Non-zero Ue3, TeV-Leptogenesis in A4 Symmetry and LHC

1. Non-zero Ue3, TeV-Leptogenesis in A4 Symmetry and LHC Y.H.Ahn (Academia Sinica) based on the on-going paper with Chian-Shu Chen 2nd LHC workshop at NCKU

2. Present Knowledges Neutrino oscillation(PRL101,141801) Bi-Large mixing angles theta13>0 Nothing is known about all three CP-vilating phases Cosmological limit (including WMAP 3-years result) upper bound on neutrino masses (JCAP10,104) Starting to disfavor the degenerate spectrum of neutrinos BAU About 20% of the Universe is made up of cold dark matter. 2nd LHC workshop at NCKU

3. All data can be explained in terms of oscillation between just 3 known species : Three possible orderings of neutrino masses 2nd LHC workshop at NCKU

4. Tri-Bimaximal The current neutrino oscillation data are well described by so called “Tri-Bimaximal mixing” matrix (Harrison, Perkins and Scott; see also Wolfenstein(1970) and He and Zee) It is suggestive of a flavor symmetry. It also suggests that flavor structure for mixing should be divorced from trying to understand the mass eigenvalues. Unless flavor symmetries are assumed, particle masses and mixings are generally undetermined in gauge theory: To understand the present neutrino oscillation data we consider A4 flavor symmetry. (E.Ma and G.Rajarasekaran; G.Altarelly and F.Feruglio; X.G.He, Y.Y.Keum and R.Volkas) For the existence of DM or LHC signal (?)(N.G.Deshpande, E.Ma) and the BAU to be explained at or around TeV scale in radiative see-saw, we also introduce extra discrete symmetry Z2 . 2nd LHC workshop at NCKU

5. A4 A4 is the symmetry group of the tetrahedron and the finite groups of the even permutation of four objects: its irreducible representations contain one triplet 3 and three singlets1,1’,1” with the multiplication rules 3×3=3+3+1+1’+1” and 1’×1’=1” Let’s denote two A4 triplets and where 2nd LHC workshop at NCKU

6. Construction of Lagrangian Under SU(2)×U(1)×A4×Z2×Z4 Hence its Yukawa interaction in the lepton sector Z2: forbidden after EW symmetry breaking Z4: To prevent direct couplings of the right-handed neutrinos to and , and 2nd LHC workshop at NCKU

7. In the charged lepton sector: Assumption: the VEVs of A4 triplets can be equally aligned, i.e, “Tri-maximal” Charged lepton mass matrix comes from and has the form U(w)×Diag.(arbitrary eigenvalues) • In the neutrino sector: • : unit matrix No Leptogenesis and No CP-violation( ) • In the lagrangian level, assume that above a cutoff-scale Λ there is no CP-violation term in the neutrino Yuawa interaction, which for scales below Λ is expressed in terms of 5-D operator. • : off-diagonal matrix • The breaking scale of A4×Z4 is assumed to be lower than the cutoff scale Λ. 2nd LHC workshop at NCKU

8. Spontaneous Breaking of A4 Taking the scale of A4×Z4 symmetry breaking to be above EW scale, And assuming the vacuum alignment, and , Keeping • Right-handed Maj. mass term : where It will give rise to “Bi-maximal” While, Neutrino Yukawa coupling matrices CP-asymmetry≠0 • Theta13 ≠0 where CP-asymmetry=0 • Theta13=0 2nd LHC workshop at NCKU

9. In a basis where both charged lepton and heavy Mj. Neutrino mass matrices are diagonal where “Bi-maximal” 2nd LHC workshop at NCKU

10. The couplings with leptons and scalars : Concerned with CP violation, the CP phases coming from as well as the CP phase from obviously take part in low-energy CP violation. Leptogenesis is associated with both itself and the combination of the Yukawa neutrino matrix with which implies both CP-phases in and take part in Leptogenesis. 2nd LHC workshop at NCKU

11. Radiative seesaw Due to Z2 symmetry, we can not get the neutrino Dirac masses, and therefore the usual seesaw does not operate any more: The light neutrino mass matrix can be generated through one-loop diagram with the quartic scalar interactions (E.Ma) After EW symmetry breaking, i.e. with where and • We assume , so the lightest Z2 odd neutral particle of is stable and can be a candidate of DM or LHC signal: with 2nd LHC workshop at NCKU

12. A very attractive feature of Seesaw ? • In addition to the explanation of neutrino masses, seesaw has another appearing feature so-called “Leptogenesis” • We are in the energy scale where A4 symmetry is broken but the SM gauge group remains unbroken. Choose at or around TeV scale • Flavor effects: (PRD49,6394) • wash-out factor with • At TeV scale, • this will make a generated lepton asymmetry be strongly washed out . 2nd LHC workshop at NCKU

13. Light neutrino mass matrix • To prevent a produced CP-asymmetry from being strongly washed out at or around TeV scale, • we should consider the case where is the lightest of the heavy Mj.neutrinos. hggkjhkjk The light neutrino mass matrix can be obtained where • In the limit of x→0, • this matrix can be diagonalized by TB mixing with the eigenvalues 2nd LHC workshop at NCKU

14. Mixing Angles The mass eigenvalues can be roughly expressed as The TB mixing angles are corrected by the parameters x and ø For x=0 agrees with the results of TB In order for to be in the experimental bounds, the relation should be satisfied; for the size of x should be small. 2nd LHC workshop at NCKU

15. Mass orderings of light neutrino Because of the observed hierarchy , and the requirements of MSW resonance for solar neutrinos, there are two possible neutrino mass ordering: • Normal ordering (m1<m2<m3)↔ • with • with • Degenerate light neutrino mass spectrum very small x (or very small ) • (2) Inverted ordering (m3<m1<m2)↔ • with • with • Degenerate light neutrino mass spectrum 2nd LHC workshop at NCKU

16. Overall scale of neutrino masses Parameters κ(or a, b), x, φ can be determined by experimental data, whereas is arbitrary: however, the value of depends on the magnitude of in the case that is determined as where and are used, denotes . the value of only depends on the size of : Dark matter : The mass splitting is controlled by , which is stable against radiative corrections. Opens the interesting possibility of explaining the DAMA annual modulation data; is needed to realize DAMA (JHEP0907;090,2009) could Not give a successful leptogenesis in our scenario. 2nd LHC workshop at NCKU

17. Can we extract the signal of η at the LHC ? • Production of scalar pair at the LHC In order for LHC signal to be briefly considered, we consider, with Z2×Z4 symmetry the most general scalar potential of invariant under SU(2)×U(1): After EW sym. Breaking, the masses of the resulting scalar particles where is the mass of and 2nd LHC workshop at NCKU

18. Scalar interactions: scalar and interact with Higgs boson h of the SM and among themselves • Gauge interactions: Being electroweak doublet, they have gauge int. , but not directly interact with SM fermions. Assume The dominant decay of is into through the gauge interaction, where f=SM fermion and is the missing energy. • The dominant decay of is into and through the gauge interaction, 2nd LHC workshop at NCKU

19. Leptogenesis If LHC gives a signal, then, a successful leptogenesis can be implemented in our scenario: In the case of 2nd LHC workshop at NCKU

20. Conclusions Hierarchical normal mass spectrum of light neutrino can give a large theta13 within experimental bounds, on the other hand, degenerate case only gives very small theta13 less than 2 degree. Upcoming LBL, Reactor experiments and LHC signal of scalar η will give a test of our model. 2nd LHC workshop at NCKU