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Duality in Left-Right Symmetric Seesaw Mechanism

Duality in Left-Right Symmetric Seesaw Mechanism. Michele Frigerio Service de Physique Théorique, CEA/Saclay. in collaboration with Evgeny Kh. Akhmedov Phys. Rev. Lett. 96, 061802 (2006) [hep-ph/0509299] & in preparation. Rencontres de Physique des Particules

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Duality in Left-Right Symmetric Seesaw Mechanism

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  1. Duality in Left-Right Symmetric Seesaw Mechanism Michele Frigerio Service de Physique Théorique, CEA/Saclay in collaboration withEvgeny Kh. Akhmedov Phys. Rev. Lett. 96, 061802 (2006) [hep-ph/0509299] & in preparation Rencontres de Physique des Particules March 3, 2006 - Institut Henri Poincaré

  2. Neutrino mass in Left-Right models Pati, Salam, Mohapatra, Senjanovic, Georgi, Fritzsch, Minkowski Left-Right gauge symmetry: SU(2)L x SU(2)R x U(1)B-L SU(2)L x U(1)Y extensions: SU422, SO(10) , … • Leptons: L = (L lL)T Lc = (Rc lRc)T • Yukawa couplings: • VEVs: - vR = <DR0> breaks SU221 into SU21 • v = <F0> breaks SU21 into U(1)em • vL = <DL0> v2/vR is induced by EW breaking • Mass matrix in (L, Rc) basis:

  3. Seesaw in Left-Right models f determines heavy n masses and mixing f directly contributes to light n masses • Seesaw mechanisms: • v << vR (Type I seesaw) • vL << v (Type II seesaw) Minkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle • Effective mass matrix of light neutrinos: Type I and II contributions are strictly intertwined.

  4. A very well motivated framework • Seesaw explains (i) smallness of n mass; (ii) baryogenesis via leptogenesis • Left-Right models (i) incorporate naturally RH neutrinos; (ii) explain maximal parity violation • Several completely realistic models (for unification, fermion masses, p-decay, …) do not contain sources of n mass other than type I and II seesaw (fermion triplets, double seesaw, radiative mechanisms, extra dimensions, …) • Supersymmetry can be easily incorporated. If only (B - L)-even Higgs bosons acquire VEVs, then R-parity is automatically unbroken. Let us take the LR seesaw formula seriously!

  5. LR seesaw: the parameter space • v2 = (174 GeV)2 (EWSB) • 0  vL GeV (  ≈ - 2 vL2 / v2 ) • TeV vR MPl (no RH weak currents) • 0 (m)ij  eV: partially known from oscillations data • 0 yij 1 : in general unknown Yukawa couplings, but • Minimal SUSY LR: y = tan  ye • Minimal SO(10): y = yu • Seesaw + mSUGRA: yij << 1 to suppress, e.g.,    • 0 fij 1 : completely unknown Yukawa couplings Bottom-up approach: what is the structure of the matrix f ? To what extent we can reconstruct the seesaw heavy sector ?

  6. Seesaw duality Non-linear matrix equation in f Multiple solutions Different structures of f are viable physical options ^ Duality: f solution if and only if f is • One generation: f 2- (mn/vL) f - v2y2/(vLvR) = 0  f= f± • Three generations: f= f1± , … , f4± 4 pairs of dualf structures reproduce the same m

  7. Ambiguity on the seesaw type Suppose type II dominates: Suppose type I dominates: LR-symmetry  y = yTduality holds  fII + fI = m fII is a solution if and only if fI is! If in a model f = fII, there is always another model where f = fI (with the same values for vL,R, mn, y)

  8. A realistic numerical example Tribimaximal mixing: tan2 q23 = 1 tan2 q12 = 0.5 tan2 q13 = 0 No CP violation Eigenvalues: -0.1, 0.2, 0.9 Normal hierarchy with Dm2sol / Dm2atm = 0.038 EX EX TH vLvR = v2 (natural when scalar potential couplings are of order 1) Neglect CKM-like rotations (both charged lepton and neutrino Yukawa couplings diagonal in the same basis) y1 = 10-2 y2 = 10-1 y3 = 1 (inter-generation hierarchy slightly weaker than for charged fermions) There are 4 dual pairs of f structures such that:

  9. Features of the solutions

  10. Features of the solutions Consider a given pair of dual solutions: Seesaw Duality: Dual structure is hierarchical, with dominant 33-entry; small 2-3 mixing f4 structure has dominant 23-block; large (but non-maximal) 2-3 mixing One seesaw type dominance in m12, m22, m23 : type II in the case of f4, type I in the dual. Mixed seesaw in m11, m13, m33 .

  11. Perspectives • Identification of flavorsymmetries in the structures of f. • Radiative stability of the LR seesaw formula: • Running below the LR-symmetry breaking scale • Baryogenesis via Leptogenesis: lepton asymmetry from the decays of nR or DL • The matrix f determines masses and mixingof nR’s as well as couplingsof DL to leptons • Each solution for f leads to different asymmetry • More options for model-building • Different forms off available to accommodate n mass • Extra symmetries of the model as selection criterion

  12. Summary • Neutrino mass inLeft-Right symmetric models • Analysis of the LR symmetric seesaw formula • 8 structures of f reproduce the same mn and y • Duality among solutions: f  (mn / vL - f) • Criteria to identify the dominant seesaw type • General analytic method to solve for f • Spin-off both in phenomenology and theory M.Frigerio &E. Kh. Akhmedov,PRL 96, 061802 (2006) [hep-ph/0509299] and in preparation

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