Minimal Flavour Violation and leptogenesis

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1 Minimal Flavour Violation and leptogenesis in collab. with Vincenzo Cirigliano and Gino Isidori Flavour problem and motivation for the MFV hypothesis High energy constraints: leptogenesis Low energy predictions: e, Planck06,, Paris Valentina Porretti Università di Roma Tre

2 the MFV answer to the flavour problem B, L, CP conserved U(3) 5 max symmetry group can accomodate all precision tests up to now Given the exp. info: ΔS=2 EDMs Proton life time, neutrino masses >10 6 GeV >10 7 GeV >10 15 GeV if we like ~TeV, it is reasonable to assume that new physics operators respect B, L, flavour conserving CP break the U(3) 5 flavour group just like the SM does Yukawa as the only source of flavour breaking R.S.Chivukula and Georgi 87, A.Buras et al.01, G.D Ambrosio et al.02 MFV A popular example: SUSY with universal soft scalar masses and trilinear soft terms proportional to Yukawa couplings.

3 The model independent way to find out all the operators compatible with the MFV hypothesis: G.D Ambrosio et al.02 quark sector Treat the Yukawa matrices as spurion fields. Their transformation properties make the Yukawa Lagrangian formally invariant under the SU(3) 3 flavour group Identify the basic FCNC bilinear structures at leading order in the Yukawa couplings For ex: for processes with external quarks Build the complete basis of dimension 6 FCNC operators, suppressed by FV 2 For ex: F=2 Experiments constrain the scale FV m d FV > 2 TeV small! No flavour problem and determine the coefficients of these operators in the effective Lagrangian

4 If, as the huge experimental info suggests, some kind of MFV mechanism is at work in the quark sector, it is plausible the same happens in the LEPTON SECTOR Now we know that neutrinos are massive the flavour structure of the lepton sector could be an exact replica of the quark sector (zero phenomenology option) But the numbers are quite different m << m of any charged fermion The U MNS is strongly off diagonal, the V CKM is close to the identity matrix indications in favor of the see saw mechanism neutrino mass scale scale of lepton number violation Λ LN >> Λ FV

5 in the lepton sector we assume MFV + see saw MFV + see saw type I In exact analogy with the quark sector: Only Yukawa are treated as spurions This is not enough to make all the Lagrangian invariant under the SU(3) 3 flavour group We recover a SU(3) 2 x O(3) imposing M R =1 In the basis with e diagonal, the basic FCNC bilinears at leading order in are and the complete basis of dimension 6 FCNC operators can be built. V.Cirigliano et al. 05

6 this is the case in well motivated models About the hypothesis M I it is in more strict analogy with the quark sector: only Yukawa couplings break flavour symmetry. MFV in the lepton and quark sector can be unified identifying the LFV scales and imposing some GUT relation between the diagonalization matrices of quark and lepton Yukawa matrices. it yields a predictive and testable scenario, and this is very important, given the very few experimental constraints that will be available, if at all. a more general scheme where also M is treated as a spurion is possible. No new operators with respect to the case M I can give observable FV at low energy, but the direct link with the U MNS and m is lost (5 additional param s enter). A top down approach in this case is probably better interesting implications for leptogenesis (viable for M~TeV, in SUSY no gravitino problem)

7 Connection with the observable sector in principle measurable CP limit basic unit of FCNC for ex LN >> FV is better predictable in terms of oscillation parameters and neutrino masses, modulo the scale ambiguity still predictive taking ratio of observables, but can t tell what scales FV you are testing. But what happens without the hypothesis of CP conservation?

8 Bottom up parametrization complex orthogonal real orthogonal complex hermitian and H T =H * If M R = 1 save 2 eigenvalues 3 real rotation angles (lagrangian is O(3) invariant) Casas and Ibarra 01 Pascoli et al. 03 If no complex phases save 2 majorana phases, 1 phase of the U MNS 3 leptogenesis phases 1, 2, 3 (H=I) Hyperbolic functions in H The requirement <1, permit for ex. i as large as 3 for M=10 10 GeV and m=0.001 ev > H = O(10 2 ) destroy CP conserving predictions Is leptogenesis viable for small phases? Leptogenesis at high energy / v 2 FCNC at low energy / v 2 get info about H

9 Leptogenesis in MFV An issue itself: can we generate enough asymmetry with Yukawa couplings as the only source of flavour breaking

10 Non vanishing leptogenesis requires 3) H = I 4) a mass splitting for right handed neutrinos The most general structures compatible with the MFV group give + higher order terms In addition, a general analysis in terms of CP invariants shows that if only a non vanishing zero asymmetry T.Hambye et al. 04 if a non vanishing non zero asymmetry, but all the three param s in H ( 1, 2, 3 ) must be non vanishing also in the a l = 0 case, this condition is quantitatively necessary in order to generate the observed baryon asymmetry Caution: only order of magnitude statements are possible in a model independent approach. SM formulae used. S.Blanchet, P.Di Bari, 06

