Thermal Leptogenesis. Michael Plümacher. Max Planck Institute for Physics Munich

Transcription

1 Max Panck Institute for Physics Munich

2 Introduction Introduction Probem #1: the universe is made of matter. Baryon asymmetry (from nuceosynthesis and CMB): η B n b n b n γ must have been generated during the evoution of the universe Probem #: ν masses are 0 but orders of magnitude smaer than any other known masses Both probems cannot be soved in the Standard Mode need extended mode

3 Introduction Introduction Probem #1: the universe is made of matter. Baryon asymmetry (from nuceosynthesis and CMB): η B n b n b n γ must have been generated during the evoution of the universe Probem #: ν masses are 0 but orders of magnitude smaer than any other known masses Both probems cannot be soved in the Standard Mode need extended mode

4 Introduction Introduction Probem #1: the universe is made of matter. Baryon asymmetry (from nuceosynthesis and CMB): η B n b n b n γ must have been generated during the evoution of the universe Probem #: ν masses are 0 but orders of magnitude smaer than any other known masses Both probems cannot be soved in the Standard Mode need extended mode

5 Introduction Standard Mode: eft- and right-handed quarks and charged eptons neutrinos ony eft-handed. Why? Introduce right-handed neutrinos N First prediction: neutrino masses (type I seesaw) m ν v /M v 100GeV: SM mass scae; M: mass of N. Observed ight neutrino masses yied cues on M m ν 0.05eV M GeV Second prediction: epton number L is vioated B and L not independent at T 100GeV (sphaerons) η B = cη L with c 1 3 L vioating processes can be used to generate η B

6 Introduction Standard Mode: eft- and right-handed quarks and charged eptons neutrinos ony eft-handed. Why? Introduce right-handed neutrinos N First prediction: neutrino masses (type I seesaw) m ν v /M v 100GeV: SM mass scae; M: mass of N. Observed ight neutrino masses yied cues on M m ν 0.05eV M GeV Second prediction: epton number L is vioated B and L not independent at T 100GeV (sphaerons) η B = cη L with c 1 3 L vioating processes can be used to generate η B

7 Introduction Standard Mode: eft- and right-handed quarks and charged eptons neutrinos ony eft-handed. Why? Introduce right-handed neutrinos N First prediction: neutrino masses (type I seesaw) m ν v /M v 100GeV: SM mass scae; M: mass of N. Observed ight neutrino masses yied cues on M m ν 0.05eV M GeV Second prediction: epton number L is vioated B and L not independent at T 100GeV (sphaerons) η B = cη L with c 1 3 L vioating processes can be used to generate η B

8 Leptogenesis Leptogenesis A free unch: Leptogenesis in type I seesaw Right-handed neutrinos can aso give rise to η B (Fukugita and Yanagida 86) Yukawa coupings: L Y N λ ν N M N Ns are unstabe, decay to epton-iggs pairs: Γ D m 1 = v M 1 (λ νλ ν ) 11 N interactions vioate L L 0, partiay converted to B 0 by sphaerons λ ν compex CP vioation ε i N 1 + N 1 + N 1

9 Leptogenesis Chaenge #1: ow do the N get produced? (Luty 9; M.P. 96; Piaftsis and Underwood 03) N scattering processes are important a production processes m 1 q N 1 need arge m 1 for efficient production u Chaenge #: L vioating scatterings can destroy η B (Fukugita & Yanagida 90; Buchmüer, Di Bari & M.P. 0; Giudice et a. 03) Two contributions to reaction rate: resonant contribution from N 1 : m 1 remainder: M 1 m, m = m ν i need sma m 1 and M 1 m to avoid washout Two conficting requirements network of Botzmann equations

10 Leptogenesis Chaenge #1: ow do the N get produced? (Luty 9; M.P. 96; Piaftsis and Underwood 03) N scattering processes are important a production processes m 1 q N 1 need arge m 1 for efficient production u Chaenge #: L vioating scatterings can destroy η B (Fukugita & Yanagida 90; Buchmüer, Di Bari & M.P. 0; Giudice et a. 03) Two contributions to reaction rate: N resonant contribution from N 1 : m 1 remainder: M 1 m, m = m ν i need sma m 1 and M 1 m to avoid washout Two conficting requirements network of Botzmann equations

