/T B ) = 0 =

Baryogenesis Mechanism Electroweak Baryogenesis Leptogenesis via Heavy Majorana Neutrino Affleck-Dine Mechanism . . . . . .

Electroweak Baryogenesis B violation Sphaleron Process C, CP violation Kobayashi-Maskawa 1st order EW phase Out of Equilibrium transition Electroweak Baryogenesis

Vacuum Structure of SU(2) gauge Field Multiple Vacuum Structure E A a µ Chern-Simons Number g 2 � � � A j ∂ j A k − ig d 3 x � ijk Tr N CS = 3 A i A j A k 32 π 2 A 0 = 0 gauge

Baryon Number Current Q γ µ Q = 1 B ∼ ¯ 2[ ¯ Q γ µ (1 − γ 5 ) Q + ¯ j µ Q γ µ (1 + γ 5 ) Q ] EW Fermions couple chirally to W, B Anomaly J µ W n f : number of generation B W aµ ν = 1 ˜ 2 � µ ναβ W αβ W � � � 2 g 2 W aµ ν − g ∂ µ j µ B = ∂ µ j µ 32 π 2 W a µ ν ˜ 32 π 2 F µ ν ˜ L = n f F µ ν � � � d 4 x ∂ µ j µ d 3 xj 0 d 3 xj 0 ∆ B = B = B = n f [ N CS ( t f ) − N CS (0)] B − t = t f t =0

� g 2 32 π 2 ∂ µ K µ − g � 2 � ∂ µ j µ B = ∂ µ j µ 32 π 2 ∂ µ k µ L = n f β − g K µ = � µ ναβ � � W a να A a 3 � abc A a ν A b α A c β k µ = � µ ναβ F να B β � d 4 x ∂ µ j B � t = t f d 3 xj 0 � t =0 d 3 xj 0 B = ∆ B = B − = n f g 2 �� t =0 d 3 xK 0 � t = t f d 3 xK 0 − � 32 π 2 k − g K 0 = � ijk � W a ij A a 3 � abc A a i A b j A c � k k − g = � ijk � ( ∂ i A a j − ∂ j A a i + g � abc A b i A c j ) A a 3 � abc A a i A b j A c � k k + 2 g = � ijk � 2 ∂ i A a j A a 3 � abc A 1 i A b j A c � k A i ∂ j A k − ig = � ijk Tr � � 3 A i A j A k � � � d 4 x ∂ µ j µ d 3 xj 0 d 3 xj 0 ∆ B = B = B = n f [ N CS ( t f ) − N CS (0)] B − t = t f t =0

Sphaleron Multiple Vacuum Structure E A a ∆ B = ∆ L = n f = 3 µ Tunneling by instanton µ ν − ˜ µ ν ) 2 ≥ 0 � d 4 x ( W a W a d 4 x [ Tr ( W µ ν W µ ν ) + Tr ( ˜ W µ ν ˜ W µ ν ) − 2 Tr ( W µ ν ˜ � W µ ν ] ≥ 0 ⇒ � 16 π 2 N CS ≥ 0 ⇒ S E ≥ 8 π 2 � 4 S E − 2 g 2 N CS g 2 � � − 4 π too small ! ∼ 10 − 170 Γ ∼ exp α W

Sphaleron Multiple Vacuum Structure E A a ∆ B = ∆ L = n f = 3 µ � � − 4 π Tunneling by instanton ∼ 10 − 170 Γ ∼ exp α W too small ! Finite Temperature Sphaleron  � � − 2 M W M 4 T < W exp ∼ M W  α W T Γ ∼ ( α W T ) 4 T � M W 

