Abstract
An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation)
m
τ
≃1776.80
MeV from the experimental values of
m
e
and
m
μ
, in agreement with
m
exp
τ
=
1777.00
+0.30
−0.27
MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations
ν
μ
→
ν
τ
is
∼1/2
and
|
m
2
ν
τ
−
m
2
ν
μ
|∼(0.0003to0.01)e
V
2
, as seems to follow from atmospheric-neutrino experiments, this ansatz predicts
m
ν
e
≪
m
ν
μ
∼(0.2to1)×
10
−2
eV and
m
ν
τ
∼(0.2to1)×
10
−1
eV
, and also the amplitude of neutrino oscillations
ν
e
→
ν
μ
∼
2
+4
−2
×
10
−4
(in the vacuum). Such a very small amplitude for
ν
e
→
ν
μ
is implied by the value of
m
exp
τ
−1776.80
MeV used to determine the deviation of the diagonalizing matrix
U
^
(e)
from
1
^
in the lepton Cabibbo-Kobayashi- Maskawa matrix
V
^
=
U
^
(ν)†
U
^
(e)
. Here,
U
^
(ν)
by itself gives practically no oscillations
ν
e
→
ν
μ
, while it provides the large oscillations
ν
μ
→
ν
τ
.