PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

in chapter 5 [3] we have build a model based on the group A 4 . We have considered the
most generic scenario with all possible one dimensional Higgs representations that can be
accommodated within this A 4 model. The Higgs fields which are charged under the symmetry
group A 4 , are standard model gauge singlets and they are knows as flavons. In our
model [3] we have two flavon fields φ S,T which transform as three dimensional irreducible
representation of the groupA 4 . In addition, we also have three other flavons ξ,ξ ′ ,ξ ′′ which
transform as 1, 1 ′ and 1 ′′ respectively. The Lagrangian describing the Yukawa interaction
between the different standard model leptons, Higgs and the flavons follows the effective
field theoretical description. The different flavon fields take the vacuum expectation values,
thereby resulting in a spontaneous breaking of the symmetry group A 4 . We have
explored the conditions on VEVs and Yukawa couplings needed for obtaining exact TBM
mixing in this present set-up. In particular, we have checked which combinations of the
different one dimensional Higgs fields ξ, ξ ′ and ξ ′′ would produce TBM mixing and under
what conditions. We have explicitly shown that the A 4 triplet field φ S can alone generate
the tribimaximal mixing in the neutrino sector if all the vacuum expectation values v si of
its component fields areequal. However it gives the atmospheric mass splitting ∆m 2 31 = 0,
and hence is clearly incompatible with the neutrino oscillation data. To generate viable
neutrino mass splittings in association with tribimaximal mixing, the one dimensional
representations has to be included. Although the representation 1 which was originally
proposed by Altarelli and Feruglio is the minimalistic choice to recover the correct mass,
this particular choice ends up with a severe fine-tuning between the different parameters
of the theory. The product of the VEV and Yukawa of this singlet is determined completely
by the VEV and Yukawa of the triplet. Other than this, the normal hierarchy
(∆m 2 31 > 0) between the standard model neutrino masses is the only allowed possibility.
Inverted hierarchy can be possible if we have at least two or all three Higgs scalars with
nonzero VEVs. The extreme fine-tuning in the parameter space is also gets reduced if one
introduces two or three flavon fields at a time. Deviation from the particular relations
between thedifferent Higgs vacuum expectation values andYukawas will lead to deviation
from tribimaximal mixing. In the charged lepton sector the diagonal charged lepton mass
matrix emerges as a consequence of an additional discrete symmetry Z 3 , as well as the
vacuum alignment of the flavon field φ T .
In chapter 6 we have constructed aflavor model based onthesymmetry groupS 3 [4],
which reproduces the observed neutrino mass and mixing, as well as the standard model
charged lepton mass hierarchy. We use two SU(2) Higgs triplets (∆) with hypercharge
Y = 2, arrangedinadoublet of S 3 , andthe standardmodel singlet Higgs(φ e , ξ) which are
also put as doublets of S 3 . Due to the appropriate charge assignment under additional
discrete symmetry groups Z 4 and Z 3 , the flavon φ e enters only in the charged lepton
Yukawa, whereas the other flavon ξ enters both in the neutrino as well as in the charged
lepton Yukawa. The Higgs triplets ∆ and the flavon field ξ take vacuum expectation
value, and generate standard model neutrino masses. To reproduce the observed lepton
masses and mixings, the symmetry group S 3 has to be broken such that the neutrino
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