Cosmological Family Asymmetry and CP violation

Transcription

1 Cosmological Family Asymmetry and CP violation Satoru Kaneko (Ochanomizu Univ.) 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)

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

3 This work We discuss cosmological lepton family asymmetry (YL = Ye + Y + Y ) produced in right-handed neutrino decay (leptogenesis) in the mininal seesaw model. SM + 2 heavy right-handed neutrino (m 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)

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

5 2. CP violation in minimal seesaw model L = y i l L i l Ri φ + y ik ν ( i = e, µ, τ, k = 1, 2 ) m i = y i l v/ 2, L i N k φ N c k M k N k + h.c. m Dik = y ik ν v/ 2 Nk : right-handed Majorana neutrinos (v << Mk) (1) bi-unitary parametrization (2) unit vector parametrization m D = (m D1, m D2 ) = m De1 m De2 m Dµ1 m Dµ2 m Dτ1 u k = m Dk m Dk ; m Dk = m Dk m Dτ2 = (u 1, u 2 ) m ν = (y νv) 2 M m D = U L m V R : U L = U(θ L23, θ L13, θ L12, δ L ) diag(1, e i γ L 2, e i γ L 2 ) : V R = V (θ L12 ) diag(1, e i γ R 2, e i γ R 2 ) ( md1 m D2 ) m Di2 are taken to be complex (3 CP violating phases)

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

7 (Thermal) Leptogenesis Majorana neutrino decay ---> Lepton number violation CP violation Out of equilibrium Lepton asymmetry (YL 0) sphaleron Baryon asymmetry (YB 0) L=B=0 L=-1, B=0 L=-2/3, B=1/3 CMB : η CMB B BBN : η BBN B n B n B n γ = (6.3 ± 0.3) (2003) n B n B n γ = (6.1 ± 0.5) (2001, 2003)

8 ɛ k = CP violation in heavy neutrino decay i=e,µ,τ ɛ k i Br(N k l ± i φ ) ; ɛ k i = Γ(N k l i φ + ) Γ(N k l + i φ ) Γ(N k l i φ + ) + Γ(N k l + i φ ) T. Endoh, T. Morozumi, Z. Xiong, Prog.Theor.Phys ( 04) lepton family asymmetry φ + N Rk l i N Rk l + j N Rk φ N Rk l i N Rk φ + N Rk l i N Rk (a) φ + (b) φ l i l + j (c) φ + l j (d) φ + ɛ k i = 1 I(x k 8π k) Im [ (y νy ν ) kk (y ν ) ik(y ν ) ik 1 Im [ (y νy ν ) k + k(y ν ) ik(y ν ) ik (y k k ν ) ik 2 1 x k k (y ν ) ik 2 ( x k k = Mk 2 /M 2 k, I(x) = [ x ] ) 1 x + (1 + x) ln x 1 + x ] ]

9 Baryogenesis via leptogenesis η B 10 2 k ɛ k κ( m k, M k m 2 k) ( m k (m Dm D ) kk M k, m 2 k m m m 2 3 ) efficiency factor (washout due to scattering processes) l + i t N Rk l i l i l j l i φ φ + φ + N Rk N Rk N Rk (a) b b (b) t φ + (a) φ + φ (b) l j Baryon asymmetry can be systematically calculated by solving Boltzmann equations.

10 3. Cosmological lepton family asymmetry and low-energy observables m 1 = 0, m 2 = T. Endoh, S. K., S.K. Kang, T. Morozumi, M. Tanimoto, PRL ( 02) T. Endoh, T. Morozumi, Z. Xiong, Prog.Theor.Phys ( 04) m 2 sol ev, m 3 = θ L12 = θ sol = π 6, θ L23 = θ atm = π 4, θ L13 = 0 m 2 atm ev M 1 = GeV, M 2 = GeV Y Nk = Y eq N k, Y Li = 0 at T M 1 (z = M 1 /T = 10 2 ) (1) bi-unitary parametrization 10-2 m D = U L m V R : U L = U(θ L23, θ L13, θ L12, δ L ) diag(1, e i γ L 2, e i γ L 2 ) : V R = V (θ L12 ) diag(1, e i γ R 2, e i γ R 2 ) Y N Y N2 Y N z=m 1 /T

11 L = 0 L = Y L (10-10 ) Y e Y µ Y Y e Y µ Y -20 Y L -20 Y L z=m 1 /T z=m 1 /T Y dominant leptogenesis Y dominant leptogenesis T. Endoh, T. Morozumi, Z. Xiong, Prog.Theor.Phys ( 04)

