PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

sector contains the exact/approximate Z 2 symmetry along the ν µ − ν τ direction, while
it is broken down maximally in the charged lepton sector. This particular feature is
achieved by the vacuum alignments of the different Higgs fields ∆, φ e and ξ. Exact
µ−τ symmetry in the neutrino mass matrix is achieved as a consequence of the vacuum
alignments 〈∆ 1 〉 = 〈∆ 2 〉 and 〈ξ 1 〉 = 〈ξ 2 〉, otherwise resulting in mildly broken µ − τ
symmetry. The mild breaking of µ−τ symmetry opens up the possibility of CP violation
in the leptonic sector. We have analyzed the potential and we show that under the
most general case, the minimization condition predicts a very mild breaking of the µ−τ
symmetry for the neutrinos. The charged lepton sector offers very tiny contribution to
the physically observed PMNS mixing matrix, while the main contribution comes from
the neutrino mixing matrix. In the neutrino sector both normal and inverted hierarchy
are allowed possibilities.
Since the Higgs triplet ∆ interacts with the gauge bosons via their kinetic terms,
they can be produced at the LHC and then can be traced via their subsequent decays.
The doubly charged Higgs can decay to different states such as dileptons, gauge bosons,
singly charged Higgs H + . In our model the mixing between the two doubly charged Higgs
is very closely related with the extent of the µ−τ symmetry in the neutrino sector. In
the exact µ−τ limit the mixing angle θ between the two doubly charged Higgs is θ = π,
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whereas mild breaking of the µ−τ symmetry results in a mild deviation θ ∼ π . This close
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connection between the µ−τ symmetry and the doubly charged mixing angle significantly
effects the doubly charged Higgs-dileptonic vertices. In the exact µ−τ limit, the vertex
factors H 2 ++ −µ−τ and H 2 ++ −e−e are zero, hence the doubly charged Higgs H 2 ++ never
decays to µ + +τ + or to 2e + states. Other than this, the non observation of the eµ and
eτ states in the dileptonic decay of the doubly charged Higgs would possibly disfavor the
inverted mass hierarchy of the standard model neutrino. The presence of Higgs triplet
predicts lepton flavor violating processes such at τ → eeµ at the tree level. This and
other lepton flavor violating processes could therefore be used to constrain the model as
well as the neutrino mass hierarchy.
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