Leptogenesis and the Flavour Structure of the Seesaw

Transcription

1 Leptogenesis and the Flavour Structure of the Seesaw based on: hep-ph/ (JCAP 0611 (2006) 011) with S.F. King, A. Riotto hep-ph/ (JCAP 0702 (2007) 024) with A.M. Teixeira arxiv: (Phys. Rev. D76 (2007) ) MPIK, January 28, 2008

2 Problem in Cosmology: The baryon asymmetry of the universe How was the observed baryon asymmety of the universe (BAU) generated?

3 Problem in Particle Physics: Origin of neutrino masses LSND: if correct, not from ν-oscillations (MiniBooNE) Strong evidence for neutrino oscillations: Neutrinos have mass The SM has to be extended!

4 Summary: Present knowledge on neutrino masses & mixing quarks & charged leptons neutrinos 1 ev 1.8 x kg Two mixing angles large (θ23 close to maximal) Constraints from 0νββ-decay, Tritium β-decay & cosmology: mνi below about 0.5 ev Open questions: CP violation, mass scale & ordering, θ13,...

5 A possible solution to both problems: Type I & II seesaw mechanism Type I Seesaw 0 h 0 hh νl Yν Type I + Triplet Seesaw = Type II Seesaw 0 h H λ M νr heavy! h0 H L heavy! Yν ν L P. Minkowski (1977), Gell-Mann, Glashow, Mohapatra, Ramond, Senjanovic, Slanski, Yanagida (1979/1980) νl Y νl Lazarides, Magg, Mohapatra, Schechter, Senjanovic, Shafi, Valle, WetterichStefan (1981) Antusch

6 The 6x6 neutrino mass matrix and the seesaw (3 left-handed and 3 right-handed neutrinos) Approximate block-diagonalization for heavy right-handed neutrinos: Effective mass matrix of the light neutrinos Type II contribution Type I mass matrix (Type II) Seesaw formula

7 Leptogenesis: The mechanism Out-of-equilibrium decay of heavy RH neutrinos in the early universe Fukugita, Yanagida ('86) lepton asymmetries Lα Sphaleron processes (conserve B - L) within SM (MSSM) partly convert lepton asymmetries into baryon asymmetry B

8 Motivation Leptogenesis is an attractive mechanism, intensively studied... New aspect got attention (~ 2 years ago): Flavour-dependence! Consequence: Several issues have to be revisited: Bounds on ε1,α, MR1, TRH, ν-mass scale (?) How does the seesaw flavour structure affect thermal leptogenesis? How does leptogenesis in type I seesaw compare to leptogenesis in type II? Typically people consider leptogenesis in the context of the SM... However: Leptogenesis operates at very high energies >> MEW hierarchy problem (new leptogenesis scale(s) scales) Possible solution: low energy supersymmetry Question: Flavour-dependent leptogenesis in MSSM SM?

9 Outline Part 1: Computation of the baryon asymmetry via leptogenesis: Restrictions: thermal leptogenesis via νr1-decay; MR1 << MR2,MR3, M Include: type I and type II seesaw; flavour-dependent treatment; MSSM & SM; effects of reheating temperature Flavour-dependent decay asymmetries ε1,α Flavour-dependent Boltzmann equations efficiency factor ηα Part 2: General Bounds (ε1,α, MR1, TRH, mν (?)) Part 3: Impact of the flavour structure of the (type I) seesaw on the producede BAU from thermal leptogenesis Classes of models: 'Sequential RH neutrino Dominance (SD)' Fully general, model independent (R-matrix parametersation) Summary & Conclusions

10 When does flavour matter...? If flavour matters depends on whether the charged lepton Yukawa interactions are in/out of thermal equilibrium. For which T is yα in thermal equillibrium? Compare Γyα 5 x 10-3 yα2 T with H(T) T 2 Flavour-independent approximation (considered in most studies until recently) only appropriate for T > 1012 GeV! SM T [GeV] relevant: T ~ MR independent flavour 2 independent flavours, conflict w. MR1min 3 independent flavours ee,, Barbieri et al ('99), Abada et al ('06), Nardi et al ('06)