Sphaleron Saddle-point solution in Weinberg-Salam theory A 0 = 0 gauge, static configuration � 1 ij + 1 � � d 3 x 4 W a ij W a 4 F ij F ij + ( D i φ ) † ( D i φ ) + V ( φ ) E = F ij = 0 i = 2 � � � ija x j � τ · � φ = i v x 0 Ansatz A a f ( ξ ) h ( ξ ) 1 r 2 g √ r 2 ξ = rgv f (0) = h (0) = 0 f ( ∞ ) = h ( ∞ ) = 1 � � 2 8 � ∞ � d f 4 π v ξ 2 ( f (1 − f )) 2 E = 4 d ξ g d ξ 0 � � 2 2 ξ 2 � � � + ( h (1 − f )) 2 + 1 + 1 dh λ ξ 2 ( h 2 − 1) 2 g 2 d ξ 4

� � 2 8 � � ∞ d f 4 π v ξ 2 ( f (1 − f )) 2 E = 4 d ξ g 0 d ξ � � 2 2 ξ 2 � � � + ( h (1 − f )) 2 + 1 dh λ + 1 ξ 2 ( h 2 − 1) 2 g 2 d ξ 4

� ∞ � ∞ = 4 π v d ξ [ · · · ] = 2 4 π g 2 1 d ξ [ · · · ] E 2 gv g 0 0 � ∞ = 2 M W d ξ [ · · · ] 0 α W Sphaleron rate � � − E sph ( T ) Γ ( T ) ∼ M 4 W exp T E sph ( T ) ≡ M W ( T ) (3 . 2 < ε < 5 . 4) ε α W High temperature no Boltzmann suppression magnetic screening length = ( α W T ) − 1 Γ ( T ) = κ ( α W T ) 4 Sphaleron rate

CP Violation in Standard Model � � U j Quark ( j = 1 , · · · , n f ) ψ jL = U jR D jR D j L Mass Term − M D D jR D kL − M U jk ¯ jk ¯ U jR U kL Redefine U R , ψ L M U = diag ( m u , m c , m t ) − ˜ jk ¯ M U ˜ U jR U kL Redefine D R M D = diag ( m d , m s , m b ) j � U † ˜ − ˜ � k ¯ M D D jR D kL U † unitary matrix = CKM matrix

    d d = U † D L s D L = U s     b b L L mass eigenstate still can define phase of mass eigenstate V 1 , V 2 : diagonal unitary U ⇒ V 1 UV 2 2 n f − 1 relevant phase number of independent phases f − (2 n f − 1) − 1 2 n f ( n f − 1) = 1 n 2 2( n f − 1)( n f − 2) unitary orthogonal matrix matrix only one phase δ CP n f = 3 CP violation δ CP � = 0

EW Phase Transition High T V Higgs potential V ( φ , T = 0) = λ ( | φ | 2 − v 2 ) T=0 V takes min. at � = 0 φ v W in thermal eq. ⇐ M W ∼ 0 g 2 T 2 2 | φ | 2 g 2 | W | 2 | φ | 2 ∈ V √ V e ff � g 2 λ 2 2 T 2 | φ | 2 − 2 λ v 2 | φ | 2 ⇒ T > v ∼ g

High T V V takes min. at � = v W not in thermal eq. T=0 φ M W ∼ g φ > ∼ 3 T v for φ > ⇒ V ( φ , T ) = V ( φ , T = 0) ∼ 3 T/g 3 T v > ∼ g √ g 2 √ 6 � 2 πα W λ g λ < g v < ∼ T < 2 3 v ∼ 3 ∼ √ Higgs mass m H ∼ 2 λ v < ∼ 40GeV small Higgs mass

However, Small CP Violation EW Phase Transition is 2nd Order 1st Order Higgs mass m H ≤ 80GeV experiment m H ≥ 114GeV EW Baryogenesis may not work

Baryogenesis Mechanism Electroweak Baryogenesis Leptogenesis via Heavy Majorana Neutrino Affleck-Dine Mechanism . . . . . .

