Cosmological Family Asymmetry and CP violation Satoru Kaneko ( - PowerPoint PPT Presentation

Cosmological Family Asymmetry and CP violation Satoru Kaneko ( Ochanomizu Univ .) 2005. 9. 21 at Tohoku Univ . T . Endoh , S . K. , S . K . Kang , T . Morozumi , M . Tanimoto , PRL ( ’ 02) T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04) T. Fujihara, S.K., S. Kang, D. Kimura, T. Morozumi and M. Tanimoto, PRD (’05)

1. Introduction Low-energy physics - - - - - - - - - - - - - - - - Cosmology connection ? Neutrino oscillations Baryon asymmetry CMB, BBN, . . . SK, K2K, SNO, KamLAND . . . . Beyond the standard model Seesaw model : SM + Right-handed heavy neutrinos CP violation ------------------------------ Leptogenesis m ν = ( y ν v ) 2 Fukugita and Yanagida (’86) in ν oscillations M But, there is no direct connection (many parameters). Branco, Morozumi, Nobre and Rebelo (’01) Pascoli, Petcov and Redejohann (’03) . . .

This work We discuss cosmological lepton family asymmetry (Y L = Y e + Y μ + Y τ ) produced in right-handed neutrino decay (leptogenesis) in the mininal seesaw model. SM + 2 heavy right-handed neutrino (m ν lightest = 0) T . Endoh , S . K ., S . K . Kang , T . Morozumi , M . Tanimoto , PRL ( ’ 02) T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04) We also discuss the constraints from neutrino oscillations on concrete mass textures in which one lepton family asymmetry dominant leptogenesis can naturally realized. T. Fujihara, S.K., S. Kang, D. Kimura, T. Morozumi and M. Tanimoto, PRD (’05)

Plan of the talk 1. Introduction 2. CP violation in minimal seesaw model 3. Cosmological lepton family asymmetry and low-energy observables 4. Summary

2. CP violation in minimal seesaw model φ + 1 c ν L i N k � − L = y i ℓ L i ℓ R i φ + y ik k M k N k + h . c . 2 N ( i = e, µ, τ , k = 1 , 2 ) m ν = ( y ν v ) 2 √ √ m i = y i m D ik = y ik ℓ v/ 2 , ν v/ 2 M N k : right-handed Majorana neutrinos (v << M k ) (1) bi-unitary parametrization U L = U ( θ L 23 , θ L 13 , θ L 12 , δ L ) · diag (1 , e − i γ L 2 , e i γ L 2 ) m D = U L m V R : V R = V ( θ L 12 ) · diag (1 , e − i γ R 2 , e i γ R 2 ) : (2) unit vector parametrization   m D e 1 m D e 2 � � m D 1   m D = ( m D 1 , m D 2 ) =  = ( u 1 , u 2 ) m D µ 1 m D µ 2    m D 2 m D τ 1 m D τ 2 m Di2 are taken to be complex u k = m D k m D k = | m D k | ; (3 CP violating phases) m D k

CP violating phases In (1) bi-unitary parametrization, ) 2 U R H R ≡ m † D m D = U † R ( m diag D ---> Total lepton asymmetry in leptogenesis (A) m ν = m D M − 1 m T U R M − 1 U † D = U † L m diag R m diag U L D D ---> CP violation in neutrino oscillations (B) CPV : P ( ν e → ν µ ) − P (¯ ν e → ¯ ν µ ) � ∆ m 2 � � ∆ m 2 � � ∆ m 2 � 12 13 23 = 16 s 12 c 12 s 13 c 2 13 s 23 c 23 sin δ sin sin sin 4 E L 4 E L 4 E L � �� � ≡ J CP The phases that contributes to (A) and (B) is different.  δ L  � CP violation in ν osillation ⇐ δ   m ν seesaw m D γ L ⇒ lepton family asymmetry ρ   γ R ⇒ total lepton asymmetry 

leptogenesis Fukugita and Yanagida (’86), Luty (’92), Covi et al (’96), Buchmuller and Plumacher (’98~) . . . ↑ ↑ sphaleron : B-L conserving (Thermal) Leptogenesis Majorana neutrino decay ---> Lepton number violation CP violation Out of equilibrium Lepton asymmetry (Y L ≠ 0) sphaleron Baryon asymmetry (Y B ≠ 0) L=B=0 → L= - 1, B=0 → L= - 2/3, B=1/3 ≡ n B − n B η CMB = (6 . 3 ± 0 . 3) × 10 − 10 : ( 2003 ) CMB B n γ ≡ n B − n B η BBN = (6 . 1 ± 0 . 5) × 10 − 10 : ( 2001 , 2003 ) BBN B n γ

Fukugita and Yanagida (’86), Luty (’92), Covi et al (’96), . . . CP violation in heavy neutrino decay i = Γ ( N k → ℓ − i φ + ) − Γ ( N k → ℓ + i φ − ) ǫ k = ǫ k i Br( N k → ℓ ± ǫ k � i φ ∓ ) ; i φ + ) + Γ ( N k → ℓ + Γ ( N k → ℓ − i φ − ) i = e,µ, τ T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04) lepton family asymmetry φ + l − l − l − i i i φ + l + φ − j N R k N R k N R k N R k ′ N R k N R k ′ N R k ′ φ − l + l − j j φ + φ + φ + (a) (b) (c) (d) l − i � � � �   ( y † ν y ν ) kk ′ ( y ν ) ∗ ( y † ν y ν ) k ′ k ( y ν ) ∗ Im ik ( y ν ) ik ′ Im ik ( y ν ) ik ′ i = 1 1 ǫ k �  I ( x k ′ k ) +  8 π | ( y ν ) ik | 2 1 − x k ′ k | ( y ν ) ik | 2 k ′ � = k 1 x � � � � I ( x ) = √ x x k ′ k = M 2 k ′ /M 2 k , 1 + 1 − x + (1 + x ) ln 1 + x

Baryogenesis via leptogenesis � � m k ≡ ( m † η B ≃ 10 − 2 � D m D ) kk ǫ k κ ( � m k , M k m 2 , m 2 k ≡ m 2 1 + m 2 2 + m 2 k ) � 3 M k k ● κ : efficiency factor (washout due to scattering processes) l + l − l − i t j i N R k l − l − φ − i i N R k φ + φ + N R k l − φ − b t j (a) (b) (a) (b) N R k φ + φ + ¯ b Baryon asymmetry η B can be systematically calculated by solving Boltzmann equations.

