Matter vs Anti-matter

Transcription

1 Baryogenesis

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

3 1 BESS experiment BESS97

4 Asymmetry between matter and anti-matter How Large Asymmetry? He Baryon density # b h Big Bang Nucleosynthesis n B s = (6 8) Y p D H 3 He H !3 10!4 D/H p CMB s: entropy density 10!5 3 He/H p 10!9 Baryogenesis 7 Li/H p 5 2 before BBN after inflation 10! Baryon-to-photon ratio " 10

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

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

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

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

9 Vacuum Structure of SU(2) gauge Field E Multiple Vacuum Structure A a µ Chern-Simons Number N CS = g2 32π 2 d 3 xɛ ijk T r [A j j A k ig3 A ia j A k ] A 0 = 0 gauge

10 Baryon Number Current j µ B Qγ µ Q = 1 2 [ Qγ µ (1 γ 5 )Q + Qγ µ (1 + γ 5 )Q] EW Fermions couple chirally to W, B J µ B Anomaly W n f : number of generation B = µ j µ B = µj µ L = n f ( g 2 d 4 x µ j µ B = t=t f d 3 xj 0 B W 32π 2 W a µν W aµν t=0 W aµν = 1 2 ɛµναβ W αβ ) g 2 32π 2 F F µν µν d 3 xj 0 B = n f [N CS (t f ) N CS (0)]

11 µ j µ B = µj µ L = n f d 4 x µ j B K 0 B = ( ) g 2 32π 2 µk µ g 2 32π 2 µk µ K µ = ɛ µναβ ( W a ναa a β g 3 ɛ abca a νa b αa c β k µ = ɛ µναβ F να B β = t=t f d 3 xj 0 B t=0 d3 xj 0 B = B = n f g 2 32π 2 ( t=t f d 3 xk 0 t=0 d3 xk 0 ) = ɛ ( ijk Wij a Aa k g 3 ɛ ) abca a i Ab j Ac k = ɛ ( ijk ( i A a j ja a i + gɛ abca b i Ac j )Aa k g 3 ɛ ) abca a i Ab j Ac k = ɛ ( ijk 2 i A a j Aa k + 2g 3 ɛ ) abca 1 i Ab j Ac k = ɛ ijk T r ( A i j A k ig 3 A ) ia j A k d 4 x µ j µ B t=t = d 3 xjb 0 d 3 xjb 0 = n f [N CS (t f ) N CS (0)] f t=0 )

12 Sphaleron E Multiple Vacuum Structure B = L = n f = 3 Tunneling by instanton d 4 x(w a µν W a µν) 2 0 A a µ d 4 x[t r(w µν W µν ) + T r( W µν W µν ) 2T r(w µν W µν ] 0 ( ) 16π 2 4S E 2 g 2 N CS 0 S E 8π2 g 2 N CS Γ exp ( 4π α W ) too small!

13 Sphaleron E Multiple Vacuum Structure B = L = n f = 3 Tunneling by instanton Finite Temperature Sphaleron Γ Γ exp ( 4π α W A a µ ) M 4 W exp ( 2M W α W T ) too small! T < M W (α W T ) 4 T M W

14 Sphaleron Saddle-point solution in Weinberg-Salam theory A 0 = 0 E = d 3 x gauge, static configuration [ 1 4 W ijw a ij a + 1 ] 4 F ijf ij + (D i φ) (D i φ) + V (φ) F ij = 0 Ansatz E = 4πv g A a i = 2 ɛ ija x j g r 2 f(ξ) ξ = rgv 0 φ = i v 2 τ x r f(0) = h(0) = 0 f( ) = h( ) = 1 [ ( ) 2 dξ 4 df 8 dξ ξ (f(1 f)) ξ2 ( dh dξ ) 2 + (h(1 f)) ( h(ξ) ( 0 1 λ g 2 ) ξ 2 (h 2 1) 2 ] )

15 E = 4πv g 0 dξ ξ2 ( dh dξ [ ( ) 2 4 df 8 dξ ξ (f(1 f)) 2 2 ) 2 + (h(1 f)) ( λ g 2 ) ξ 2 (h 2 1) 2 ]

16 E = 4πv g 0 dξ[ ] = 2 4π g gv 0 dξ[ ] = 2M W α W 0 dξ[ ] Sphaleron rate Γ(T ) M 4 W exp E sph (T ) M W (T ) α W ε (3.2 < ε < 5.4) High temperature magnetic screening length Γ(T ) = κ(α W T ) 4 ( E ) sph(t ) T no Boltzmann suppression = (α W T ) 1

17 CP Violation in Standard Model Quark ψ jl = Mass Term ( Uj ) D j L U jr D jr (j = 1,, n f ) M D jk DjR D kl M U jkūjru kl Redefine U R, ψ L M U jkūjru kl M U = diag(m u, m c, m t ) Redefine D R M D jl U lk D jr D kl M D = diag(m d, m s, m b ) U unitary matrix = CKM matrix