11 Leptogenesis Chaenge #1: ow do the N get produced? (Luty 9; M.P. 96; Piaftsis and Underwood 03) N scattering processes are important a production processes m 1 q N 1 need arge m 1 for efficient production u Chaenge #: L vioating scatterings can destroy η B (Fukugita & Yanagida 90; Buchmüer, Di Bari & M.P. 0; Giudice et a. 03) Two contributions to reaction rate: N resonant contribution from N 1 : m 1 remainder: M 1 m, m = m ν i need sma m 1 and M 1 m to avoid washout Two conficting requirements network of Botzmann equations

12 Leptogenesis Baryon asymmetry determined by four parameters 1 CP asymmetry ε 1 mass of decaying neutrino M 1 3 effective ight neutrino mass m 1 ( decay width of N 1 ) 4 ight neutrino masses m = m ν 1 + m ν + m ν 3 Fina baryon asymmetry need to know: η B 10 ε 1 κ( m 1,M 1 m ) CP asymmetry ε 1 (from neutrino mass mode) efficiency factor κ parametrizes N interactions (from integration of Botzmann eqs.) (Barbieri et a. 00; Buchmüer, Di Bari & M.P. 0)

13 Leptogenesis Baryon asymmetry determined by four parameters 1 CP asymmetry ε 1 mass of decaying neutrino M 1 3 effective ight neutrino mass m 1 ( decay width of N 1 ) 4 ight neutrino masses m = m ν 1 + m ν + m ν 3 Fina baryon asymmetry need to know: η B 10 ε 1 κ( m 1,M 1 m ) CP asymmetry ε 1 (from neutrino mass mode) efficiency factor κ parametrizes N interactions (from integration of Botzmann eqs.) (Barbieri et a. 00; Buchmüer, Di Bari & M.P. 0)

14 Leptogenesis CP asymmetry ε 1 = Γ(N ) Γ(N ) Γ(N )+Γ(N ) for M,3 M 1 : upper bound on ε 1 in terms of ight ν masses: (Davidson & Ibarra 0; Buchmüer, Di Bari & M.P. 03; ambye et a. 03) two imiting cases: ε max 1 = 3 M 1 m ν3 16π v f (m νi, m 1 ) hierarchica ight νs: m ν1 0 ε max 1 = 3 16π degenerate ight νs: m ν3 = m ν1 ε max 1 = 0 M 1 m ν3 v CP asymm. suppressed if ight ν spectrum quasi-degenerate

15 Leptogenesis CP asymmetry ε 1 = Γ(N ) Γ(N ) Γ(N )+Γ(N ) for M,3 M 1 : upper bound on ε 1 in terms of ight ν masses: (Davidson & Ibarra 0; Buchmüer, Di Bari & M.P. 03; ambye et a. 03) two imiting cases: ε max 1 = 3 M 1 m ν3 16π v f (m νi, m 1 ) hierarchica ight νs: m ν1 0 ε max 1 = 3 16π degenerate ight νs: m ν3 = m ν1 ε max 1 = 0 M 1 m ν3 v CP asymm. suppressed if ight ν spectrum quasi-degenerate

16 Leptogenesis CP asymmetry ε 1 = Γ(N ) Γ(N ) Γ(N )+Γ(N ) for M,3 M 1 : upper bound on ε 1 in terms of ight ν masses: (Davidson & Ibarra 0; Buchmüer, Di Bari & M.P. 03; ambye et a. 03) two imiting cases: ε max 1 = 3 M 1 m ν3 16π v f (m νi, m 1 ) hierarchica ight νs: m ν1 0 ε max 1 = 3 16π degenerate ight νs: m ν3 = m ν1 ε max 1 = 0 M 1 m ν3 v CP asymm. suppressed if ight ν spectrum quasi-degenerate

17 Constraints on neutrino parameters Constraints on neutrino parameters 1 N 1 production processes m 1 ower imit on m 1 Washout processes: res. contrib. from N 1 m 1 upper imit on m 1 remainder M 1 m upper imit on M 1 for fixed m 3 maxima CP asymmetry M 1 ower imit on M 1 since η B ε 1 for fixed m aowed region in ( m 1,M 1 ) pane Size of aowed region depends on m since: max. CP asymm. suppressed for quasi-degenerate ight νs m 1 m ν1 upper bound on m

18 Constraints on neutrino parameters (Buchmüer, Di Bari & M.P. 03, 04) M1 GeVµ m 0 05 ev 0 15 ev 0 1 ev m 1 evµ ight ν masses: m < 0.eV m νi < 0.13eV RN masses: T B M GeV

