Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism

Transcription

1 Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism Pierre Hosteins Patras University 13th November 2007 Brussels P.H., S. Lavignac and C. Savoy, Nucl. Phys. B755, arxiv:hep-ph/ A. Abada, P.H., F-X. Josse-Michaux and S. Lavignac, arxiv:0711.xxxx Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 1 / 12

2 Left-Right Symmetric Seesaw Type I+II Seesaw Mechanism The seesaw mechanism is usually realised through couplings of LH leptons to singlet RH neutrinos N Ri (type I) or to an SU(2) L triplet L (type II). When both types are present, interactions are encoded into the following Yukawa potential: Y ν N R l L H M RN R N c R f L l c L L l L M 2 Tr( L L) + h.c. which provides a mass matrix for the light neutrinos : with v L = 0 L v 2 /M. m ν = v L f L v 2 Yν T M 1 R Y ν v Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 2 / 12

3 Left-Right Symmetric Seesaw Type I+II Seesaw Mechanism The seesaw mechanism is usually realised through couplings of LH leptons to singlet RH neutrinos N Ri (type I) or to an SU(2) L triplet L (type II). When both types are present, interactions are encoded into the following Yukawa potential: Y ν N R l L H M RN R N c R f L l c L L l L M 2 Tr( L L) + h.c. which provides a mass matrix for the light neutrinos : with v L = 0 L v 2 /M. m ν = v L f L v 2 Yν T M 1 R Y ν v To reduce the number of parameters, let us consider theories with an extended gauge sector SU(2) L U(1) Y SU(2) L SU(2) R U(1) B L and Left-Right Parity SU(2) L SU(2) R. M R then comes from the vev of an SU(2) R triplet R : M R = v R f R and we can have the relations: f L = f R = f, Y ν = Y T ν, v L v 2 v R Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 2 / 12

4 Left-Right Symmetric Seesaw Method of Reconstruction The seesaw formula we are going to study is thus: m ν = v L f v2 v R Y ν f 1 Y ν with f and Y ν symmetric Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 3 / 12

5 Left-Right Symmetric Seesaw Method of Reconstruction The seesaw formula we are going to study is thus: m ν = v L f v2 v R Y ν f 1 Y ν with f and Y ν symmetric Using the symmetry of Y ν, it can be put in the following simple form: with X X (f ). Z = αx βx 1, α = v L, β = v 2 v R Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 3 / 12

6 Left-Right Symmetric Seesaw Method of Reconstruction The seesaw formula we are going to study is thus: m ν = v L f v2 v R Y ν f 1 Y ν with f and Y ν symmetric Using the symmetry of Y ν, it can be put in the following simple form: Z = αx βx 1, α = v L, β = v 2 with X X (f ). Since Z and X are symmetric, we can diagonalise them with the same complex orthogonal matrix: Z = O T Z ẐO Z and O X = O Z, translating the equation to the eigenvalues: x ± i = z i ± z 2 i + 4αβ 2 Thus, knowledge of Y ν 8 solutions for f (Akhmedov-Frigerio) labeled by (+ + +), (+ + ), etc... v R Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 3 / 12

7 Application to SO(10) SO(10) embedding We apply this method to SUSY SO(10) GUTs, which are a natural embedding of L-R symmetric theories: realisation of LR symmetric seesaw is made with a Higgs sector 10 u + 10 d The relevant part of the superpotential is : W (Y u ) ij 16 i 16 j 10 u + (Y d ) ij 16 i 16 j 10 d + f ij 16 i 16 j 126 Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 4 / 12

8 Application to SO(10) SO(10) embedding We apply this method to SUSY SO(10) GUTs, which are a natural embedding of L-R symmetric theories: realisation of LR symmetric seesaw is made with a Higgs sector 10 u + 10 d The relevant part of the superpotential is : W Y u l L NRH c u + Y d l L erh c d f l L L l L f l R c R lr c Moreover, SO(10) gives the very useful relations : Y ν =Y u and Y e =Y d, fixing Y ν from low energy parameters up to some complex phases. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 4 / 12

