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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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
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) , …
f determines heavy n masses and mixing
f directly contributes to light n masses
Minkowski, Gell-Mann, Ramond, Slansky,
Yanagida, Glashow, Mohapatra, Senjanovic
Magg, Wetterich, Lazarides, Shafi,
Mohapatra, Senjanovic, Schecter, Valle
Type I and II contributions are strictly intertwined.
Let us take the LR seesaw formula seriously!
Bottom-up approach: what is the structure of the matrix f ?
To what extent we can reconstruct the seesaw heavy sector ?
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
Suppose type II dominates:
Suppose type I dominates:
LR-symmetry y = yTduality 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)
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:
Consider a given pair of dual solutions:
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 .
M.Frigerio &E. Kh. Akhmedov,PRL 96, 061802 (2006)
[hep-ph/0509299] and in preparation