11 When does flavour matter...? SM In the SM: - below 1012 GeV, interaction mediated by yτ in thermal eqilibrium - below 109 GeV, interaction mediated by yτ & yµ in thermal equilibrium As we will see: last case in conflict with bounds on MR1 SM: 1 or 2 independent flavours T [GeV] relevant: T ~ MR independent flavour 2 independent flavours, conflict w. MR1min 3 independent flavours ee,, Barbieri et al ('99), Abada et al ('06), Nardi et al ('06)

12 When flavour matters: MSSM Important difference in the MSSM: for e, µ, τ ymssm = ysm (1+tan2β)1/2 Consequence: relevant T by changes by x (1+tan2β)! In the MSSM: (e.g. tan β = 30) - below 1015 GeV, interaction mediated by yτ in th. eq. - below 10 GeV, interaction mediated by yτ & yµ in th. eq. 12 In the many interesting cases in the MSSM (TRH constraints), 3 independent flavours! MSSM T [GeV] relevant: T ~ MR1 example: tan β = 30 2 independent flavours, independent flavours 1010 ee,, 108 conflict w. MR1min S.A., S.F. King, A. Riotto ('06)

13 Flavour-dependent Boltzmann equations Differential equations for the number densities of the lightest RH neutrino (YN1) and for the independent B/3 Lα asymmetries (Y α) γd: production and decay of RH neutrinos ε1,α: decay asymmetries (into Lα + H) Ααβ: induces a coupling between the diff. Eqs. for the asymmetries Y α (z = M1 / T) γdα: inverse decays and scattering processes which 'wash out' asymmetries in flavour α, but are also essential for their generation SM: Barbieri et al ('99), Abada et al ('06), Nardi et al ('06) MSSM: S.A., S.F. King, A. Riotto ('06)

14 The produced BAU (SM) Y α : B/3 Lα asymmetries ε1,α: decay asymmetries (into Lα + H) ηα: efficiency factors sphaleron conversion Two ingredients: the decay asymmetries ε1,α for the independent flavours the 'efficiency factor' ηα with which the asymmetries Y α are generated (numerically, from flavour-dependent Boltzmann equations)

15 The produced BAU (SUSY case) total B/3 Lα asymmetries (particle + sparticle!) ε1,α: decay asymmetries (into Lα + H) ηα: efficiency factors sphaleron conversion Note: The above ansatz uses already where:

16 Step 1: Decay asymmetries Decay of the lightest RH neutrino (νr1 Lf Hu): Tree-level 1-loop SM SM MSSM SUSY Type I Seesaw Type I: L. Covi, E. Roulet, F. Vissani ('96) Type II Seesaw Type II: S.A., S.F. King ('04)

17 Step 1: Decay asymmetries Results: in the limit MR1 << MR2 << MR3 and MR1 << M in the SM: (Ye diagonal) link to the (type I + type II) neutrino mass matrix in the MSSM: (Ye diagonal) proportional to the dependence on the mass of νr1 Yukawa couplings to νr1

18 Step 2: Computation of the flavour-dependent efficiency factor From solving the Boltzmann equations... Efficiencies depend mainly on flavourdependent washout parametrer S.A., S.F. King, A. Riotto ('06) Simplification: off-diagonals of A neglected MSSM, tan β = 30 (Yν)f1 2 on the sum and on the matrix A Note: Aαα = O(1) Optimal efficiency for washout parameter ~

19 Main difference: Flavour-dependent vs. flavour-independent treatment Correct flavour-dependent: YB α Flavour-independent approximation: vs. YB ) β Flavour-dep. ε1,α weighted by flavour-dep. efficiency ηα! This affects the produced BAU from thermal leptogenesis with a given seesaw flavour structure...

20 Example: Flavour-dependent vs. flavour independent S.A., S.F. King, A. Riotto ('06) MSSM, tan β = 30, Type I Seesaw example SD with M1 = MA Correct flavour-dependent treatment: YB α vs. Flavour-independent approximation: YB ) β

21 Constraints on TRH The role of TRH for leptogenesis:... for thermal leptogenesis high temperatures are required in order to produce RH neutrinos in the thermal bath (naively T ~ MR1)... realised after inflation ( TRH) example in SUGA model (maybe not fully up-to-date): Typical problems of high TRH: (thermal prod. of long lived particles) i) BBN gravitino problem: constraints on reheating TRH, depending on gravitino mass m3/2! Kohri, Moroi, Yotsuyanagi ('05) Here: m3/2 free parameter heavy Note: stable gravitinos problems with long lived NLSPs; possible solutions if e.g. R-parity violated,...

