Neutrino-antineutrino transition under CP-transformation and solar neutrino puzzle

It is considered two neutrinos moving in the opposite directions. In one and the same system of reference, one of the neutrinos is CP-transformed from another neutrino, so one of two neutrinos transits into antineutrino. As a consequence a half of neutrinos produced in the spherical shell transits into antineutrinos. From this one observes a half of neutrino flux produced in the sun that may provide a solution for the solar neutrino puzzle. Weak interactions violate P-invariance and C-invariance but conserve CP-invariance [1]. Due to this neutrinos are always left-handed, and antineutrinos are always right-handed. Take the first system of reference with the coordinate x and the second system of reference P-transformed from the second system of reference x → −x. Consider neutrino moving in the direction x. In the first system of reference, one observes the spin of neutrino -1/2. In the second system of reference, one observes the spin of neutrino +1/2. P-transformation is not defined for neutrino, so it is necessary to apply CP-transformation. From this it follows that, in the second system of reference, one observes antineutrino. While dealing with a single neutrino, one can use the system of reference in which the coordinate direction coincides with the direction of the motion of neutrino. Consider two neutrinos moving in the opposite directions, the first in the direction x, the second in the direction −x. In the first system of reference, one observes the first particle as neutrino and the second particle as antineutrino. In the second system of reference, one observes the first particle as antineutrino and the second particle as neutrino. Thus in one and the same system of reference, one of two neutrinos transits into antineutrino. Consider the spherical shell producing neutrinos in the weak interactions. The total neutrino flux from the shell can be divided into the pairs of neutrinos moving in the opposite directions. For every pair, in one and the same system of reference, one of two neutrinos transits into antineutrino. So a half of neutrinos produced transits into antineutrinos, and one observes a half of neutrino flux produced in the spherical shell. As known [2], [3] experiments measured solar neutrino fluxes significantly smaller than those predicted by the standard solar model (SSM), e.g. [4], [5]. Discrepancy between the theoretical and experimental neutrino flux from the sun presents the solar neutrino puzzle. The Homestake experiment measured [6] an average Ar production rate by solar neutrinos in Cl of Rate (Chlorine) = 2.55± 0.17(stat)± 0.18(syst) SNU (1) which is 32± 5% of the 8.1 −1.2 SNU predicted by the SSM [5].