Solar neutrinos in Super-Kamiokande are measured through the following reaction;
The advantage of an experiment using this interaction is that we are able to obtain information on
The cross section for this scattering can be calculated using standard electroweak theory, and the differential cross section is
where are the Fermi coupling constant, the electron mass ,the incoming neutrino energy and the kinetic energy of the recoil electron, respectively. The parameters and are defined by
where is the Weinberg angle. From Eq(2), the overall factor in the differential cross section is
We also consider radiative corrections for the one-loop electroweak and QCD in the interaction Eq(1). A QED radiative correction is also considered. These corrections reduce the relative probability of observing recoil electrons by about 4% in our energy region for .
The cross section as a function of neutrino energy including radiative corrections is shown in Fig 1. This cross section can be calculated by integrating Eq(2) between 0 and the maximum value,, of the electron kinetic energy. Here for given is limited by kinematics as follows,
As shown in the figure, when is 10MeV, which is a typical energy of solar neutrinos, the cross section of neutrino scattering on electron is:
The differences of the cross section between and is because the scattering of on an electron can take place only through the neutral current interaction, while in case of , both neutral and charged current interactions take place. The cross section is approximately six times less than cross section.
where is the solar neutrino spectrum at earth, and is the maximum energy of solar neutrinos. Fig 2 shows the energy distribution of recoil electrons with only and hep solar neutrinos considered.
The angle, , between the direction of a recoil electron and an incoming
neutrino is given by
The angular distribution of recoil electrons is given by
Fig 3 shows the angular distribution of recoil electrons with total energy greater
than 0, 5, 7 and 10MeV. From this figure, the scattering angle is less than 20 if the
threshold energy is greater than 5MeV. For a larger threshold energy, the angular
distribution becomes much more strongly forward peaked. The angular dispersion defined by
the value which includes 68% of the distribution, is 12.3, 9.1
and 5.7for the electrons with total energy greater than 5, 7 and 10MeV,
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