9 Application to SO(10) SO(10) embedding We apply this method to SUSY SO(10) GUTs, which are a natural embedding of L-R symmetric theories: realisation of LR symmetric seesaw is made with a Higgs sector 10 u + 10 d The relevant part of the superpotential is : W Y u l L N c RH u + Y d l L e c RH d f l L L l L f l c R R l c R Moreover, SO(10) gives the very useful relations : Y ν =Y u and Y e =Y d, fixing Y ν from low energy parameters up to some complex phases. We consider a normal hierarchy (m 1 = 10 3 ev), and our free parameters are : v R [10 12, ] GeV h = β/α = v 2 u /v L v R that we take h = a dozen of phases, remnants of the fact that we cannot rephase leptons and quarks independently in SO(10) Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 4 / 12

10 Application to SO(10) M i Case V R GeV M i Case V R GeV M i Case V R GeV M i Case V R GeV Figure: 4 different mass spectra of heavy neutrinos as function of v R (dotted region contains fine-tuning in m ν) Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 5 / 12

11 Application to SO(10) M i Case V R GeV M i Case 10 9 V R GeV 10 15M i Case V R GeV M i Case V R GeV Figure: 4 different mass spectra of heavy neutrinos as function of v R (dotted region contains fine-tuning in m ν) Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 5 / 12

12 Leptogenesis Leptogenesis When the RH neutrino spectrum is hierarchical the CP asymmetry from N 1 decays in the early Universe is, in the one flavour approximation: ε 1 3 Im[YmνY T ] 11 M 1 8π (YY ) 11 vu 2 The baryon asymmetry is then given by : y B = η 1 ε = ε where η 1 1 is the wash-out factor due to lepton number violating scatterings. In type I theories where Y ν Y u is very hierarchical, M GeV, burying the hopes for a succesful leptogenesis from N 1 decays = interest of type I+II seesaw. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 6 / 12

13 Leptogenesis Ε CP Case V R GeV Ε CP Case V R GeV Ε CP Case Ε CP Case V R GeV 10 6 V R GeV (±,, +) are promising, but washout is often strong, we need to solve the Boltzmann equations. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 7 / 12

14 Leptogenesis Importance of Flavour Effects Traditional leptogenesis considers that N i decay into 1 flavour mainly. However it has been shown (Abada et al, Nir et al) that the washout can be quite different between the different flavours, for T RH tan 2 β (when y τ is in equilibrium) : ε 1 = α ε 1α and κ 1 = α κ 1α where α = e, µ, τ and : y B 10 3 α η 1α ε 1α 10 3 α η 1α β ε 1β = we can have κ = κ 1α large, thus η 1 small, but one κ 1α small so that one flavour is weakly washed out η 1α 1. Moreover, preexisting asymmetry from N 2 in flavour α can be preserved while N 1 is in the strong washout regime and all the asymmetry is exponentially washed out in the one flavour approximation (Vives, Shindou et al). Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 8 / 12

15 Leptogenesis Importance of Flavour Effects Case Case Figure: y B for different choices of phases in the flavour framework (left) and the one flavour approximation (right) In the one flavour approximation, when production of CP asymmetry from N 1 can be neglected : Y B L(z) = κ 1 f (z)y B L (z) Y fin B L Y ini B L exp ( 3π/8 κ 1 ) Here κ 1 10 so that preexisting asymmetry can be suppressed by a factor up to 10 9 Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 8 / 12

16 Leptogenesis Importance of Flavour Effects Case Case Figure: y B for different choices of phases in the flavour framework (left) and the one flavour approximation (right) In the flavour regime, the equation is split by flavour : Y α (z) = κ α f (z) β A αβ Y β Y B L Y ini α exp ( 3π/8 κ α ) and we have a mild but sufficient hierarchy in the washout parameters. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 8 / 12

17 Leptogenesis Importance of Flavour Effects Case Case Figure: y B for different choices of phases in the flavour framework (left) and the one flavour approximation (right) = N 2 decays have to be taken into account in the flavour case, where some flavours are weakly washed out by N 1 decays. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 8 / 12

18 Mass Corrections Correction to M e = M d For the moment we worked with the relations : Y e = Y d and Y ν = Y u. For a more realistic model we must add corrections. This can be implemented in our SO(10) model by antisymmetric contributions from non-renormalisable operators YNR ij Λ 10 d i.16 j : M e = v 10 d Y 10 3v 10 d Y 120 M d = v 10 d Y 10 + v 10 d Y 120 and the second contribution is Y 120 = 45 Λ Y NR with 45 M GUT. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 9 / 12