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

19 EW Phase Transition Higgs potential V High T V (φ, T = 0) = λ( φ 2 v 2 ) V takes min. at! = 0 W in thermal eq. M W 0 g 2 W 2 φ 2 V g 2 T 2 2 φ 2 V eff g2 2 T 2 φ 2 2λv 2 φ 2 2 λ T > g v v T=0 φ

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

21 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

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

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

24 Interference term Γ(N l + φ) Γ(N l + φ) ɛ 1 = Γ(N l+φ) Γ(N l+ φ) Γ(N l+φ)+γ(n l+ φ) = 3 16π 3 16π δ eff [ ] 1 (hh ) 11 Im(hh ) 2 13 M 1 M 3 + Im(hh ) 2 12 M 1 M 2 h 33 2 M 1 M 3 h 33 Largest (M 1 M 1, M 2 ) ɛ π δ eff m ν3 M 1 φ 2

25 CP Violation CP pahse in mass matrix of N Γ(N ν + φ) Γ(N ν + φ) Out of Equilibrium Condition Spharelon Process (L + B) = 0 n /s N (L B) 0 B 0 B = 8N g + 4N H 22N g + 13N H (B L) 0.3(B L) EQ N g : # of generations, N H : # of Higgs doublets 1/T Successful Baryogenesis [Fukugita-Yanagida (1986)]

26 Decay Rate Γ Ni = Γ(N i l + φ) + Γ(N i l + φ) = 1 8π (hh ) ii M i out of EQ Decay Γ Ni < H(T = M i ) g1/2 M 2 i 3M G m ν1 = (hh φ ) 2 11 M 1 4g 1/2 < 10 3 ev φ 2 M G ( ΓN1 H ) T =M 1 φ = 174GeV g 100

27 ε = M 1 = neutrino mass Plümacher (1998)

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

29 Chemical Equilibrium chemical potential for massless particles gt 2 6 µ i (fermion) n i n i = gt 2 3 µ i (boson) Sphaleron interaction O B+L = (q Li q Li q Li l Li ) i (3µ qi + µ li ) = 0 i total hypercharge = 0 (µ qi + 2µ ui µ di µ li µ ei + 2µ φ /N) = 0 i d L c L d L s L s L Sphaleron t L u L ν e ν µ b L ν τ b L

30 Yukawa interaction L = h dij dri q Lj φ h uij ū Ri q Lj φ c h eij ē Ri q Lj φ µ qi µ φ µ dj = 0 µ qi + µ φ µ uj = 0 µ li µ φ µ ej = 0 mixing in Yukawa couplings µ li = µ l µ qi = µ q µ e = 2N + 3 6N + 3 µ l µ d = 6N + 1 6N + 3 µ l µ u = 2N 1 6N + 3 µ l µ φ = 4N 6N + 3 µ l µ q = 1 3 µ l

31 n B = B 6 T 2 n L = L 6 T 2 B = N(2µ q + µ u + µ d ) L = N(2µ l + µ e ) B = 8N g + 4N H 22N g + 13N H (B L) 0.3(B L)

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

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

34 Supersymmetry (SUSY) Fermion Boson Hierarchy Problem Keep electroweak scale against radiative correction Coupling Constant Unification in GUT quark lepton photon graviton squarks slepton photino gravitino

35 SUSY Breaking Scheme Low Energy SUSY (m q, m l 1TeV m q, m l ) (A) Gravity Mediated SUSY Breaking SUSY sector M SUSY gravity Observable sector (s)quark,(s)lepton Squark, slepton masses Gravitino m q, m l M 2 SUSY M p m 3/ GeV GeV M SUSY GeV

36 (B) Gauge Mediated SUSY Breaking SUSY sector M SUSY gauge int. Messenger sector M F Squark, slepton masses gauge int. Observable sector (s)quark,(s)lepton m q, m l g2 M F 16π 2 Gravitino m 3/2 M 2 SUSY M p GeV kev GeV M F GeV

37 Affleck-Dine Mechanism Affleck, Dine (1985) In Scalar Potential (= sauark, slepton, higgs) of MSSM(minimal supersymmetric standard model) There exist Flat Directions = Φ ( Flat if SUSY and no cutoff ) (AD-field) V (Φ) = m 2 Φ Φ 2 + Φ 2n+4 M 2n + A(Φ n+3 + Φ n+3 ) + SUSY breaking U(1) symmetry Non-renormalizable term A-term U(1) A m 3/2 M n

38 Dynamics of Affleck-Dine Field During Inflation Φ has a large value H m Φ Φ Oscillation V A-term Kick in phase direction Baryon Number Generation n B = i( Φ Φ Φ Φ) θ Φ 2 ImΦ Φ ReΦ

39 AD Baryogenesis V = (m 2 Φ ch 2 ) Φ 2 + λ Φ 2n+4 M 2n + ã m 3/2 M n (Φ n+3 + Φ n+3 ) Φ q, l, H In general Φ has a baryon number U B (1) : Φ e iα Φ Noether current j B,µ = 1 2i (Φ µ Φ µ Φ Φ) baryon density n B = j B,0 Potential A-term violates U (1) B during inflation Φ e iθ 0 CP, out of eq.