19 Aternatives Resonant Leptogenesis Resonant enhancement of CP-asymmetry for M,3 M 1 M 1 : N 1 + N 1 + N 1 Amost no effect on bound on ight ν masses, but ower imit on T B,M 1 can be evaded. owever: many different resuts in iterature!? Probem: N i unstabe, i.e. cannot appear as in- or out-states of S-matrix eements Soution: scattering ampitudes of stabe partices with N i as intermediate states Factorisation: effective one-oop coupings of N i

20 Aternatives Resonant Leptogenesis Resonant enhancement of CP-asymmetry for M,3 M 1 M 1 : N 1 + N 1 + N 1 Amost no effect on bound on ight ν masses, but ower imit on T B,M 1 can be evaded. owever: many different resuts in iterature!? Probem: N i unstabe, i.e. cannot appear as in- or out-states of S-matrix eements Soution: scattering ampitudes of stabe partices with N i as intermediate states Factorisation: effective one-oop coupings of N i N

21 Aternatives Resummation of sef-energies reguarizes resonant propagator mixing effects ( S 1 ) ij = p M i Σ ij Renormaization known (Knieh & Piaftsis 96) Chira decomposition of propagator: S = P R S RR + P L S LL + P L p S LR + P R p S RL Contribute to different scattering processes: M ( r s ) h ri Sij LL h sj M ( r s ) h ri SRR ij M ( r s ) h ri SRL ij h sj M ( r s ) h ri S LR Contributions of different N i mass eigenstates? ij h sj h sj

22 Aternatives Factorization (Anisimov, Broncano & M.P. 05): Different methods: 1 Decompose scattering amp. into partia fractions, e.g.: 1 1 M ( r s ) λ r1 p ˆM 1 λ s1 + λ r p ˆM λ s +... λ ri : resummed effective N i Yukawa couping Consistency: a 4 ampitudes can be factorized simutaneousy. Diagonaization of propagators, e.g.: U S LL U T = S diag M ( r s ) ( hu T) ri Sdiag ii ( hu T ) si ( hu T ) ri : resummed effective N i Yukawa couping Consistency: for p = Mi a 4 ampitudes can be factorized simutaneousy.

23 Aternatives Resuts: Both methods yied identica resuts for physica quantities: 1 Decay widths: Γ(N i r ) λ ri = ( hu T), for p = M ri i CP-asymmetries, e.g.: ε 1 M M 1 ( M M 1) +(M Γ M 1 Γ 1 ), Previous approaches, e.g., resum ony sef-energy Σ jj of intermediate neutrino N j reguator: Γ j (Piaftsis & Underwood 04) M ε 1 M 1 ( M M1 ) + M 1 Γ Different neutrino favours are treated differenty!

24 Aternatives Resuts: Both methods yied identica resuts for physica quantities: 1 Decay widths: Γ(N i r ) λ ri = ( hu T), for p = M ri i CP-asymmetries, e.g.: ε 1 M M 1 ( M M 1) +(M Γ M 1 Γ 1 ), Previous approaches, e.g., resum ony sef-energy Σ jj of intermediate neutrino N j reguator: Γ j (Piaftsis & Underwood 04) M ε 1 M 1 ( M M1 ) + M 1 Γ Different neutrino favours are treated differenty!

25 Aternatives Reative one-oop correction to coupings of N 1 Our resut (thick ine) compared to the one of Piaftsis et a.: -10 M 10 =M λ 11 -h 11 h p /M 1 thin ine has resonance at p = M, i.e. contributions from different neutrino mass eigenstates not propery separated in previous approaches. 10

26 Aternatives CP asymmetry Our resut (thick ine) compared to the one of Piaftsis et a.: ε =M /M Both the position of the resonance and the maximum vaue for ε 1 have shifted by an order of magnitude (detais depend on neutrino mass mode used).

27 Concusions Concusions Type I seesaw naturay expains the cosmoogica baryon asymmetry and the smaness of neutrino masses Quasi-degenerate ight ν masses are incompatibe with eptogenesis: m νi < 0.13 ev ower bound on the baryogenesis temperature: T B 10 9 GeV, t B 10 5 s possibe way out: resonant eptogenesis eptogenesis works best in neutrino mass window 10 3 ev m νi 0.1eV consistent with neutrino osciations

28 Concusions