In this research, we reviewed how to get the relationship of the neutrino oscillation
probability in the two flavor approximation, and tested the theoretical model of the
oscillation solution. We show that the oscillation probability of neutrino re
lates with
neutrino energy, length of the baseline (the distance between the source and the detector),
mixing angle , and square mass difference
2
2
2
1
2
12 m m m . This research shows that in
order to occur the oscillation of neutrino, it must be at least one of the mass states different
of zero. This means that the relationship 0 2
12 m must be verify. In other words neutrino
must have non zero mass. This result holds a huge physical importance. The first regards
the Standard Model of elementary particles, which considered neutrino massless. The
second regards the OPERA experiment, where neutrino have non zero mass, and cannot
spreading fast equal to the speed of light and so this does not agree with the experience of
OPERA, which found that the neutrino spreading faster than the speed of light in a
vacuum.
In this research the differential cross section for elastic scattering of electron neutrino (or anti neutrino) on the electron was calculated within and outside the frame work of the Standard Model (SM) of elementary particle physics. The mathematica
l relation of deviation from this model was also calculated. This study showed that there is a deviation from the standard model of the order for the electron neutrino flavor. The reference [16] was not able to appear it quite clearly and independently, but It showed the deviation on average for all flavors of neutrino together. Due to this deviation is very small, one can be neglected and therefore do not need to expand the framework of the standard model to include the electron neutrino mass, because in this case, it is located inside its framework.