12 L = / Y L (10-10 ) Y e Y µ Y Y L z=m 1 /T T. Endoh, T. Morozumi, Z. Xiong, Prog.Theor.Phys ( 04)

13 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 = (m D1, m D2 ) = m De1 m De2 m Dµ1 m Dµ2 m Dτ1 u k = m Dk m Dk ; m Dk = m Dk m Dτ2 = (u 1, u 2 ) ( md1 m D2 ) m Di2 are taken to be complex (3 CP violating phases) M = ( M1 M 2 ) m ν = m D M 1 m T D = u 1 u T 1 X 1 + u 2 u T 2 X 2 ; X k m2 Dk M k (k = 1, 2)

14 CP violation in neutrino oscillation J CP = (m 2 1 m 2 2)(m 2 2 m 2 3)(m 2 3 m 2 1), = Im[(m νm ν) eµ (m ν m ν) µτ (m ν m ν) τe ] = ( 1 u 1 u 2 2) [ X 4 1X 2 2 { ( ) Im[ u e1 u e2 u µ1 u µ2 uτ1 2 + ( u µ1u µ2 u τ1 uτ2) ue1 2 + (u τ1u τ2 u e1 u e2) u µ1 2 ] } +X 3 1X 3 2 X 2 1X 4 2 { Im[(u e1 u e2 )(u 1 u 2 )( u τ1 u µ2 2 u µ1 u τ2 2 ) + (u µ1u µ2 )(u 1 u 2 )( u e1 u τ2 2 u τ1 u e2 2 ) +(u τ1u τ2 )(u 1 u 2 )( u µ1 u e2 2 u e1 u µ2 2 )] } ( ( ) Im[ u e1 u e2 u µ1 u µ2 uτ2 2 + ( ) u µ1u µ2 u τ1 u τ2 ue2 2 + (u τ1u τ2 u e1 u e2) u µ2 2 ] )] is determined by uik and Xk.

15 (1) u 1 u 2 = 0 Two interesting cases No leptogenesis Non-vanishing CP violation in neutrino oscillation = X 2 1 X 2 2 (X 2 1 X 2 2) Im[u τ1u τ2 u e1 u e2] (2) u 1 u 2 = u a1u a2 (a = e, µ, τ) One family dominant leptogenesis Natural possibility : consider two zero elements in m D

16 Type I 0 allowed --> (90%CL) Type Type I (a) e-leptogenesis Type I(b) e-leptogenesis Type I (a) µ leptogenesis Type I (b) µ leptogenesis Type I (a) τ leptogenesis Type I (b) τ leptogenesis u e1 u e2 u µ1 0 0 u τ2 u e1 u e2 0 u µ2 u τ1 0 u e1 0 u µ1 u µ2 0 u τ2 0 u e2 u µ1 u µ2 u τ1 0 u e1 0 0 u µ2 u τ1 u τ2 0 u e2 u µ1 0 u τ1 u τ2 (1 u e1 u e2 2 )X 3 1X 3 2Im(u e1u e2 ) 2 ( u τ2 2 u µ1 2 ) (1 u e1 u e2 2 )X 3 1X 3 2Im(u e1u e2 ) 2 u τ1 2 u µ2 2. (1 u µ1 u µ2 2 )X 3 1X 3 2Im(u µ1u µ2 ) 2 ( u τ2 2 u e1 2 ) (1 u µ1 u µ2 2 )X 3 1X 3 2Im(u µ1u µ2 ) 2 ( u e2 2 u τ1 2 ) (1 u τ1 u τ2 2 )X 3 1X 3 2Im(u τ1u τ2 ) 2 ( u e1 2 u µ2 2 ) (1 u τ1 u τ2 2 )X 3 1X 3 2Im(u τ1u τ2 ) 2 ( u e2 2 u µ1 2 ) Type II = 0 = 0 type (a) (b) V MNSN V MNSI type II (e-leptogenesis) type II (µ -leptogenesis) type II (τ -leptogenesis) u e1 u e2 0 u µ2 0 u τ2 0 u e2 u µ1 u µ2 0 u τ2 0 u e2 0 u µ2 u τ1 u τ2 u e1 u e2 u µ1 0 u τ1 0 u e1 0 u µ1 u µ2 u τ1 0 u e1 0 u µ1 0 u τ1 u τ

17 Regions of observable parameters type Ve1 MNS Ve2 MNS Ve3 MNS Vµ3 MNS Vτ3 MNS J exp. (90%) I(a) µ normal X 1 X I(b) µ normal X 2 X I(a) τ normal X 1 X I(b) τ normal X 2 X All other textures and hierarchies are excluded (90%CL). <--- I (a) normal

18 4. Summary We study CP violation in neutrino oscillations and its possible connection with lepton family asymmetries generated from heavy Majorana neutrino decays. This strongly depends on left-handed CP violating phase L. We identify the two zeros texture models in which lepton asymmetry is dominated by a particular family asymmetry (e-, m-, t-leptogenesis). We have predicted the possible ranges of and the low energy CP violation observable JCP.

19 Questions How can we observe cosmological lepton family asymmetry? What is the solution of cosmological gravitino problem? (SUSY model)