PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

It is evident that the masses of the heavy charged leptons obtained from Eqs. (3.33) and
(3.35) are approximately the same as that obtained for the neutral heavy fermion using
Eq. (3.22). Indeed a comparison of these equations show that at tree level, the difference
between the neutral and charged heavy fermions are of the order of the neutrino mass
and can be hence neglected. One-loop effects bring a small splitting between the masses
of the heavy charged and neutral fermions, which is of the order of hundred MeV. This
allows the decay channel Σ ± = Σ 0 +π ± at colliders, as discussed in detail in [14,15]. In
this work we neglect this tiny difference and assume that the masses of all heavy fermions
are the same.
The matrices ˜m † l ˜m l and ˜M † ˜M H H are diagonalized by U l and Uh L giving,
( )
Ul 0
U L =
0 Uh
L . (3.36)
Similarly the ˜m l˜m † l
and ˜M H ˜M†
H matrices are diagonalized by U r and Uh R and hence give,
( )
Ur 0
U R =
0 Uh
R . (3.37)
Finally, the low energy observed neutrino mass matrix is given by
U PMNS = U † l U 0. (3.38)
Here both U l and U 0 are unitary matrices and hence U PMNS is unitary.
3.3 A µ-τ Symmetric Model
As discussed in the introduction we wish to impose µ-τ symmetry on our model in order
to comply with the neutrino data so that θ 13 = 0 and θ 23 = π/4. Henceforth, we impose
the µ-τ exchange symmetry on both the neutrino Yukawa matrix Y Σ and the Majorana
mass matrix for the heavy fermions M. Therefore, the neutrino Yukawa matrix takes the
form
⎛
Y Σ = ⎝ a ⎞
4 a 11 a 11
a ′ 11 a 6 a 8
⎠, (3.39)
a ′ 11 a 8 a 6
In addition to the µ-τ symmetry, we also assume (for simplicity) that a ′ 11 = a 11, which
reduces the number of parameters in the theory. For simplicity, we also assume all entries
of Y Σ to be real. The heavy Majorana mass matrix is given by
⎛ ⎞
M 1 0 0
M = ⎝ 0 M 2 0 ⎠, (3.40)
0 0 M 2
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