19 Mass Corrections Correction to M e = M d For the moment we worked with the relations : Y e = Y d and Y ν = Y u. For a more realistic model we must add corrections. This can be implemented in our SO(10) model by antisymmetric contributions from non-renormalisable operators YNR ij Λ 10 d i.16 j : M e = v 10 d Y 10 3v 10 d Y 120 M d = v 10 d Y 10 + v 10 d Y 120 and the second contribution is Y 120 = 45 Λ Y NR with 45 M GUT. = consequence : Y e and Y d not diagonal in the same basis but still Y ν = Y u : Y ν = Y u = U T m V T CKMŶuV CKM U m U m is a unitary matrix : 3 angles θ m ij and 6 phases. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 9 / 12

20 Mass Corrections Correction to M e = M d If we take a general U m we can have non-negligible modifications. Here we take θ m 12 [0; π 4 ] and display the deformation of the curves ε 1,τ and m 1,µ as a function of v R. Ε 13 Case 10 6 V R GeV m 12 ev 10 2 Case V R GeV When fitting fermion masses we have some freedom on θ12 m. We take as limiting cases two kinds of sets, with θ12 m 0.2 and θm 12 1, and take dynamical initial conditions for the Boltzmann Equations. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 9 / 12

21 Mass Corrections Numerical results for y B (T in = GeV) Type II-like solutions (±, +, +) can yield good values of y B without any problem thanks to large values of M 1 at large v R : Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 10 / 12

22 Mass Corrections Numerical results for y B (T in = GeV) For cases (±, ±, ) with small M 1, experimental constraints are only reachable for the solutions with M 2 increasing with v R. N 2 decays could be sufficient for (,, ) but N 1 reduces by a factor 10. y B : case Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 10 / 12

23 Mass Corrections Numerical results for y B (T in = GeV) The interesting cases (±,, +) can yield sufficient baryon asymmetry thanks to M e = M d corrections with the large θ m 12 fits Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 10 / 12

24 Mass Corrections Influence of other parameters T in : lowering T in to GeV to reduce tension with gravitino constraint in generic SUSY models eliminates any (±, ±, ) with M GeV but preserves the others. (±, +, +) with large M 1 become marginally allowed. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 11 / 12

25 Mass Corrections Influence of other parameters T in : lowering T in to GeV to reduce tension with gravitino constraint in generic SUSY models eliminates any (±, ±, ) with M GeV but preserves the others. (±, +, +) with large M 1 become marginally allowed. m 1 : going to quasi-degenerate light neutrino spectrum can modify RH neutrino spectrum and increase washout parameters, preventing the possibility of N 2 leptogenesis Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 11 / 12

26 Mass Corrections Influence of other parameters T in : lowering T in to GeV to reduce tension with gravitino constraint in generic SUSY models eliminates any (±, ±, ) with M GeV but preserves the others. (±, +, +) with large M 1 become marginally allowed. m 1 : going to quasi-degenerate light neutrino spectrum can modify RH neutrino spectrum and increase washout parameters, preventing the possibility of N 2 leptogenesis θ 13 : large θ 13 tends to lower y B in some solutions, θ 13 = 0 is preferred. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 11 / 12

27 Mass Corrections Influence of other parameters T in : lowering T in to GeV to reduce tension with gravitino constraint in generic SUSY models eliminates any (±, ±, ) with M GeV but preserves the others. (±, +, +) with large M 1 become marginally allowed. m 1 : going to quasi-degenerate light neutrino spectrum can modify RH neutrino spectrum and increase washout parameters, preventing the possibility of N 2 leptogenesis θ 13 : large θ 13 tends to lower y B in some solutions, θ 13 = 0 is preferred. Y ν = Y u : relaxing equality of the eigenvalues of Y ν and Y u can have important consequences since for (±,, +) for example, M 1 y 2 2 allows fits with small θ m 12 to work, which is desirable since large θm 12 creates tensions with µ eγ experimental constraints. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 11 / 12

28 Conclusion Conclusion We introduced a method for extracting the RH neutrinos mass matrix in the LR symmetric seesaw. We found several new solutions for the RH neutrino spectrum, in accordance with previous work new possibilities for successful leptogenesis in SO(10) models. Flavour effects are crucial in some cases for N 2 leptogenesis to be efficient. Some solutions yield successful leptogenesis with a large B L breaking scale corrections for realistic fermion masses are preponderant. Order one deviations from Y ν = Y u can provide large enhancements and allow to avoid tensions with Lepton Flavour Violating constraints. Successful Leptogenesis in the Left-Right Symmetric Seesaw Mechanism 13th November 2007 Brussels 12 / 12