11 Baryonic asymmetry as a function of c ev a l =0 a l =0 loop hierarchy between the coefficients c a l c 2 a a The mass splitting is numerically dominant Self energy close to the resonance The term with e is sub leading in a wide range of M R The effect of 13 and low energy phases is negligible

12 Baryonic asymmetry as a function of M R Y B Y B = WMAP+SLOAN a l =0 a ll =0 ev M R >10 12 GeV in order to have enough asymmetry, except in fine tuned configuratios for large M R, the mass splitting becomes numerically comparable to and dominates the generation of the asymmetry. are not innaturally small.

13 Baryonic asymmetry as a function of i >1 For small phases H 1 and For large phases H * =H T and H + =H imply a cancellation between the terms contributing to i. The cancellation is exact in the limit of equal phases and degenerate light neutrino masses. i i as a function of m M R =10 13 M R =10 14 M R =10 15 GeV GeV GeV ev

14 As in general not enough asymmetry is generated, all the param s are significantly constrained and little freedom is left CLEAR INDICATIONS FROM LEPTOGENESIS - in reasonable ranges, the coefficients of the mass splittings are not determinant. However a significant enhancement of the asymmetry is possible increasing a /a In any case, they are irrelevant in the see saw reconstruction. right handed neutrino mass M > GeV: Good news! enhances FV rates at low energies breaks the scale ambiguity M/L - phases in the range [ ] enhancement of FV rates at low energies (BR H 4 ), but the direct link with the observable sector, valid in the CP limit, is in most (not all) cases lost. - hierarchical spectrum for light neutrinos preferred (m < 0.01 ev).

15 Low energy predictions Effective Lagrangian at the scale FV The operators O i contain the FCNC basic unit / v 2 FCNC observables are proportional to constrain FV only with info on LN ratios of the same observables for different lepton families depend on neutrino masses, oscillation parameters, Majorana and leptogenesis phases, do not depend on the details of the model. ratios of observables involving the same lepton families give access to the coefficients of the operators the specific MFV model behind hints on Several patterns that falsify the MFV hypothesis can be identified, but measurements are needed! 13, and hierarchy, 2 0, l i l i, 4 fermion processes ( 3e,, e conversion in nuclei, e, Y ) V.Cirigliano, B.Grinstein 06

16 in the meanwhile the realistic expectation is for e and Leptogenesis strongly constrains M R >10 12 GeV FCNC enhanced Scale ambiguity M/ FV 2 broken SUSY is a special case J.Hisano et al, 95 SUSY masses

17 What scales of FV are we testing with MFV? with constraints on M from leptogenesis a rough estimate is now possible already large! should be observed soon, if MFV has to solve the flavour problem NOW NOW?? SuperB PSI Log 10 FV (GeV) Log 10 FV (GeV) Events generated in the full range of all parameters; plotted the subset satisfying the leptogenesis constraint

18 Effect of leptogenesis phases ideal case no lepotg. phases for super heavy R MFV leptog. viable & CP conserving prediction valid M = GeV generic case enhancement but loss of predictivity sin 13 = 0 = events generated in the full range of all parameters; plotted the subset satisfying the leptogenesis constraint In any case sin 13 BR ( e ) < BR ( ) True for every combination of low and high energy phases and for every neutrino hierarchy.

19 Summary I The MFV symmetry principle (Yukawa as the only source of flavour breaking) keeps the scale of new physics naturally low (~ TeV) and can be implemented in several models. An advantage of MFV is the minimum number of free parameters. The extensive experimental searches in the quark sector constitute a non trivial indication in favour of MFV, or some variant of it. The extension of MFV to the lepton sector could be eventually testable only adding high energy assumptions. The most reasonable and predictive one is the see-saw type I. We assume the right-handed Majorana mass to be the identity in flavour space the Yukawa couplings are the only source of flavour breaking, exactly as in the quark sector.

20 Summary II In MFV, flavour violation at low energy is proportional to M/, which is 1) completely determined by the U MNS matrix and the light neutrino masses in the CP limit. 2) enhanced by heavy M. MFV can account for the observed baryon aymmetry. This requires - heavy right handed neutrinos mass M R >10 12 GeV enhancement of FV rates at low energy anambigous determination of the FV scales we are testing in experiments - leptogenesis phases O( ) BR ( e ) and BR ( ) are already testing flavour violation scales of 1-10 TeV: should be observed soon Predictions of FV at low energy in the CP conservation limit are correct for very large M R = GeV, where leptogenesis imply phases O(0.01). The prediction BR ( e ) < BR ( ) is valid in every range of parameters satisfying the leptogenesis constraint. In connection with measurements of m, m, four lepton FV processes, more checks of MFV will be possible.