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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

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

Neutrino mass in left right models
Neutrino mass in Left-Right models

Pati, Salam,






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:

Seesaw in left right models
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.

A very well motivated framework
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!

Lr seesaw the parameter space
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 ?

Seesaw duality
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

Ambiguity on the seesaw type
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)

A realistic numerical example
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




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:

Features of the solutions1
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 .


  • 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


  • 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