PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Figure 6.5: The Jarlskog invariant J CP (left panel) and sinθ 13 as a function of the µ−τ
symmetry breaking parameter |ǫ|.
symmetry will allow θ 23 to deviate from maximal and θ 13 from zero. Any non-zero θ 13 will
open up the possibility of low energy CP violation in the lepton sector. For the sake of
illustration we consider a particular µ−τ symmetry breaking for m ν which results from
the deviation of the VEV alignment from Eq. (6.11). We will see in the next section
that this deviation is small and could come from v 1 ≠ v 2 and/or u 1 ≠ u 2 . For the sake
of illustration we consider only the breaking due to v 1 ≠ v 2 . We will see that from the
minimization of the scalar potential one can take v 1 = v 2 (1+ǫ). As a result the neutrino
mass matrix (6.10) becomes
m ν = 2v 2
⎛
⎝
y 4 u ′ (2+ǫ) y 3 y 3 (1+ǫ)
y 3 y 1 u ′ y 2 u ′ (2+ǫ)
y 3 (1+ǫ) y 2 u ′ (2+ǫ) y 1 u ′ (1+ǫ)
155
⎞
⎠ . (6.34)