Solar neutrino interactions in the detector

Solar neutrinos in Super-Kamiokande are measured through the following reaction;

wpe1.gif (1127 ?o?C?g),

(1)

The advantage of an experiment using this interaction is that we are able to obtain information on

(1)
the direction of the incident neutrinos because the recoil electrons in Eq((1)) are scattered to almost same direction as the neutrinos,
(2)
the exact arrival time of the incident neutrinos and
(3)
the energy distribution of the recoil electrons which reflects the energy spectrum of the incident neutrinos.

The cross section for this scattering can be calculated using standard electroweak theory, and the differential cross section is

wpe2.gif (2876 ?o?C?g),

(2)

where wpe3.gif (1455 ?o?C?g) are the Fermi coupling constant, the electron mass ,the incoming neutrino energy and the kinetic energy of the recoil electron, respectively. The parameters wpe4.gif (932 ?o?C?g) and wpe5.gif (813 ?o?C?g)are defined by

wpeB.gif (904 ?o?C?g),
wpeC.gif (655 ?o?C?g),
wpeC.gif (727 ?o?C?g),

where is the Weinberg angle. From Eq(2), the overall factor in the differential cross section is

,

(3)

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,

(4)

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:

,

(5)

,

(4)

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.

chap3-29.gif (85914 ?o?C?g)

Fig 1:

The cross section of the interaction for , with electoron as a function of neutrino energy.


The energy distribution of recoil electrons scattered by solar neutrinos is given by

,

(7)

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.

b8nue.gif (4117 ?o?C?g)

Fig 2: The energy spectrum of recoil electrons scattered off by and hep solar neutrinos.

The angle, , between the direction of a recoil electron and an incoming neutrino is given by

(8)

The angular distribution of recoil electrons is given by

.

(9)

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, respectively.

koshio.gif (11509 ?o?C?g)

Fig 3: The angular distribution of recoil electrons from incident solar neutrinos. Here,"ALL" means over the and hep SSM spectra.


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