Leptogenesis Heavy Majorana Neutrino small neutrino mass by see-saw mechanism Super-K discovery � ν + φ ( ∆ L = +1) ν neutrino , φ Higgs N → ν + φ ¯ ( ∆ L = − 1) Deacy Process φ φ ν N ν N ν N φ

Interference term Γ ( N → � + φ ) � = Γ ( N → ¯ � + ¯ φ ) = Γ ( N → � + φ ) − Γ ( N → ¯ � + ¯ φ ) � 1 Γ ( N → � + φ )+ Γ ( N → ¯ � + ¯ φ ) � � 3 1 Im( hh † ) 2 M 3 + Im( hh † ) 2 M 1 M 1 = 13 12 16 π ( hh † ) 11 M 2 | h 33 | 2 M 1 3 ( M 1 � M 1 , M 2 ) 16 π δ e ff � M 3 h 33 Largest m ν 3 M 1 3 � 1 � 16 π δ e ff � φ � 2

CP Violation CP pahse in mass matrix of N Γ ( N → ν + φ ) � = Γ ( N → ¯ ν + φ ) Out of Equilibrium Condition n /s N Spharelon Process ( L + B ) = 0 EQ ( L − B ) � = 0 ⇒ B � = 0 1/T 8 N g + 4 N H B = ( B − L ) � 0 . 3( B − L ) 22 N g + 13 N H N g : # of generations , N H : # of Higgs doublets Successful Baryogenesis [Fukugita-Yanagida (1986)]

Decay Rate = Γ ( N i → � + φ ) + Γ ( N i → ¯ � + ¯ φ ) Γ N i 8 π ( hh † ) ii M i 1 = out of EQ Decay Γ N i < H ( T = M i ) � g 1 / 2 M 2 i 3 M G � Γ N 1 � � φ � 2 � φ � 2 M 1 � 4 g 1 / 2 = ( hh † ) 11 m ν 1 ∗ M G H T = M 1 ∼ 10 − 3 eV < � φ � = 174GeV g ∗ � 100

ε = − 10 − 16 M 1 = 10 10 neutrino mass Plümacher (1998)

Y EQ Y N Y L Buchmuller, Plümacher (2000)

Chemical Equilibrium chemical potential for massless particles gT 2  (fermion) 6 µ i  n i − ¯ n i = gT 2 (boson)  s L 3 µ i s L t L Sphaleron interaction c L b L � Sphaleron O B + L = ( q Li q Li q Li � Li ) d L b L i d L ν τ � (3 µ q i + µ � i ) = 0 u L ν µ ν e i total hypercharge = 0 � ( µ q i + 2 µ u i − µ d i − µ � i − µ e i + 2 µ φ /N ) = 0 i

Yukawa interaction u Ri q Lj φ c − h e ij ¯ L = − h d ij ¯ d Ri q Lj φ − h u ij ¯ e Ri q Lj φ µ q i − µ φ − µ d j = 0 µ q i + µ φ − µ u j = 0 µ � i − µ φ − µ e j = 0 mixing in Yukawa couplings µ � i = µ � µ q i = µ q · · · µ d = − 6 N + 1 µ e = 2 N + 3 6 N + 3 µ � 6 N + 3 µ � 4 N µ u = 2 N − 1 µ φ = 6 N + 3 µ � 6 N + 3 µ � µ q = − 1 3 µ �

n B = B n L = L 6 T 2 6 T 2 B = N (2 µ q + µ u + µ d ) L = N (2 µ � + µ e ) 8 N g + 4 N H B = ( B − L ) � 0 . 3( B − L ) 22 N g + 13 N H

Baryogenesis Mechanism Electroweak Baryogenesis Leptogenesis via Heavy Majorana Neutrino Affleck-Dine Mechanism . . . . . .

Affleck-Dine Mechanism Affleck, Dine (1985) In Scalar Potential (= sauark, slepton, higgs) of MSSM (minimal supersymmetric standard model) There exist Flat Directions = (AD-field) Φ ( Flat if SUSY and no cutoff ) Baryon Dynamics of Number AD Field Generation