A new method for measuring the absolute neutrino mass
Abstract
The probability of the event that a neutrino produced in pion decay is detected in the intermediate
T
shorter than the life-time
τ
π
,
T≤
τ
π
, is sensitive to the absolute mass of the neutrino. With a newly formulated S-matrix
S[T]
that satisfies the boundary conditions of the experiments at a finite
T
, the rate of the event is computed as
Γ
0
+
g
~
(
ω
ν
,T;
τ
π
)
Γ
~
1
, where
g
~
(
ω
ν
,T;
τ
π
)
depends weakly on
τ
π
and
ω
ν
=
m
2
ν
c
4
/(2
E
ν
ℏ)
,
c
is the speed of light.
Γ
0
is the standard one and the correction,
g
~
(
ω
ν
,T;
τ
π
)
Γ
~
1
, reflects relativistic invariance and is rigorously computed via the light-cone singularity of the system and reveals the diffraction pattern of a single quantum. The formula explains unsolved anomalies of neutrino experiments and indicates the heavy neutrino mass,
0.098±0.022
or
0.083±0.026
{eV}/
c
2
for normal or inverted mass hierarchies, respectively.