22 Constraints on TRH Typical problems of high TRH: ii) Gravitino decay LSP (R-parity assumed, neutralino LSP) LSPs produced non-thermally from gravitino decays. From ΩLSP< Ωm example in SUGA model (maybe not fully up-to-date): constraints on reheating TRH TRH < 2 x 1010 GeV ~ for neutralino mass GeV has to be <~ 0.13 WMAP Consequence: constraints on leptogenesis ( flavour structure) Kohri, Moroi, Yotsuyanagi ('05)

23 Leptogenesis efficiency and TRH Assuming that the decays of the inflaton reheat only MSSM particles (Note: non-th. νr1-prod. (gravitino prod.) can improve ηα (lower TRHmax)): MSSM, tan β = 30 ηα strong dependence! MSSM, tan β = 30 Note: Aαα = O(1) S.A., A. Teixeira ('06) Results (Mathematica function!) available!

24 General considerations: Bounds on the decay asymmetries Abada et al. ('06) Type I seesaw: proportional to the mass of νr1 supression for quasi-degenerate neutrino masses if optimal flavoured washout parameter (~ 10-3 ev) proportional to the absolute neutrino mass scale note: only in type I S.A., S.F. King ('04) S.A. ('07) Type II seesaw: no supression for quasi-degenerate neutrino masses leptogenesis more efficient if mν Observation: For mν, type I bound stronger (below ~ 0.5 ev, for optimal efficiency/washout) whereas type II bound relaxed!

25 General considerations: Bounds on the decay asymmetries Using the bounds on ε1,α, and results for ηα, we obtain a bound for MR1! S.A. ('07) MSSM, tan β = 30 Note: for hierarchical neutrinos, almost unchanged compared to flavour-independent approximation; changes for mν

26 Constraints on TRH and on mν Type I Seesaw: mνmin TminRH MSSM, tan β = 30 same bound for mνmin=0 S.A. ('07) Type II Seesaw: mνmin TminRH

27 Sequential RH neutrino dominance Mass matrix of RH neutrinos (diagonal) (Note: within type I seesaw!) Neutrino Yukawa matrix (Ye diagonal,lr conv.) Note: permuations A B C possible! Yν Low energy: neutrino mass operator ('Seesaw formula') Sequential dominance condition: S.F. King ('98,'02) 'subsubdominant RH neutrino' (mass MC) gives smallest contribution (hierarchical ν-masses, mν1) Leading contribution to mν from 'dominant RH neutrino' (mass MA) Sub-leading contribution to mν from 'subdominant RH neutrino' (mass MB)

28 SD and neutrino masses and mixing angles Yukawa couplings of dominant RH neutrino Defining MNS mixing angles Yukawa couplings of subdominant RH neutrino Almost maximal θ23 A2 A3 Small θ23 A1 << A2, A3 Large θ12 B1 B2 &/or B3 } O(m2/m3) Neutrino masses CP phases (+ conditions θ12,θ13 real δ)

29 Decay asymmetries and washout factors in SD (3 classes of models) leading contribution } } M1: lightest RH neutrino subleading (suppressed) contribution

30 Ideal conditions for leptognesis? S.A., S.F. King, A. Riotto ('06) Decay asymmetries: Can in general be optimal, but potential cancellation in ε1,α Washout parameters: if θ12 close to tri-bimaximal via A = (0,-1,1), B = (1,1,1)! *(At least) one of them is O(m2); optimal washout possible...

31 MNS CP phase δ and leptogenesis S.A., S.F. King, A. Riotto ('06) 3 characteristic cases: M1 = MA and 2 texture zeros: strong δ MNS leptogenesis link! M1 = MB and 2 texture zeros: strong δ MNS leptogenesis link! C3 M1 = MC: no MNS leptogenesis link! C3

32 R-matrix parameterisation of the seesaw degrees of freedom Completely model-independent: Start with seesaw equation: (Note: here type I!) (basis: low energy: 12 parameters high energy: 21 parameters Strategy: find with Solution can be expressed in terms of complex orthogonal matrix R Casas, Ibarra ('01) )

33 R-matrix vs. Sequential Dominance M1 = MA: Yν = (A,B,C) (θ1,θ2,θ3) (π/2,0,π/2) Yν = (A,C,B) (θ1,θ2,θ3) (π/2,π/2,0) M1 = MB: Yν = (B,A,C) (θ1,θ2,θ3) (0,0,π/2) Yν = (B,C,A) (θ1,θ2,θ3) (π/2,π/2,π/2) M1 = MC: Yν = (C,A,B) (θ1,θ2,θ3) (π/2,0,0) Yν = (C,B,A) (θ1,θ2,θ3) (0,0,0) Other angles interpolate between SD cases!

