PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

if we neglect terms proportional to v ′2 . The mixing matrices U l and U r which diagonalize
˜m † l ˜m l (cf. Eq. (3.34)) and ˜m l˜m † l
(cf. Eq. (3.32)) respectively, turn out to be unit matrices
at leading order.
⎛ ⎞ ⎛ ⎞
1 0 0 1 0 0
U l ≃ ⎝0 1 0⎠, U r ≃ ⎝0 1 0⎠, (3.44)
0 0 1 0 0 1
Finally, we show in Fig. 3.3 the impact of µ-τ symmetry breaking on the low energy
neutrino parameters. For the sake of illustration we choose a particular form for this
breaking, by taking M 3 ≠ M 2 . Departure from µ-τ symmetry results in departure of
U e3 from zero and sin 2 θ 23 from 0.5. We show in Fig. 3.3 the U e3 (left hand panel) and
|0.5−sin 2 θ 23 | generated as a function of the symmetry breaking parameter ǫ = M 3 −M 2 .
The figure is generated for a 4 = −0.066, a 11 = 0.171, a 6 = 0.064, a 8 = 0.0037 and
m 0 = 0.745 eV. We have fixed M 1 = M 2 = 299 GeV in this plot. For ǫ = 0, µ-τ
symmetry is restored and both U e3 and 0.5−sin 2 θ 23 go to zero. We show only points in
this figure for which the current data can be explained within 3σ. We note that for ǫ > 0
the curve extends to about M 3 = M 2 + 2.6 GeV, for this set of model parameters. For
ǫ < 0, the allowed range for ǫ is far more restricted.
We next turn our attention to the predictions of this model for the heavy fermion
sector. The 6×6 mixing matrices, which govern the mixing of the heavy leptons with light
ones, can also be obtained as discussed before. We will see in the next section that all the
four 3×3 blocks of the matrices U, S and T are extremely important for phenomenology
at the LHC. We denote these 3×3 blocks as
U =
S =
T =
( )
U11 U 12
=
U 21 U 22
( )
(Wν ) 11 U 0 (W ν ) 12 U Σ
, (3.45)
(W ν ) 21 U 0 (W ν ) 22 U Σ
( ) (
S11 S 12 (WL )
= 11 U l (W L ) 12 Uh
L
S 21 S 22 (W L ) 21 U l (W L ) 22 Uh
L
( ) (
T11 T 12 (WR )
= 11 U r (W R ) 12 Uh
R
T 21 T 22 (W R ) 21 U r (W R ) 22 Uh
R
)
, (3.46)
)
, (3.47)
The matrices W ν , W L and W R have been given in Eqs. (3.20), (3.30) and (3.31) respectively.
Hence, the 3×3 blocks in S,T and in U can be estimated for our choice of m D , M
and m l . In particular, we note that S 11 and T 11 are close to 1, while U 11 is given almost
by U PMNS . The off-diagonal blocks U 12 , U 21 , S 12 and S 21 , are suppressed by ∼ m D /M,
while T 12 and T 21 are suppressed by ∼ m D m l /M 2 . Finally, the matrices U 22 = (W ν ) 22 U Σ ,
S 22 = (W L ) 22 Uh L, and while T 22 = (W R ) 22 Uh R ≃ UR h . To estimate these we need to evaluate
first the matrices which diagonalize the heavy fermion mass matrices ˜M, ˜M† ˜M H H ,
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