3. Cosmological lepton family asymmetry and low-energy observables T . Endoh , S . K ., S . K . Kang , T . Morozumi , M . Tanimoto , PRL ( ’ 02) T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04) sol ≃ 7 × 10 − 3 eV , atm ≃ 5 × 10 − 2 eV � � ∆ m 2 ∆ m 2 m 1 = 0 , m 2 = m 3 = θ L 12 = θ sol = π θ L 23 = θ atm = π θ L 13 = 0 6 , 4 , M 1 = 2 × 10 11 GeV , M 2 = 2 × 10 12 GeV Y N k = Y eq Y L i = 0 at T ≪ M 1 ( z = M 1 /T = 10 − 2 ) N k , (1) bi-unitary parametrization -2 10 U L = U ( θ L 23 , θ L 13 , θ L 12 , δ L ) · diag (1 , e − i γ L 2 , e i γ L 2 ) -3 m D = U L m V R : 10 V R = V ( θ L 12 ) · diag (1 , e − i γ R 2 , e i γ R 2 ) -4 : 10 Y N -5 Y N2 Y N1 10 -6 10 -7 10 -8 10 -2 -1 10 10 1 10 z=M 1 /T

μ μ γ L = 0 γ L = π 5 0 0 -5 -5 -Y L (10 -10 ) Y e Y e -10 -10 Y µ Y µ -15 -15 Y Y Y L Y L -20 -20 -25 -25 -30 -2 -1 2 -2 -1 2 3 10 10 1 10 10 10 10 1 10 10 10 z=M 1 /T z=M 1 /T Y μ dominant leptogenesis Y τ dominant leptogenesis T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04)

μ γ L = π /2 150 Y e 100 Y µ Y 50 Y L -Y L (10 -10 ) 0 -50 -100 -150 -2 -1 2 10 10 1 10 10 z=M 1 /T T . Endoh , T . Morozumi , Z . Xiong , Prog . Theor . Phys ( ’ 04)

Connection to low-energy observables T. Fujihara, S.K., S. Kang, D. Kimura, T. Morozumi and M. Tanimoto, PRD (’05) (2) unit vector parametrization   m D e 1 m D e 2 � � m D 1   m D = ( m D 1 , m D 2 ) =  = ( u 1 , u 2 ) m D µ 1 m D µ 2    m D 2 m D τ 1 m D τ 2 m Di2 are taken to be complex u k = m D k m D k = | m D k | ; (3 CP violating phases) m D k � � M 1 M = M 2 X k ≡ m 2 − m ν = m D M − 1 m T D = u 1 u T 1 X 1 + u 2 u T D k 2 X 2 ; ( k = 1 , 2) M k

CP violation in neutrino oscillation ∆ ∆ = Im[( m ν m † ν ) eµ ( m ν m † ν ) µ τ ( m ν m † J CP = ν ) τ e ] 1 ) , ( m 2 1 − m 2 2 )( m 2 2 − m 2 3 )( m 2 3 − m 2 � 1 · u 2 | 2 � 1 − | u † ∆ = × � | u τ 1 | 2 + | u e 1 | 2 + ( u ∗ � � � � � � X 4 1 X 2 e 2 ) | u µ 1 | 2 ] Im[ u ∗ e 1 u e 2 u µ 1 u ∗ u ∗ µ 1 u µ 2 u τ 1 u ∗ τ 1 u τ 2 u e 1 u ∗ 2 µ 2 τ 2 � e 1 u e 2 )( u † 1 · u 2 )( | u τ 1 u µ 2 | 2 − | u µ 1 u τ 2 | 2 ) + ( u ∗ µ 1 u µ 2 )( u † 1 · u 2 )( | u e 1 u τ 2 | 2 − | u τ 1 u e 2 | 2 ) + X 3 1 X 3 Im[( u ∗ 2 � τ 1 u τ 2 )( u † 1 · u 2 )( | u µ 1 u e 2 | 2 − | u e 1 u µ 2 | 2 )] +( u ∗ �� | u τ 2 | 2 + | u e 2 | 2 + ( u ∗ � � � � � − X 2 1 X 4 e 2 ) | u µ 2 | 2 ] Im[ u ∗ e 1 u e 2 u µ 1 u ∗ u ∗ µ 1 u µ 2 u τ 1 u ∗ τ 1 u τ 2 u e 1 u ∗ 2 µ 2 τ 2 Δ is determined by u ik and X k.

Two interesting cases (1) u † 1 · u 2 = 0 No leptogenesis Non-vanishing CP violation in neutrino oscillation ∆ = X 2 1 X 2 2 ( X 2 1 − X 2 2 ) Im[ u ∗ e 2 ] τ 1 u τ 2 u e 1 u ∗ (2) u † 1 · u 2 = u ∗ a 1 u a 2 ( a = e, µ, τ ) One family dominant leptogenesis Natural possibility : consider two zero elements in m D