34 Decay asymmetries and washout factors in R-matrix parameterisation Decay asymmetries Washout parameters dependence on R-matrix angles and RH ν-masses dependence on mνi and UMNS

35 Leptogenesis bounds on TRH and MR1 In type I seesaw (using the upper bound for ε1,α (& Σ ε1,α) and optimal ηα): maximally possible BAU (type I seesaw) Here and in the following: MSSM case, tan β = 30, type I seesaw, normal ν-mass hierarchy mν1 = 10-3 ev Colour code: grey: WMAP x [1/5,1/2] green: WMAP x [1/2,1] dark blue: WMAP range light blue: ~ WMAP x [1,2] red: >~ WMAP x 2 For given TRHmax: (example TRHmax = 2 x 1010 GeV): 'viablility window' for MR1 ( mn1) S.A., A. Teixeira ('06) 10 Next: Flavour structure compatible with TRHmax = 2 xmpi 10für GeV Physik (Munich)

36 Leptogenesis constraints on Seesaw parameters (MSSM) Constraints on R matrix angles θ2 and θ3 TRHmax = 2 x 1010 GeV Type I seesaw, hierarchical ν-masses S.A., A. Teixeira ('06) TRHmax = 2 x 1010 GeV Colour code: grey: WMAP x [1/5,1/2] green: WMAP x [1/2,1] dark blue: WMAP range light blue: ~ WMAP x [1,2] red: >~ WMAP x 2

37 Leptogenesis constraints on Seesaw parameters (MSSM) The role of the R matrix angle θ1 Type I seesaw Colour code: grey: WMAP x [1/5,1/2] green: WMAP x [1/2,1] dark blue: WMAP range light blue: ~ WMAP x [1,2] red: >~ WMAP x 2 Note: 'interpolates' between Yν = (C,A,B) Yν = (C,B,A)

38 Leptogenesis constraints on Seesaw parameters (MSSM) The case of real R matrix: CP violation only from δmns? Type I seesaw

39 Leptogenesis constraints on Seesaw parameters (MSSM) Real R matrix case: CP violation from Majorana phases? Type I seesaw

40 Leptogenesis constraints on Seesaw parameters New allowed regions due to flavour-dependent effects (large complex Stefan θ2, θ3) in SD: within/ interpolation between classes M1 Antusch = MB & M1 = MA!

41 Which region of SUSY Seesaw parameters is most favoured? Most favoured by thermal leptogenesis: small and complex θ2 (and θ3) Type I seesaw Colour code: grey: WMAP x [1/5,1/2] green: WMAP x [1/2,1] dark blue: WMAP range light blue: ~ WMAP x [1,2] red: >~ WMAP x 2 Sequential Dominance: correspond to M1 = MC

42 Summary and Conclusions (I) Flavour-dependent effects have important impact on the produced baryon asymmetry Main difference to flavour-in. approx.: ~ ~ Σ ε1,α ηα(m1,α) (Σ ε1,α) x ηind(σ m1,α) (correct, fl. dep.) (flavour-ind.) Temperature where flavour-effects are relevant differs in SM and MSSM (MSSM: typically 3 or 2 independent flavours, SM: only 2 or 1) MSSM T [GeV] tan β = 30 2 independent flavours, independent flavours 1010,, ee 108 conflict w. MR1min

43 Summary and Conclusions (II) Leptogenesis in SUSY: constrained but not ruled out. Quite robust bound (local SUSY) TRHmax = 2 x 1010 GeV To analyse TRH-constraints on thermal leptogenesis: Flavour-dependent efficiency factor (incl. TRH) public S.A., A. Teixeira ('06) Produced baryon asymmetry from thermal leptogenesis depends strongly on the flavour structure of the seesaw! (best: LG via e and/or µ flavours; R-matrix small θ2,θ3; SD M1= MC) ηα